Resource management and joint-planning in fragmented societies

Ecological Economics 171 (2020) 106481

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Ecological Economics journal homepage: www.elsevier.com/locate/ecolecon

Resource management and joint-planning in fragmented societies Bill Schultz

T

Department of Political Science, Florida State University, 113 Collegiate Loop, Tallahassee, FL, USA

ARTICLE INFO

ABSTRACT

Keywords: Diversity Identity Harvest planning Game theory Information Resource management Group decision-making Uncertainty

Does the division of a society into identity groups increase the risk of unsustainable resource use? This study considers the theory that diversity leads to degradation by preventing joint-planning across a community of resource users. A cooperative game theory model is used to derive conditions that should make this problem appear. When resource users can plan extraction choices together, sufficient uncertainty about the value of a shared resource (“environmental uncertainty”) will incentivize them to stably make decisions in as large a group as possible. However, that is only true when players are also pessimistic about the behavior of community members not directly involved in joint planning with themselves. If those conditions are met, the probability that a community will deplete their shared resource rises as they fragment into more and more identity groups that do not make decisions together. In sum, this study demonstrates that a combination of pessimism about the behavior of non-coalition members and sufficient environmental uncertainty give rise to a negative effect of social diversity. Among other things, these findings may help explain the mixed effectiveness of some conservation policies, and improve our understanding of how events that prime inter-group tensions can have downstream sustainability consequences.

1. Introduction Is managing shared resources more difficult in a society divided into multiple identity groups (i.e., in the presence of “social diversity”)? Researchers have linked ethnic diversity, for instance, to a variety of other political and economic problems. However, other researchers question these arguments for over-simplifying ethnic identity (Chandra, 2006; Habyarimana et al., 2007; Dunning and Harrison, 2010; Selway, 2011). Similarly, there is reason to hesitate before drawing simple conclusions about the relationship between social diversity and environmental degradation. The available literature provides nebulous lessons about (1) the ways social diversity could threaten sustainability, and (2) how noteworthy these threats are (Varughese and Ostrom, 2001; Poteete and Ostrom, 2004; Adhikari and Lovett, 2006a; Naidu, 2009). That quagmire appears, in part, because the potential the effects of social diversity on environmental outcomes remain undertheorized. Scholars have explored how social diversity could undermine local resource management institutions (Adhikari and Lovett, 2006a; Naidu, 2009), but they have devoted somewhat less attention to the idea that social diversity might influence resource use patterns themselves. In this study, I emphasize one potential explanation for such a relationship: when users from different identity groups do not plan their activities together or share information across social fault lines (“social fragmentation”), it prevents a community

from avoiding environmental externalities and increases the risk of overuse. There are compelling empirical illustrations of the threat fragmentation can pose (Barnes et al., 2013, 2016a; Barnes et al., 2016b), but we do not know enough about the conditions that cause these consequences to appear. Indeed, the benefits of collaboration for both sustainability and community welfare appear inconsistent. Using a cooperative game theoretic model, I help address that theoretical shortfall. Resource users in my model confront the risk of a destructive threshold: if collective use becomes too high, the resource will be depleted. Previous research illustrates that this threat can serve as a focal point to encourage sustainable coordination (Barrett, 2013; Walker et al., 2015; Diekert, 2017). Can social fragmentation have consequences in a case where efficient behavior should be easier to maintain? My analysis shows that a well-defined community of consumers in this setting may use a depletable resource efficiently even when they are members of identity groups that will not, or cannot, work together. When uncertainty about the value of this resource (“environmental uncertainty”) is not too severe, the steady state outcome is efficient with or without joint-planning— a breakdown in cross-group coordination and cooperation has no welfare or sustainability implications.1 When environmental uncertainty becomes severe enough, though, players with sufficiently pessimistic expectations about the behavior of others have an incentive to stably collaborate at the identity group level.

E-mail address: [email protected]. I model environmental uncertainty by assigning the value of the shared resource using a uniform distribution with publicly known parameters (Budescu et al., 1992; Gustafsson et al., 1999). 1

https://doi.org/10.1016/j.ecolecon.2019.106481 Received 5 September 2018; Received in revised form