Cooperative R&D investments and licensing breakthrough technologies: International environmental agreements with participation game

Journal Pre-proof Cooperative R&D investments and licensing breakthrough technologies: International environmental agreements with participation game Nobuyuki Takashima PII:

S0959-6526(19)34103-4

DOI:

https://doi.org/10.1016/j.jclepro.2019.119233

Reference:

JCLP 119233

To appear in:

Journal of Cleaner Production

Received Date: 24 July 2019 Revised Date:

5 November 2019

Accepted Date: 8 November 2019

Please cite this article as: Takashima N, Cooperative R&D investments and licensing breakthrough technologies: International environmental agreements with participation game, Journal of Cleaner Production (2019), doi: https://doi.org/10.1016/j.jclepro.2019.119233. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.

1

Cooperative

R&D

investments

and

licensing

breakthrough

2

International environmental agreements with participation game

technologies:

3 4

Nobuyuki Takashima

5

Kyushu University Platform of Inter / Transdisciplinary Energy Research (Q-PIT)

6

744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan

7

Tel: +81-92-802-5501; Fax: +81-92-802-5501

8

E-mail: [email protected]

9

10

JEL Classification: Q54; Q52; D64; C72

11 12

1

13

Abstract

14

This study examines international environmental agreements (IEAs) with cooperative

15

R&D, which can bring about a substantial reduction in greenhouse gas emissions. To

16

achieve a large IEA size consisting of more than four countries, we propose a novel

17

method of cooperative R&D investment and recovery and a licensing fee for the

18

adoption of advanced technology, by applying the mechanism of a joiner’s gain function.

19

The core findings of this study reveal that: (i) a large agreement can be achieved by

20

considering R&D investment, R&D recovery, and a licensing fee; (ii) the diffusion

21

process of advanced technology is clarified; (iii) non-investors’ adoption of an advanced

22

abatement technology can be prevented by setting a licensing fee and instead, they

23

participate and invest in R&D via agreement; (iv) a full participation state can be more

24

easily sustained than any other number of participants. Our approach shows the

25

diffusion process of advanced abatement technology after R&D. Consequently, this

26

paper fills a research gap in cooperative R&D methods and the diffusion process of

27

advanced technologies and provides a hopeful prospect for achieving full participation

28

in IEAs and a large reduction in GHG emissions by way of cooperative R&D.

29

30

2

31

Keywords: international environmental agreements; environmental R&D; breakthrough

32

technology; participation game; investment

33

34

Abbreviations

35

CR: collective response

36

GHG: greenhouse gas

37

IEA: international environmental agreement

38

R&D: research and development

39

UA: unilateral action

40

UNFCCC: United Nations Framework Convention on Climate Change

41

WRP: weakly renegotiation-proof

42

3

43

1. Introduction

44

Broad, international cooperation is required to ensure that the global temperature

45

increase during this century is far less than 2 °C above pre-industrial levels, and to

46

encourage countries to limit temperature increases to 1.5 °C. Countries generally

47

participate and meet their commitments to global agreements such as the Kyoto

48

Protocol and Paris Agreement. In 2015, all parties to the United Nations Framework

49

Convention on Climate Change (UNFCCC) Paris Agreement agreed to uphold and

50

promote international cooperation to reduce greenhouse gas (GHG) emissions

51

(UNFCCC, 2016).

52

There is a rapidly expanding body of literature on transboundary pollution at local

53

and global scales. At local scale, the latest literature addresses climate change mitigation

54

by focusing on various factors. Ma et al. (2019) assessed the intensity and total values

55

of CO2 mitigation in the residential building sector of China, at household scale. Qiao et

56

al. (2019) investigated peak coal consumption, using cases of CO2 emissions in China,

57

at national, regional, and individual provincial levels. Sedghamiz et al. (2018)

58

developed a conjunctive use model to optimize water allocation to different agricultural

59

sectors, considering the virtual water concept and game theory simultaneously. Wahba

60

et al. (2018) examined the energy reduction advantages of adding greenery atop

4

61

buildings in the hot, arid climate of Egypt. Striebig et al. (2019) investigated GHG

62

emissions caused by food transport and compared GHG emissions owing to local and

63

non-local food production. Pash et al. (2017) identified the main and sub-indices in

64

assessing the environmental impact of ports, to set goals for reducing pollution in ports.

65

Battaglia et al. (2018) investigated the relationship between adoption of domestic

66

environmental agreements and their stimulus to a green economy and green jobs

67

creation.

68

The results of these studies are helpful in updating the policymakers’ knowledge, to

69

improve decision-making regarding domestic or regional environmental plans. These

70

recent papers provide fundamental insights and methodologies for climate change

71

mitigation at domestic or regional level. It is expected that greater effects of climate

72

change prevention can be obtained if many countries abate GHG emissions by applying

73

these fundamental methodologies and insights. Carrascal Incera et al. (2017) explored

74

the determinants of gray water increases, which were only analyzed at local level, in an

75

international context and provided insights into water pollution dynamics worldwide.

76

To achieve global cooperation for climate change, countries have ratified

77

international environmental agreements (IEAs), such as the Kyoto Protocol and Paris

78

Agreement. Barret (2006) stated that effective IEAs for climate change must promote

5

79

the joint supply of two global public goods: climate change mitigation and knowledge

80

of new abatement technologies. In the 21st Session of the Conference of the Parties to

81

the United Nations Framework Convention on Climate Change in 2015, it was agreed to

82

enhance climate technology development and transfer (UNFCCC, 2016). Technological

83

innovation is a critical accelerator and enhancer of efforts to implement national action

84

for climate change and to achieve the Paris Agreement goals (UNFCCC, 2017).

85

Reflecting the aim of the Paris Agreement, Japan’s Ministry of the Environment (2017)

86

stated that diffusion of Japanese technologies, know-how, and findings within and

87

outside of the country is important for international cooperation and contributing to

88

global improvement. It is essential for countries to promote technological innovation by

89

investing cooperatively in R&D via global climate change treaties aimed at the

90

development and diffusion of breakthrough technologies.

91

Several papers have presented important findings on the development of abatement

92

technologies through R&D efforts and diffusion of advanced abatement technologies

93

among countries using an IEA framework and a participation game model. Barrett

94

(2006) presented pioneering work on IEA models in which each country can choose

95

novel or existing abatement technologies in the context of IEAs. However, it is assumed

96

that the breakthrough level is sufficiently large that the costs function changes from

6

97

quadratic to linear, and all countries choose their R&D level before the coalition is

98

formed. Following Barrett (2006), Hoel and de Zeeuw (2010) considered that each

99

country chooses its R&D investment level collectively (cooperatively) or individually

100

(non-cooperatively); however, their analysis was conducted under the case where

101

non-cooperative R&D is beneficial for all.

102

Karp and Simon (2013) showed that IEAs consisting of more than four countries are

103

possible by lowering the slope of the marginal abatement costs function. However, in

104

their model, R&D costs for technological innovation were not considered. El-Sayed and

105

Rubio (2014) examined IEAs in which countries decide their investment levels, to

106

minimize the agreement costs of controlling emissions. Those authors reported

107

relatively pessimistic results regarding the effect of R&D on IEA size; the maximum

108

participation in agreements with R&D consisted of six countries. Rubio (2017) showed

109

that full participation can be sustained if marginal damages are large enough to justify

110

development of a breakthrough technology that completely eliminates emissions and if

111

technology spillovers are not very large. However, such drastic change in abatement

112

technology seems unrealistic, and even if it were possible, it is expected that enormous

113

costs are needed to achieve such change.

114

Through the review of the existing literature, thus, little consideration has been

7

115

given to obtaining investment levels for innovation of abatement technologies, to

116

achieve broad participation in IEAs, considering methods to recover countries’ R&D

117

expenditure. Additionally, little work has been done on revealing the mechanism by

118

which advanced technology diffuses inside and outside of a coalition. Therefore,

119

without assuming non-cooperative R&D and unrealistic (excessively drastic) innovation

120

of abatement technologies, the following three questions are proposed for the success of

121

IEAs with R&D and technological innovation.

122




Q1: How should countries invest in R&D and how much R&D investment is

123

needed to sustain IEAs in which many countries participate and invest in R&D

124

without assuming non-cooperative R&D and excessively drastic (unrealistic)

125

abatement technology innovation?

126




Q2: What kind of process can be used to diffuse advanced abatement technologies?

127




Q3: Can we design IEAs that motivate non-investors to participate in agreements

128

and invest in R&D?

129

The present study addresses above the questions by applying a joiner’s gain function.

130

More precisely, we provide new R&D methods that integrate: (i) a cooperative R&D

131

effect; (ii) a method of recovering R&D investment; (iii) a licensing fee under an IEA

132

framework, applying a joiner’s gain function. For (i), we assume that the efficiency in

8

133

R&D costs works if countries cooperatively invest in R&D. That is, the investment in

134

R&D decreases if countries cooperatively invest in R&D. This assumption is based on

135

Bosetti et al. (2008) who considered that international knowledge spillovers tend to

136

decrease R&D investment. Applying the joiner’s gain function and cooperative R&D,

137

we consider that signatories who receive a joiner’s gain equally share the R&D costs, as

138

a rule of R&D expenditure. For (ii), we consider a method of recovering R&D

139

investment via improved abatement technologies. For (iii), payment of a licensing fee is

140

needed if countries that have not invested in R&D adopt the new advanced technologies.

141

These three mechanisms are considered by applying the mechanism of a joiner’s gain

142

function.

143

The key distinguishing features of our model are as follows. First, we propose a

144

novel R&D method by applying the mechanism of a joiner’s gain function. Second, this

145

study is the first to reveal a process of technology diffusion by applying the joiner’s gain

146

function. Regarding IEAs with R&D for climate change, to the author’s best knowledge,

147

such analytical methods have not been proposed (see Table 1).

148

The following results are obtained: (i) a large IEA size consisting of more than four

149

countries can be achieved by considering R&D investment and R&D recovery; (ii) the

150

diffusion process of advanced technology is clarified; (iii) adoption of advanced

9

151

abatement technology by non-investors is prevented by setting a licensing fee and

152

instead, non-investors participate and invest in R&D by agreement; (iv) a full

153

participation state can be more easily sustained than any other number of participants.

154

Integration of the joiner’s gain function and methods of R&D investment, R&D

155

recovery, and a licensing fee represent a hopeful prospect for achieving participation in

156

agreements by all countries and a large reduction in GHG emissions through

157

cooperative technological innovation with collective R&D.

158

The remainder of this paper proceeds as follows. Section 2 describes the

159

participation game model and joiner’s gain function. Section 3 introduces our model

160

and game stages when considering R&D. Section 4 presents the conditions for R&D

161

expenditure and R&D efficiency for a larger number of participating countries. Section

162

5 introduces the licensing fee by which non-investors in R&D can adopt new advanced

163

technologies and shows the ease of achieving a full participation agreement. In Section

164

6.1, we confirm whether our results completely answer the questions raised in Section

165

1; in Section 6.2, we examine whether our results can be explained using a different

166

approach. Section 7 provides our conclusions, including core findings, policy

167

implications, and upcoming studies. Figure 1 illustrates the flowchart of the present

168

study.

10

169

Insert Table 1

170

Insert Figure 1

171

172

2. Participation game and joiner’s gain function

173

This section introduces the concept of the participation game and joiner’s gain function.

174

As no supranational authority exists for resolving transboundary environmental

175

problems such as climate change, each country has to negotiate emissions reductions

176

and ratify IEAs. To achieve the long-term low carbon vision of the Paris Agreement,

177

cooperation by all countries is essential. Every country benefits from other countries’

178

abatement of transboundary pollutants in a non-exclusive and non-competitive manner.

179

Because of the public nature of transboundary pollutant abatement, the effectiveness of

180

IEAs depends on the number of participating countries and level of public good

181

provision. However, each country can free ride on others’ abatement efforts. Therefore,

182

the design of IEAs should prevent free riding and sustain a larger number of

183

participating countries.

184

Several studies have analyzed the design of a grand coalition in which all countries

185

participate, using a participation game model. A participation game model depicts

186

formation of an IEA in a one-shot game where a game represents any situation in which

11

187

countries negotiate and decide their pollution abatement levels, typically focusing on

188

participation. However, in early studies of IEAs, Barrett (1994) and Carraro and

189

Siniscalco (1993) showed that an agreement that substantially improves global welfare

190

is sustainable only if a few countries join. Those authors thus provided a pessimistic

191

view of cooperation in solving global environmental problems.

192

In the framework of a participation game model, a coalition is stable if it satisfies

193

conditions of internal and external stability. First, no signatory should have an incentive

194

to withdraw from the agreement (internal stability). Second, no non-signatory should

195

have an incentive to join the agreement (external stability). Later studies aimed to

196

increase the size of agreement by considering different policies such as trade sanctions

197

(Barrett, 1997), matching schemes (Fujita, 2013), and altruism (van der Pol et al., 2012)

198

to increase the number of countries participating in IEAs. However, an increase in

199

coalition size as well as in the total abatement are important dimensions of climate

200

change mitigation.

201

Applying the concepts of internal and external stability, Karp and Simon (2013)

202

introduced a novel decomposition of the gains from participation in IEAs. Those

203

authors expanded on the pessimistic results of Barrett (1994) and Carraro and Siniscalco

204

(1993) related to the size of sustainable IEAs. A joiner’s gain function merges the

12

205

external and internal stability conditions into one condition, that is, whether a joiner can

206

gain from the agreement. Thus, countries participate as long as they can gain from

207

participation. Karp and Simon (2013) revealed how many countries participate in

208

agreement under a certain abatement technology and what kind of process is needed for

209

countries to participate in agreement.

210

The present research, based on the joiner’s gain function, takes a different approach

211

toward formation of IEAs with R&D in comparison with previous studies of the

212

participation game model. Generally, the literature on IEAs with a participation game

213

model aimed to determine the number of participating countries obtained endogenously

214

as a stability condition of IEAs, i.e., the number of participating countries when a stable

215

coalition is obtained. However, our model can reveal the R&D investment levels needed

216

to sustain a larger number of participating countries by applying a joiner’s gain function.

217

Additionally, our approach leads to better understating of the process of participation in

218

agreement.

219

220

221

222

13

223

3. Model and stages of a participation game with R&D

224

Below, we summarize the notations used in this section:

225


: total number of countries;

226 227

228

229 230

231 232 233

234

235

: number of signatories in an agreement;   =  +
−   ,

where   : total abatement level,

 : abatement level of a signatory,

  : abatement level of a non-signatory;

    =   : benefits that each country receives from total abatement   ; 

   =  ⁄2    =    ⁄2: costs owed by a signatory (non-signatory), depending on its individual abatement level  (  ), under abatement technology M;   : payoff of a signatory;

 : payoff of a non-signatory;

236

  = ∑   : total payoff of the coalition of signatories;

237

E: level of innovation of an abatement technology;

238

: R&D efficiency;

239

I: R&D expenditure per signatory.

240

14

241

3.1. The model

242

Consider a world with  = 1, ⋯ ,
! identical countries. The benefit of reducing

243

emissions in a single country is proportional to its abatement and affects all countries’

244

benefits whereas the abatement costs are proportional only to its abatement level. When

245

 ≥ 2 countries participate, under the current abatement technology, the payoff

246

functions for the signatories and non-signatories are, respectively,

247

248

249

250

251

252

253

  =     −   ,

(1)

 =     −   ,

(2)

and

where  denotes the abatement levels of the signatories,   the abatement levels of the non-signatories, and   equals  +
−   . Each country receives benefit   from total abatement , and owes a cost depending on its individual abatement

level  . The subscripts $ and % denote the signatories and non-signatories, respectively, and the superscript  the number of signatories. Each signatory selects

 as an optimal solution that maximizes the coalition payoffs and each non-signatory

254

selects   as the optimal solution that maximizes its individual payoff. As in Karp and

255

Simon (2013), we assume that a country chooses to join if it is indifferent regarding

256

joining an IEA.

15

257

We consider that   =  and   =   ⁄2 for  ∈ ℝ( , respectively. As

258

per Karp and Simon (2013), we use a non-parametric expression to avoid specific

259

functional forms and reliance on parametric examples; additionally, this provides

260

simplicity and mathematical convenience. In terms of the cost function, the marginal

261

cost to reduce emissions is thought to increase as environmental quality improves and

262

treatment activities progress. Let   be the total payoff of the coalition of signatories,

263

that is,   = ∑   from (1). Differentiating   with respect to  , the first-order

264

condition for maximizing total payoff is )   ⁄) = ) ⁄) − )  ⁄2 = 0.

(3)

265

Differentiating  with respect to   in (2), and the assumption of an interior solution,

266

the first-order condition for maximizing an individual country’s payoff is )  ,)  = ) ⁄)  − )   ⁄2 = 0.

267

268

269

270

271

272

(4)

From (3) and (4),  solves  =   and   solves 1 =  . Therefore,  

is independent of k, and we define   as  . Additionally, under abatement technology  , we have  =  and  =  . Under   =  and   =   ⁄2 , the unique stable equilibrium is  = 3 (see Remark 2 in Karp and Simon (2013)).

Additionally, an agreement with  ≥ 4 is achieved if abatement costs are reduced by kinking the slope of  .

16

273

3.2. Stages of game

274

Formally, we have the following four-stage game:

275

Stage 1. Individual countries choose whether to join the coalition.

276

Stage 2. If some countries accede to the agreement, signatories choose R&D

277

expenditure levels for developing abatement technologies.

278

Stage 3. The coalition chooses whether to adopt the new technology.

279

Stage 4. Non-investors individually choose whether to adopt the advanced technology.

280

281

Signatories collectively choose the abatement levels that maximize the coalition

282

payoff whereas non-signatories choose the abatement levels that maximize each

283

country’s individual payoff. As in Hoel and de Zeeuw (2010) and El-Sayed and Rubio

284

(2014), signatories choose R&D expenditures after the participation stage. That is, once

285

a coalition forms in Stage 1, it remains a coalition after the investment decision in Stage

286

2. Stage 2 reflects signatories’ cooperative R&D efforts toward innovation of abatement

287

technologies. We consider a trade-off between R&D and marginal abatement costs, as in

288

Hoel and de Zeeuw (2010). That is, countries reduce their marginal abatement costs by

289

investing in R&D.

290

We adopt the following assumption for countries’ R&D investment:

17

291

Assumption 1.

292

The  signatories that accede to the agreement in Stage 1 decide the lowest R&D level

293

at which the th joiner’s gain with R&D costs is equal to 0.

294

295

The logic behind this assumption is as follows. Signatories in Stage 1 decide on the

296

improvement levels for the abatement technology, to make the IEA with R&D profitable.

297

Even if they expect their payoffs to increase with future participation by non-investing

298

countries, each country would not likely participate in such an agreement because the

299

“loss” could negatively affect the nation, even if temporarily. Hence, each country

300

participates in an IEA where investing countries can immediately and definitely recover

301

their R&D costs. In Stage 3, signatories (i.e., investors) collectively choose the

302

abatement levels that maximize the coalition payoff, including R&D costs, after

303

advanced abatement technology development if they adopt the advanced technology.

304

Adoption means that signatories invest in R&D and improve abatement technologies

305

based on R&D expenditure levels decided in Stage 2. If the new technology is not

306

adopted, the agreement consisting of  countries is not sustained.

307

We allow non-investors to adopt the advanced technology in Stage 4, following

308

Hoel and de Zeeuw (2010). In Stage 4, those countries that adopted the new technology

18

309

(i.e., investors in Stage 3 and non-investors that adopt the advanced technology in Stage

310

4) collectively choose those abatement levels that maximize the increased coalition

311

payoff if non-investors adopt the advanced technology. Non-investors who do not adopt

312

the advanced technology choose the reduction levels that maximize each country’s

313

individual payoff. Therefore, this study adopts the following assumption.

314

315

Assumption 2.

316

A non-investor is a “new participant” in an IEA with advanced abatement technology if

317

it adopts the advanced technology in Stage 4.

318

319

The rationale behind this assumption is as follows. Non-investors have an incentive

320

to adopt advanced technology because they can receive the joiner’s gain. Moreover,

321

existing signatories have no incentive to refuse their participation. Thus, they choose an

322

abatement level that maximizes the coalition, including the non-investors. Therefore, we

323

consider non-investors to be new participants in the IEA with advanced abatement

324

technology if they adopt the advanced technology in Stage 4. The number of

325

participants equals the sum of the original participants in Stage 1 (i.e., investors) and

326

new participants (i.e., non-investors) that adopt the advanced technology in Stage 4.

19

327

3.3. Joiner’s gain function with R&D cost

328

Karp and Simon’s (2013) joiner’s gain function represents the incremental increase (or

329

decrease) in a non-signatory’s payoff if it joins the agreement as the kth member. We

330

consider that signatories choose R&D expenditure I to improve abatement technology.

331

Let /   denote the abatement costs after innovations in emission abatement

332

technology and 0 ≥ 0 denote the signatory’s investment in R&D to change    to

333

/  . The joiner’s gain function with advanced abatement technology and with R&D

334

costs is 1  =  +  −  − /   − 2  −

335

134

(5)

+  −  + 1 −  5 − 0,

Rearranging (5), we have 1  =   − 34  + 34 −  

− 2/   −  34  +  34  −  5 − 0.

(6)

336

From (3) and (4),  solves  =   and  solves 1 =   . We can

337

decompose (6) into 1  = 6  − 78  − 0,

338

(7a)

where

20

78  =  34  −   − 34 −   > 0 339

(7b)

and 6 =   − 34  − 2/   −  34 5 > 0.

(7c)

340

UA (unilateral action) denotes the utility loss of a non-signatory if it increases its

341

abatement from  to 34 , which the signatories to an agreement with  − 1

342

members produce, and other countries maintain their abatement levels. Because  is

343

individually optimal and independent of the number of participating countries , the

344

increase in cost is greater than that in benefits for unilateral action, as (7b) states.

345

Additionally, we know that 78 2 = 0 when  = 2 because  = 4 .

346

CR (collective response) denotes the utility gain of the signatory when all

347

signatories to the coalition with an additional member increase their abatement levels

348

from 34 to  , as in (7c). Because  is collectively optimal for this enlarged

349

350 351

352

353

coalition with  members, the increment in benefits owing to the aggregate reduction

level is greater than the cost increment. Additionally, when  = 2, 6 2 ≥ 0 because  = 4 .

The joiner’s gain function with R&D costs shows that each country has an incentive to participate as long as 6  − 78  − 0 ≥ 0.

354

21

355

4. R&D and technological innovation

356

We examine levels of R&D improvement and R&D costs to satisfy the condition that

357

0 = 6  − 78 .

358

359

4.1. R&D efficiency and recovery

360

Our model considers that the sum of the signatories’ joiner’s gain will recover the R&D

361

costs and that R&D investment works effectively if countries collectively (i.e.,

362

cooperatively) develop the abatement technology (i.e., R&D efficiency).

363

Let us consider an IEA in which  ≥ 4 countries participate by considering that

364

they (i.e., investors) invest in R&D and improve abatement technology. To recover

365

; , which is larger than :, R&D costs, we consider an improved abatement technology :

366 367

368 369

; to sustain the number of by paying additional R&D costs. That is, : is extended to : participants  ≥ 4. Let < > 0 be the level of abatement technology innovation, ; and :; that is, : ; − : = <, and let parameter denoted by the difference between :

 > 0 denote R&D efficiency. We assume that the effect of  results only if countries

370

cooperatively invest in R&D. A lower level of  denotes higher R&D efficiency. This

371

effect is similar to that of Bosetti et al. (2008) where international knowledge spillovers

372

tend to decrease investment in R&D. Therefore, we express the change in R&D costs

22

373

; = : + < as =  − 2 − 1> + <. from  to :

374

The logic behind R&D efficiency is as follows. Efficient cooperative R&D can

375

result from cooperating countries taking full advantage of the latest technologies.

376

Additionally, we assume that : −  = ∞ when the abatement costs function changes

377

from quadratic to linear. Therefore, such drastic improvement in abatement technology

378

is impossible.

379

As a rule of R&D expenditure, we consider that signatories who receive the joiner’s

380

gain equally share the R&D costs. For joiner’s gain of the first and second participants,

381

we set the following assumption.

382

383

Assumption 3.

384

First and second participants simultaneously receive the same level of joiner’s gain.

385

386

This is because a coalition consisting of a single country is not considered an

387

agreement. Therefore, we consider that two countries (i.e., the first and second

388

participants) simultaneously participate in agreement. After that, other countries join the

389

agreement in order. Thus, all participants can receive the joiner’s gain and pay the R&D

390

cost from their joiner’s gain. This assumption does not affect the third and later

23

391

participants’ joiner’s gain because UA occurs from the third participant (see Section

392

3.3).

393

Figure 2, adapted from Karp and Simon (2013), shows that the number of investors

394

in R&D (participants)  increases if marginal costs curve is kinked. In Figure 2, we

395

396

denote the R&D expenditure per country with the dotted area in blue, < ⁄2; that is, 0 = < ⁄2. We confirm that  countries can owe an R&D cost of < ⁄2. From (7a), (7b),

397

; , as also shown in and (7c),  = , 34 =   − 1, and  = 4  = . Under :

398

Karp and Simon (2013), the magnitude relationship among each signatory in the k

399

members’ coalition’s joiner’s gain is 1  + 1 < 0 ≤ 1  < 1  − 1 < ⋯ < 1 2.

400 401

402

(8)

If the th participant can owe R&D costs, then the other countries can also owe R&D costs. For R&D cost and efficiency, we provide the following proposition.

403

404

Proposition 1.

405

The agreement consisting of  ≥ 4 countries with R&D costs is sustained by

406

advanced technology : + < if

24

<=

=  − 2 − 1>  and  < .  2 2−

407

Proof. Let us confirm each signatory’s joiner’s gain when they owe R&D costs and

408

recover them. By investing in R&D, parameter  in the abatement costs function,

409

410

411 412

413

; > : > . From Karp and Simon (2013), : −  is   =   ⁄2 , changes to : ; − : = <, the cost to equal to   − 2 − 1 when 6  = 78 . Assuming :

; is =  − 2 − 1> + < . If 6  − 78  = =  − 2 − change  to : 1> + <, then the R&D costs are recovered and the kth joiner’s gain equals 0. ; = : + < is The R&D cost change from  to :

=  − 2 − 1> + < = < ⁄2.

(9)

414

From condition (8), we know that all signatories can invest in R&D if the above

415

equality is satisfied.

416 417

418

419

420 421

As shown in Figure 2, and as in Karp and Simon (2013), 78  is represented by

the area under the marginal cost curve   between  and 34 minus the area

represented by the rectangle with boundaries  and 34 and height 1. 6  is the

area of the rectangle with boundaries 34 and  and height  minus the area under the marginal cost curve between 34 and  . Rearranging (9) with E, we have

25

<= 422

In (10), < is positive if

=  − 2 − 1>  2−

(10)

 . ∎ 2

(11)

<

423

; = : + < =   − 2 + =  − 2 − 1>⁄ ⁄2 −  . Therefore, we have :

424

425 426

; , the level of R&D Proposition 1 yields following results. To change  to : expenditure is ⁄2 ⁄2 −  . Additionally, we have the

427

technological innovation level to sustain number of participants  . That is,

428

technological development levels are decided depending on the number of participants,

429

meaning that  is an exogenous variable. The result provides an accurate level of the

430

R&D expenditure that is needed to yield a profitable agreement with advanced

431

technology consisting of  countries. In other words, this result denotes that the

432

number of signatories in Stage 1 is decided depending on the amount that each country

433

can invest in R&D. Proposition 1 also shows that R&D efficiency, , must be below ⁄2. From Figure

434 435

2,

we

obtain

436

; =  − 1 +   − 2 + =  − 2 − 1>⁄ ⁄2 − .  = 34 + :

437

Therefore, introducing R&D costs promotes the development of reduction technology 26

438

and increases abatement levels by <, as shown in Figure 2. Additionally, for / ′ , we

439

have / H  = IJ +  ⁄ : + < if  >  − 1,

440

441

where : >  and the y-intercept at 0, IJ , equals  − 1 1 − ⁄ : + <

because 34 =  − 1 and / H 34  =  − 1 from Figure 2.

442

Insert Figure 2

443 444

445

4.2. The additional participation of non-investors

446

We examine the possibility that non-investors adopt the advanced technology. After

447

improving the abatement costs, for M =  + 1, ⋯ , NOP, non-investor j can gain by

448

449

adopting the advanced technology if 6 M ≥ 78 M. For O ∈ ℝ( , we denote as NOP

the greatest integer weakly less than O and as QOR the smallest integer larger than O.

450

Therefore, QOR > O ≥ NOP >  . Regarding the number of original and new

451

participants (investors and non-investors), the following proposition is obtained.

452

453

Proposition 2.

454

The number of participating countries,NOP, is sustained if there exists an O such that

27

O = 2 + S  − 2 +

2=  − 2 − 1> > .  − 2

455

Proof. We seek the condition for 6 O = 78 O, where O ≥ NOP ≥ , under the

456

advanced abatement technology. In this case, non-investors have an incentive to adopt

457

the advanced technology. Therefore, we have O − 2  1 =  − 2 − 1> = T  − 2 + U.  2 2 2−

458

Rearranging (12) with regard to O, from  ≥ 4 and  − 1⁄2 > , we obtain O = 2 + S  − 2 +

459

460

(12)

2=  − 2 − 1> .  − 2

(13)

Therefore, NOP countries, the greatest integer weakly less than the right-hand side of the condition (13), participate. ∎

461

462

Proposition 2 indicates the condition where no non-investors have an incentive to

463

adopt the advanced technology (i.e., additional participation). Even if non-investors

464

adopt the new technology, : + < , the abatement technology remains unchanged

465

466

467

468

because the  members have already made the R&D investment.

From (13), we know that O ≥ . If O ≥  + 1 (or NOP > ), then there is room

for additional non-adopters to adopt the advanced technology whereas if  + 1 ≥ O ≥  (or NOP = ), then there is no room for additional adoption.

28

469

470

We first look at the condition that O ≥  + 1. Let us confirm the condition

that O ≥  + 1:

2 + S  − 2 +

471

2=  − 2 − 1> ≥  + 1.  − 2

(14)

Rearranging (14) with regard to , because k is an exogenous parameter, we obtain

472

 ≥ 2 − 3⁄2  − 2 . From  ≥ 4 , we have ⁄2 > 2 − 3⁄2  − 2. From

473

Proposition 1, we obtain

 2 − 3 ≥≥ . 2 2  − 2

(15)

474

If (15) is satisfied, then non-investors adopt the advanced technology as long as they

475

receive the joiner’s gain.

476

477

We have  + 1 > O ≥  if

 2 − 3 > > . 2 2  − 2

(16)

If (16) is satisfied, no non-investors adopt the advanced technology.

478

479

480

481

The number of investors in R&D is  and the total number of countries that adopt

the advanced technology is NOP. The QORth country will not participate because 6 QOR − 78 QOR < 0.

482

From the condition in Proposition 2, we obtain the following results. After

483

improving the abatement costs, if O ≥  + 1 (or NOP > ), then non-investors have 29

484

an incentive to adopt the advanced technology as long as 6 M > 78 M for

485

non-investor j. From (1), we know that the original participants have no reason not to

486

refuse adopt the advanced abatement technology because their payoffs increase as

487

cooperators increase. Whether O ≥  + 1 or  + 1 ≥ O ≥  depends on the

488

parameter values (see Proof of Proposition 2). If  + 1 ≥ O ≥  (or NOP = ), then

489

no non-investors adopt the new technology; therefore only investors adopt the advanced

490

technology.

491

492

493

We seek the condition that )< ⁄) ＜0. From Proposition 1, the condition that

)< ⁄) ＜0 is

)< ⁄) =   − 4 + 8 − 3 < 0.

Rearranging the inequality (17) with respect to , from  ≥ 4, we have >

494

495

(17)

 − 3 . 4 − 8

(18)

Thus, from (11) and (18), the R&D cost per country decreases as  increases if   − 3  >> . 4 − 8 2

(19)

In (19), from  ≥ 4, we can easily obtain   − 3⁄ 4 − 8 < ⁄2 . Thus, upon

496

condition (19), the R&D expenditure per signatory decreases as  rises. Additionally,

497

non-investors have an incentive to participate because condition (15) is satisfied if

498

condition (19) is satisfied.

30

499

However, an unfair imbalance exists between investors and non-investors in terms

500

of R&D expenditure because non-investors adopt the technology innovation funded by

501

investors without having to pay any R&D costs. To address this problem, we consider

502

implementing a licensing fee, described below.

503

504

5. Full participation IEAs

505

5.1. Licensing fee

506

We aim to prevent non-investors from adopting the new advanced technology and force

507

non-investors to participate in Stage 1 rather than allowing non-investors to pay a

508

licensing fee to IEA members when they adopt the advanced technology developed

509

through the investment of  countries. As shown in Section 4.2, for M =  + 1, ⋯ , NOP,

510

non-investor j has an incentive to adopt the advanced technology to reduce emissions if

511

O ≥ M.

512 513 514

Non-investor M =  + 1, ⋯ , NOP pays a licensing fee if they adopt the advanced

technology, after k countries fund R&D for the innovation. We set the licensing fee for j, WX , as

WX = 6 − 78X ,

515

(20)

where 6 denotes non-investor country j’s collective response and 78X denotes its

31

516

unilateral action. The subscript of 78X denotes that the size of unilateral action

517

increases as the number of joiners increases; the size of CR does not change if

518

non-investors participate because only R&D investment can change the size (see

519

Section 4.1). Additionally, (20) denotes that the levels of licensing fee vary by country,

520

depending on their joiner’s gain. Thus, for all M =  + 1, ⋯ , NOP , country M

521

participates in agreement, even though the participant’s joiner gain is 0 when it pays a

522

licensing fee, because of our assumption in Section 3.1 that a country chooses to join if

523

it is indifferent about joining an IEA.

524

For example, we consider the Y th ( + 1 ≤ Y ≤ NOP) country’s joiner’s gain

525

function with advanced technology under two cases. In case (i), a country adopts the

526

advanced technology by paying licensing fee shown in (20), as the Yth member of NOP

527

members with no R&D expenditure, after the technology innovation has been

528

developed through R&D investment by the original participants (Proposition 2) in Stage

529

4. In case (ii), a country participates as the Yth member and invests in R&D in Stages 1

530

and 2. It is obvious that the joiner’s gain in case (i) is always less than or equal to that in

531

case (ii) because non-investors cannot obtain a joiner’s gain when they adopt the new

532

technology from (20).

533

Next, we see the effectiveness of the licensing fee shown in (20) for NOP countries’

32

534

choosing the case (ii). If the licensing fee is less than (20), the NOPth participant has an

535

incentive to choose case (i) when NOP < O because its joiner’s gain with R&D costs in

536

case (ii) is 0 and that in case (i) is greater than 0.

537

Finally, we note the possibility of additional participation by non-investors when

538

NOP countries participate in agreement and investment in R&D. In case (ii),

539

non-investors (NOP + 1th and later countries) may have an incentive to adopt the

540

advanced technology developed from NOP countries’ R&D. In this case, new

541

participants must also pay a licensing fee. Thus, the number of countries that participate

542

and invest in R&D is decided at the level of no additional participation (i.e., the

543

condition that  + 1 ≥ O ≥  is satisfied or full participation). We discuss a state of

544

full participation below.

545

546

5.2. R&D efficiency for full participation

547

Herein, we describe the condition that minimizes the R&D costs per signatory if all

548

countries participate and invest in R&D. Under this condition, all countries choose to

549

participate in the IEA and invest in R&D in Stage 1 if non-investors must pay a

550

licensing fee to adopt the advanced technology, as described in Section 5.1.

551

From

≥4

and

condition

(19)

in

Section

4.2,

we

have

33

552

553

554

555

)   − 3⁄ 4 − 8⁄) =  − 3  − 1⁄4  − 2 , and ) ⁄2⁄) = 1⁄2. From  − 3  − 1⁄4  − 2 < 1⁄2 , the range between the upper and lower

bounds of  according to  (depicted as a vertical line according to the number of countries in Figure 3) expands as  increases. Moreover, the lower bound of 

556

increases as  increases. In other words, the condition of R&D efficiency becomes

557

relaxed as the number of signatories increases. In particular, we show that the value of

558

< is smallest if all countries participate in the range of
 − 3⁄ 4
− 8 <  <
⁄2

559

from (19).

560

From Section 4.2, if  + 1 ≥ O ≥  , then no non-investors adopt the new

561

technology and only investors adopt the advanced technology; if O ≥  + 1, then

562

non-investors have an incentive to adopt the new emissions abatement technology. In

563

the former case (i.e.,  + 1 ≥ O ≥ ), it is easier to achieve full participation rather

564

than any other participation level because an IEA with more participating countries

565

requires less R&D expenditure and lower R&D efficiency. In the latter case (i.e.,

566

O ≥  + 1), it is also easier to reach full participation than any other level of

567

participation if the licensing fee is set as in Section 5.1.

568

569

Insert Figure 3

34

570

In conclusion, a larger number of participants (countries that adopt the advanced

571

technology) can not only expand the range between the upper and lower bounds of the

572

levels of R&D efficiency , this can also decrease the lower bound of the level of R&D

573

efficiency. Surprisingly, the full participation and adoption states tend to occur as levels

574

of R&D efficiency decrease (i.e., levels of  become larger) under condition (19) if the

575

licensing fee is set as in (20).

576

577

6. Results and Discussions

578

6.1. Sustainability of IEAs with R&D investment

579

In this section, we confirm whether our results answer the questions posed in Section 1.

580

From Section 4.1, a larger IEA consisting of more than four countries can be achieved

581

with recovery of each signatory’s R&D expenditure via abatement technology

582

innovation. We also revealed accurate R&D investment levels and the range of R&D

583

efficiency, as shown in Proposition 1. These results completely answer question 1 in

584

Section 1.

585

By applying the concept of a joiner’s gain function, the process of advanced

586

abatement technology diffusion after R&D investment is clarified, as shown in Section

587

4.1. Additionally, after R&D investment in abatement technology by the signatories, we

35

588

revealed that non-investors may have an incentive to adopt advanced abatement

589

technologies, as shown in Section 4.2. These results completely answer question 2 in

590

Section 1.

591

If countries can adopt advanced technologies without incurring R&D costs, there is

592

an unfair imbalance between investors and non-investors. To address this issue, we

593

considered a method to prevent adoption of new advanced technologies by

594

non-investors. We showed that it is better for non-investors to choose to participate and

595

invest in R&D from the beginning than to pay a licensing fee to adopt new technology

596

developed by other countries. The results obtained in Section 4.2 completely answer

597

question 3 in Section 1.

598

During the process of our analysis to answer the above questions, we obtained

599

several new and important results. In Section 5, we identified the condition under which

600

the R&D expenditure per signatory decreases as the number of signatories increases. In

601

addition, we revealed that the range between the upper and lower bounds of R&D

602

efficiency increases and the condition of R&D efficiency becomes relaxed as the

603

number of signatories increases. At these points, a full participation state can be more

604

easily sustained than any other number of participants.

605

36

606

6.2. Can a full-participation state with an increased abatement level be achieved

607

through a different approach?

608

This study showed that a state of full participation with increased abatement levels can

609

be achieved by considering cooperative R&D, R&D recovery, and a licensing fee.

610

Through our analysis, the following question is raised: which of our results is achieved

611

that cannot be obtained using a different approach? We discuss this below using the

612

approach of game theory.

613

Generally, as introduced in Asheim et al. (2006) and Hovi et al. (2015), two

614

theoretical models are used to analyze the formation of an IEA: a participation game

615

model or a compliance model. A compliance model is also called a repeated game

616

model. A compliance model assumes that the game is repeated infinitely and that

617

countries agree during the first period of the game (i.e., pre-play communication), which

618

must be enforced in subsequent periods under threat of punishment. In a compliance

619

game model, punishment denotes that some of the signatories to the IEA abandon their

620

abatement action because their abatement action is the provision of public goods.

621

In a compliance model, before the game begins, countries are assumed to enter into

622

an agreement that participants must enforce throughout the game using the punishment

623

(credible threats) prescribed in the strategy. This means that an agreement is enforced

37

624

using a strategy that specifies the countries’ behavior. That is, the compliance model

625

analyzes the conditions under which countries that are participating in an agreement will

626

meet their commitments as prescribed in the strategy.

627

The stability concept of the compliance model is referred to as a weakly

628

renegotiation-proof (WRP) equilibrium (Farrell and Maskin 1989, pp. 330–331), where

629

participants meet their commitments under a punishment clause. Most recent

630

compliance model literature ensures WRP equilibrium by considering a strategy based

631

on the “grim trigger” strategy, typically one that prescribes punishment for

632

noncompliance, as introduced in Hovi et al. (2015) and Takashima (2018). For example,

633

the “regional cooperative” strategy (Takashima, 2017b) and “regional penance” strategy

634

(Asheim et al., 2006) consider the formation of regional agreements. In the “getting

635

even” strategy (Barrett, 1999, 2003), only a limited number of participants is possible if

636

the agreement substantially improves social welfare. The “consensus treaty” (Barrett,

637

2002) achieves full participation in an IEA but where the abatement level of each

638

country is low.

639

Let us discuss whether full participation with an efficient abatement level is

640

achieved using a repeated game approach. The “penance-m” strategy, adopted by

641

Asheim and Holtsmark (2009), Froyn and Hovi (2008), and Takashima (2017a), reaches

38

642

the conclusion of IEA with full participation. That is, in terms of full participation, our

643

results can be obtained using a compliance model approach. However, to the author’s

644

best knowledge, our findings are the first to show that full participation is more easily

645

sustained than any other number of participants.

646

Additionally, there is a possibility that an IEA is not sustained if technological

647

innovation occurred in a compliance model. IEA investigations that use a repeated game

648

obtain conditions for WRP equilibrium as the number of punishing countries is decided

649

by lower and upper bounds of the number of punishing countries.

650

As explained above, in many studies of IEA with a compliance model, the number

651

of punishing countries is decided by the lower and upper bounds of the number of

652

punishing countries. Thus, the signatories cooperate in accordance with the strategy for

653

fear of the punishment decided before the agreement begins (or the first period of the

654

game). If the abatement cost function is changed by R&D investment in the middle of

655

the periods, these lower and upper bounds of number of punishing countries can be

656

changed. This means that the WRP condition can be broken and thus, the IEA can be

657

collapsed. If innovation in abatement technology is considered, the hopeful prospect for

658

full participation is not observed using existing compliance model approach. Our

39

659

discussion herein further strengthens the importance of considering the formation of

660

IEAs with R&D using the concept of joiner’s gain.

661

662

7. Conclusion

663

Below, we describe our core findings, policy implications, and upcoming studies.

664

665

7.1. Core findings

666

According to our findings, we reached the following conclusions.

667




A large size IEA consisting of more than four countries is sustainable with

668

cooperative investment in R&D and recovery of R&D expenditures.

669

By applying a joiner’s gain function and considering R&D for technological

670

innovation, we could achieve a large sized agreement including more than four

671

countries with increased abatement levels, as in Proposition 1. Karp and Simon (2013)

672

achieved a large IEA by innovation in abatement technology, but they did not consider

673

R&D costs. To address the problem of R&D cost, we considered a method to recover

674

R&D expenditure. Proposition 1 also indicates the condition of R&D efficiency. In this

675

proposition, accurate levels of R&D expenditure per country and condition of R&D

40

676

efficiency are obtained. We also showed that the R&D level and the R&D expenditure

677

level owed by each signatory are decided depending on the IEA size. These results were

678

not obtained in other previous studies such as Barrett (2006) and Hoel and de Zeew

679

(2010), Karp and Simon (2013).

680




The diffusion process of advanced technology is clarified.

681

As introduced in Section 2, the joiner’s gain function focuses on the order of

682

participation in agreement. This study revealed that the mechanism of joiner’s gain

683

clears the diffusion process of advanced abatement technology developed through the

684

effort of signatories’ R&D. This study is the first to clarify this process by applying a

685

joiner’s gain function. Diffusion will be stopped when the joiner’s gain of the country

686

that adopts a new advanced technology is zero. However, this result leads to the

687

possibility of adoption of advanced technologies by non-investors, as described in

688

Section 4.2.

689




690

Non-investor’s adoption of advanced technology is prevented if they must pay a licensing fee to adopt the advanced technology.

691

Proposition 2 reveals the possibility of additional participation by non-investors.

692

Countries have an inventive to participate in an IEA if they can gain by participating.

41

693

However, there is an unfair imbalance between investors and non-investors in terms of

694

R&D expenditure. As a solution to this issue, we considered the concept of a licensing

695

fee with a joiner’s gain function and adapted it in an IEA model. Applying the

696

mechanism of a joiner’s gain, we set a licensing fee for adopting the new technology;

697

the fee is set to equal each non-investors’ joiner’s gain (see condition (20), Section 5.1).

698

As a result, non-investors tend to have an incentive to participate in IEAs and invest in

699

R&D to avoid paying licensing fees to adopt advanced abatement technologies.

700




Full participation and adoption states may be more achievable than any other sized

701

agreement.

702

In Section 5, we revealed that a state of full adoption can be easily achieved. More

703

precisely, the R&D cost per country decreases and the condition of R&D efficiency for

704

full participation become relaxed with an increasing number of participating countries.

705

One might expect more efficient R&D investment to facilitate the diffusion of advanced

706

technologies; however, our results show that lower R&D efficiency tends to lead to all

707

countries participating in agreement and investing in R&D. Technological innovation

708

and licensing fees are key factors to achieving full participation in an IEA with R&D.

709

Overall, this result appears to indicate that prospects are good for global innovation and

42

710

diffusion of advanced technologies.

711

Lastly, we mention limitation of our approach. First, participants’ joiner’s gain

712

depends on their order of participation in agreement; participants can receive higher

713

levels of joiner’s gain if they participate at earlier orders. The participation order might

714

affect the success of such agreements. Our current approach using a joiner’s gain

715

function involves some uncertainty at this point. Second, our analysis is based on a case

716

of symmetric countries. When considering the case of asymmetric countries, our R&D

717

methods should be modified. We discuss the possibility of further analysis to address

718

these limitations in Section 7.3.

719 720

7.2. Policy implications

721

Based on the aforementioned core findings, we describe the following policy

722

implications. The UNFCCC describes that developing and transferring technologies to

723

support national action on climate change has been an essential element since the

724

beginning of the UNFCCC process.1

725

From our results, R&D cost per country can decrease as the number of participating

726

countries increases. Thus, a cooperative framework for technological innovation should 1

See the UNFCCC website (https://unfccc.int/topics/climate-technology/the-big-picture/what-is-technology-development-and-tr ansfer). 43

727

be discussed more in negotiations, such as the Paris Agreement, where broad

728

participation is achieved. Considering technological innovation in abatement

729

technologies, countries should invest in R&D cooperatively, not individually, via a

730

climate treaty. Our findings support that these activities should be conducted

731

cooperatively, in combination with climate change treaties.

732

Our results also indicate that licensing fees are needed to promote participation in

733

IEAs and investment in R&D by all countries. The countries participating in climate

734

treaties need to set fees for non-investors and non-participants in agreement who wish to

735

adopt the advanced technology. As described in Section 1, the UNFCCC emphasizes the

736

importance of technology transfer to support climate action. Our results suggest that a

737

technology transfer scheme with a licensing fee should be introduced in treaties.

738

However, in reality, countries can be divided into two types: developing (or less

739

developed) and developed countries. Thus, an application of our new R&D methods to

740

asymmetric countries’ case is interesting challenge that we leave for future research.

741

742

7.3 Upcoming studies

743

The directions for future research seem promising. First, we must consider the case in

744

which R&D efficiency increases as the number of countries that invest in R&D

44

745

increases, by applying the concept of returns to scale (Barret, 2006). Second, as

746

mentioned in Section 7.1, we must focus on the order of participation in an IEA because

747

this influences the level of joiner’s gain. A method to determine the order of

748

participation can further expand our analysis.

749

Third, as also mentioned in Sections 7.1 and 7.2, our analysis should be considered

750

in the case of asymmetric countries. Biancardi and Villani (2018) examine IEA

751

formation with R&D using a dynamic pollution abatement model in a world with two

752

asymmetric groups of symmetric countries: less developed and developed countries.

753

Considering the case of asymmetric countries and a participation game model, Barrett

754

(2001), Biancardi and Villani (2010), and Chou and Sylla (2008) used a monetary

755

transfer scheme to expand the IEA size. 2 McGinty (2007) considers transfers

756

implemented through a system of tradable pollution permits in a world with n

757

asymmetric countries. Our approach in the case of asymmetric countries can provide

758

further insights into climate change treaties with technological innovation, making it

759

possible to investigate the effects of technology transfer from developed to less

2

Chou and Sylla (2008) and Biancardi and Villani (2010), as well as Biancardi and Villani (2010), consider two types of countries: less developed and developed countries. Barrett (2001) implicitly assume less developed and developed countries in a world with two asymmetric groups of symmetric countries. 45

760

developed countries on IEAs and the link between other transfer and technology transfer

761

schemes.

762

Fourth, we must consider the case in which firms, not countries, invest in R&D for

763

innovation of emissions abatement technology, based on “environmental agreements”.

764

The concept of cooperative R&D efforts is also considered in domestic environmental

765

policies. For examples, Ouchida and Goto (2014, 2016) considered the R&D efficiency

766

in R&D expenditure at domestic firm level. For domestic policy that encourages firms

767

to engage in GHG abatement, an environmental agreement model should be considered.

768

Cabugueira (2001), Jiménez (2007), and Wakabayashi and Arimura (2016) assessed the

769

effectiveness of voluntary environmental agreements (VAs) on environmental protection.

770

Particularly, public voluntary programs, a type of VA, have characteristics similar to an

771

IEA model in that each player can decide whether to participate in agreement.3 Thus,

772

we can consider firms’ cooperative investment in technological innovation in terms of

773

local and global environmental cooperation by linking VAs and IEAs.

774

Lastly, Karimi and Nickpayam (2017) provided insight into a gamification approach

775

from the viewpoint of motivation.4 We must adopt gamification in IEAs, considering

3

VAs are classified into two categories: negotiated agreements and public voluntary programs. For details, see Wakabayashi and Arimura (2016). 4 As explained in Karimi and Nickpayam (2017), gamification is a strategy that uses game mechanics, techniques, and theory in areas that have not traditionally functioned like a game; gamification attempts to influence players’ actions by activating individual motives via game design 46

776

each country’s motivation in emissions abatement, such as rewards and reputation in

777

comparison to other countries, in cooperating with GHG emissions mitigation.

778

779

Acknowledgements

780

The author would like to thank the three anonymous reviewers for their helpful

781

comments and suggestions. The author is also grateful to Toshiyuki Fujita, Hiroshige

782

Tanaka, Tadahisa Ohno, Satoshi Honma, Yasunori Ouchida, and participants in the

783

2019 Spring Meeting of the Japan Association for Applied Economics for their

784

constructive comments. This research is partially supported by JSPS KAKENHI [grant

785

number JP19K13685].

786

787

References

788

Asheim, G.B., Froyn, C.B., Hovi, J., Menz, F.C., 2006. Regional versus global

789

cooperation for climate control. J. Environ. Econ. Manage. 51, 93–109. Doi:

790

http://dx.doi.org/10.1016/j.jeem.2005.04.004

791

792

Asheim, G.B., Holtsmark, B., 2009. Renegotiation-proof climate agreements with full participation: Conditions for Pareto-efficiency. Environ. Resour. Econ. 43, 519–533.

elements. 47

793

794

795

796

Doi: http://dx.doi.org/10.1007/s10640-008-9247-3 Barrett, S., 1994. Self-enforcing international environmental agreements. Oxf. Econ. Pap. 46, 878–894. Doi: http://www.jstor.org/stable/2663505 Barrett, S., 1997. The strategy of trade sanctions in international environmental

797

agreements.

798

http://dx.doi.org/10.1016/S0928-7655(97)00016-X

799

800

801

802

803

804

Resour.

Energy

Econ.

19,

345–361.

Doi:

Barrett, S., 1999. A theory of full international cooperation. J. Theor. Politics. 11, 519– 541. Doi: http://dx.doi.org/10.1177/0951692899011004004 Barrett, S., 2001. International cooperation for sale. Eur. Econ. Rev. 45, 1835–1850. Doi: http://dx.doi.org/10.1016/S0014-2921(01)00082-4 Barrett, S., 2002. Consensus treaties. J. Inst. and Theor. Econ. 158, 529–547. Doi: http://dx.doi.org/10.1628/0932456022975169

805

Barrett, S., 2003. Environment and Statecraft. Oxford University Press, New York.

806

Barrett, S., 2006. Climate treaties and “breakthrough” technologies. Am. Econ. Rev. 96,

807

22–25. Doi: http://www.jstor.org/stable/30034607

808

Battaglia, M., Cerrini, N., Annesi, N., 2018. Can environmental agreements represent an

809

opportunity for green jobs? Evidence from two Italian experiences. J. Clean. Prod.

810

175, 257–266. doi: https://doi.org/10.1016/j.jclepro.2017.12.086

48

811

Biancardi, M., Villani, G., 2010. International environmental agreements with

812

asymmetric

countries.

Comput.

Econ.

813

http://dx.doi.org/10.1007/s10614-010-9197-z

36,

69–92.

Doi:

814

Biancardi, M., Villani, G., 2018. Sharing R&D investments in international

815

environmental agreements with asymmetric countries. Commun. Nonlinear. Sci.

816

Numer. Simulat. 58, 249–261. Doi: http://dx.doi.org/10.1016/j.cnsns.2017.06.034

817

Bosetti, V., Carraro, C., Masetti, E., Tavoni, M. 2008. International Energy R&D

818

spillovers and the economics of greenhouse gas atmospheric stabilization. Energy

819

Econ. 30, 2912–2929. Doi: http://dx.doi.org/10.1016/j.eneco.2008.04.008

820

Cabugueira, M.F.M., 2001. Voluntary Agreements as an environmental policy

821

instrument–evaluation

822

https://doi.org/10.1016/S0959-6526(00)00064-0

823

criteria.

J.

Clean.

Prod.

9,

121–133.

Doi:

Carraro, C., Siniscalco, D., 1993. Strategies for the international protection of

824

the environment.

J.

Public

Econ.

825

http://dx.doi.org/10.1016/0047-2727(93)90037-T

52,

309–328.

Doi:

826

Carrascal Incera, A., Avelino, A.F.T., Franco Solís, A., 2017. Gray water and

827

environmental externalities: International patterns of water pollution through a

828

structural decomposition analysis. J. Clean. Prod. 165, 1174–1187. Doi:

49

829

http://dx.doi.org/10.1016/j.jclepro.2017.07.200

830

Chou, P.B., Sylla, C., 2008. The formation of an international environmental agreement

831

as a two-stage exclusive cartel formation game with transferable utilities. Int.

832

Environ. Agreem. 8, 317–341. Doi: http://dx.doi.org/10.1007/s10784-008-9082-6

833

El-Sayed, A., Rubio, S. J., 2014. Sharing R&D investments in cleaner technologies to

834

mitigate

835

http://dx.doi.org/10.1016/j.reseneeco.2014.07.003

836

837

climate

change.

Resour.

Energy

Econ.

38,

168–180.

Doi:

Farrell, J., Maskin, E., 1989. Renegotiation in repeated games. Game. Econ. Behav. 1, pp. 327–360. Doi: http://dx.doi.org/10.1016/0899-8256(89)90021-3

838

Finus, M., Rübbelke, D.T.G., 2013. Public good provision and ancillary benefits: The

839

case of climate agreements. Environ. Resour. Econ. 56, 211–226. Doi:

840

http://dx.doi.org/10.1007/s10640-012-9570-6

841

842

Froyn, C.B., Hovi, J., 2008. A climate agreement with full participation. Econ. Lett. 99, 317–319. Doi: http://dx.doi.org/10.1016/j.econlet.2007.07.013

843

Fujita, T., 2013. A self-enforcing international environmental agreement on matching

844

rates: Can it bring about an efficient and equitable outcome? Strateg. Behav.

845

Environ. 3, 329–345. Doi: http://dx.doi.org/10.1561/102.00000033

846

Hoel, M., de Zeeuw, A., 2010. Can a focus on breakthrough technologies improve the

50

847

performance of international environmental agreements? Environ. Resour. Econ. 47,

848

395–406. Doi: http://dx.doi.org/10.1007/s10640-010-9384-3

849

Hovi, J., Ward, H., Grundig, F., 2015. Hope or despair? Formal models of climate

850

cooperation.

Environ.

Resour.

Econ.

851

http://dx.doi.org/10.1007/s10640-014-9799-3

62,

665–688.

Doi:

852

Jiménez, O., 2007. Voluntary agreements in environmental policy: an empirical

853

evaluation for the Chilean case. J. Clean. Prod. 15, 620–637. Doi:

854

https://doi.org/10.1016/j.jclepro.2005.11.025

855

Karimi, K., Nickpayam, J., 2017. Gamification from the viewpoint of motivational

856

theory. Ital. J. Sc. Eng. 1, 34–42. Doi: http://dx.doi.prg/10.28991/esj-2017-01114

857

Karp, L., Simon, L., 2013. Participation games and international environmental

858

agreements: A non-parametric model. J. Environ. Econ. Manag. 65, 326–344. Doi:

859

http://dx.doi.org/10.1016/j.jeem.2012.09.002

860

Ma, M., Ma, X., Cai, W., Cai, W., 2019. Carbon-dioxide mitigation in the residential

861

building sector: A household scale-based assessment. Energy Convers. Manag.

862

Forthcoming. Doi: https://doi.org/10.1016/j.enconman.2019.111915

863

864

McGinty, M., 2007. International environmental agreements among asymmetric nations. Oxf. Econ. Pap. 59, 45–62. doi: http://dx.doi.org/10.1093/oep/gpl028

51

865

Ministry of the Environment, Government of Japan, 2017. Outline of long-term

866

low-carbon vision. https://www.env.go.jp/press/103822/713.pdf (accessed 8 July

867

2019).

868

Pash, H.S., Ebadi, T., Pourahmadi, A.A., Parhizkar, Y.R., 2017. Analysis of most

869

important indices in environmental impacts assessment of ports. Civ. Eng. J. 3,

870

868–880. Doi: http://dx.doi.org/10.28991/cej-030921

871

Ouchida, Y., Goto, D., 2014. Do emission subsidies reduce emission? In the context of

872

environmental

R&D

organization.

Econ.

873

http://dx.doi.org/10.1016/j.econmod.2013.10.009

Model.

36,

511–516.

Doi:

874

Ouchida, Y., Goto, D., 2016. Environmental research joint ventures and time-consistent

875

emission tax: Endogenous choice of R&D formation. Econ. Model. 55, 179–188.

876

Doi: http://dx.doi.org/10.1016/j.econmod.2016.01.025

877

Qiao, H., Chen, S., Dong, X., Dong, K., 2019. Has China’s coal consumption actually

878

reached its peak? National and regional analysis considering cross-sectional

879

dependence

880

https://doi.org/10.1016/j.eneco.2019.104509

881

882

and

heterogeneity.

Energy

Econ.

Forthcoming.

Doi:

Rubio, S.J., 2017. Sharing R&D investments in breakthrough technologies to control climate

change.

Oxf.

Econ.

Pap.

69,

496–521.

Doi:

52

883

http://dx.doi.org/10.1093/oep/gpw067

884

Sedghamiz, A., Heidarpour, M., Nikoo, M.R., Eslamian, S., 2018. A game theory

885

approach for conjunctive use optimization model based on virtual water concept.

886

Civ. Eng. J. 4, 1315–1325. Doi: http://dx.doi.org/10.28991/cej-0309175

887

Striebig, B., Smitts, E., Morton, S., 2019. Impact of transportation on carbon dioxide

888

emissions from locally vs. non-locally sourced food. Emerg. Sci. J. 3, 222–234.

889

Doi: http://dx.doi.org/10.28991/esj-2019-01184

890

Takashima, N., 2017a. International environmental agreements with ancillary benefits:

891

Repeated

games

analysis.

Econ.

Model.

892

http://dx.doi.org/10.1016/j.econmod.2016.10.011

61,

312–320.

Doi:

893

Takashima, N., 2017b. The impact of accidental deviation by natural disaster-prone

894

countries on renegotiation-proof climate change agreements. Environ. Model.

895

Assess. 22, 345–361. Doi: https://doi.org/10.1007/s10666-016-9542-2

896

Takashima, N., 2018. International environmental agreements between asymmetric

897

countries: A repeated game analysis. Jpn. World Econ. 48, 38–44. Doi:

898

https://doi.org/10.1016/j.japwor.2018.08.001

899

900

UNFCCC (United Nations Framework Convention on Climate Change). 2016. Report of the Conference of the Parties on its twenty-first session, held in Paris from 30

53

901

November to 13 December 2015.

902

URL: http://unfccc.int/resource/docs/2015/cop21/eng/10a01.pdf (accessed 9 July

903

2019).

904

UNFCCC (United Nations Framework Convention on Climate Change). 2017. TEC

905

Brief

906

URL:https://unfccc.int/ttclear/misc_/StaticFiles/gnwoerk_static/brief10/8c3ce94c2

907

0144fd5a8b0c06fefff6633/57440a5fa1244fd8b8cd13eb4413b4f6.pdf (accessed 5

908

October 2019).

909

10:

Technological

Innovation

for

the

Paris

Agreement.

van der Pol, T., Weikard, H.-P., van Ierland, E., 2012. Can altruism stabilise

910

international

climate

agreements?

Ecol.

Econ.

911

http://dx.doi.org/10.1016/j.ecolecon.2012.06.011

81,

112–120.

Doi:

912

Wahba, S. M., Kamel, B.A., Nassar, K.M., Abdelsalam, A.S., 2018. Effectiveness of

913

green roofs and green walls on energy consumption and indoor comfort in arid

914

climates. Civ. Eng. J. 4, 2284–2295. Doi: http://dx.doi.org/10.28991/cej-03091158

915

Wakabayashi, M., Arimura, T.H., 2016. Voluntary agreements to encourage proactive

916

firm action against change: an empirical study of industry associations’ voluntary

917

action

918

http://dx.doi.org/10.1016/j.jclepro.2015.10.071

plans

in

Japan.

J.

Clean.

Prod.

112,

2885–2895.

Doi:

54

Tab. 1. Comparison of this study with other studies analyzing IEAs with R&D in a participation game model. Authors Barrett, 2006

Main features ・The required breakthrough level is that the costs function changes from quadratic to linear. ・The R&D phase precedes the coalition formation stage and technological innovation; all countries choose their R&D levels before the coalition is formed.

Karp and Simon, 2013

・A decomposition of the gains from participation, a joiner’s gain function, is introduced. ・ R&D costs of developing abatement technologies are not considered.

Hoel and de Zeeuw, 2010

・Compared with Barret (2006), an R&D phase follows coalition formation, in which abatement technologies depend on R&D investment levels. ・ Each country chooses its R&D investment level collectively (i.e., cooperatively) or individually (i.e., noncooperatively).

El-sayed and Rubio, 2014

・Countries decide on their investment levels so as to minimize agreement costs of controlling emissions.

Contributions

・IEAs with R&D and breakthrough technology perform better if the breakthrough level is sufficiently high and the breakthrough technology has increasing returns to scale.

・IEAs consisting of more than four countries are possible by lowering the slope of the marginal abatement costs function.

・Even without increasing returns to scale, the potential for a large agreement to be sustained with non-cooperative R&D is beneficial for all.

・The maximum participation in agreement with R&D consists of six countries.

controlling emissions. ・Signatories to the IEA pool their R&D efforts so as to fully internalize spillover effects. Rubio, 2017 ・Signatories not only coordinate their levels of R&D investment but also pool their R&D efforts, to fully internalize the spillovers of their investment. This paper

・The participation in agreement decreases as spillover effects increase until the minimum size of agreement (three countries) is reached. ・Full participation agreement is stable if marginal damages are large enough to justify development of a breakthrough technology that completely eliminates emissions, and if technology spillovers are not very large.

・A participation game with joiner's gain function ・The diffusion process of advanced is applied in IEAs with R&D. abatement technology is clarified. ・A new R&D method (cooperative R&D, recovery of R&D expenditure, licensing fee) is considered by applying a joiner's gain.

・A full participation state can be more easily sustained than any other number of participants by preventing non-investors' adoption of advanced technology.

Section 6.2 Section 1

Sections 3 and 4

Question 1: How should countries invest in R&D and how much R&D investment is needed to sustain IEAs in which many countries participate and invest in R&D without assuming non-cooperative R&D and excessively drastic (unrealistic) abatement

Stages of a game Stage 1: Individual countries choose

Methodology Cooperative investment in R&D

whether to join the coalition. Stage 2: If some countries accede to

Recovery of R&D investment

the agreement, signatories

technology innovation? Question 2:

Question 3:

What kind of process

Can we design IEAs that

can be used to diffuse

motivate non-investors

advanced abatement

to participate in

technologies?

agreements and invest in

choose R&D expenditure levels for developing abatement technologies. Stage 3: The coalition chooses whether to adopt the new technology.

R&D?

Applying joiner's gain function

Joiner's gain function Applying joiner's gain function

Non-investors individually

Section 6.1 Answer to Question 1 in Section 1

Answer to Question 2 in Section 1

Licensing fee

Results newly obtained in the process of answering the three questions in Section 1.

Section 7 Core findings

Answer to Question 3 in Section 1

Section 5 Stage 4:

Discussion of whether our results can be obtained using a different approach.

Policy implications

choose whether to adopt the advanced technology.

Section 2 Introduction of the concept of the participation game and joinerʼs gain function.

Fig. 1. Flowchart of this study.

Upcoming studies

K− K

E

M MC (q), IEA size k

~ C’(q)

C’(q)

k

CR(k)

1 k −1

k −2 UA(k)

1

0

qf

q ks −1

q sk

abatement level q

Fig. 2. The number of investors (participants), k, with kinked marginal costs and R&D investment.

Parameter of R&D efficiency α 100

α=k/2

80

α = (k2 −3) / (4k −8)

60

Area in which ∂E ⁄ ∂k < 0 is satisfied.

40

20

0

50

100

150

200

Fig.3. The number of countries that adopt advanced technology and R&D efficiency.

Number of signatories k

Cooperative

R&D

investments

and

licensing

breakthrough

technologies:

International environmental agreements with participation game Nobuyuki Takashima

Highlights


We examined international environmental agreements (IEAs) with cooperative R&D.




IEA signatories invest in R&D cooperatively to improve abatement technologies.




Investors’ R&D expenditure can be recovered via the advanced abatement technology.




Non-investors must pay a licensing fee to adopt the advanced technology.




Full participation IEAs can be more achievable than any other sized IEA.

1

Declaration of Interest Statement The author declares no conflicts of interest associated with this article.

Nobuyuki Takashima, Ph. D. Kyushu University Platform of Inter / Transdisciplinary Energy Research (Q-PIT) 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan Tel: +81-92-802-5501; Fax: +81-92-802-5501 E-mail: [email protected]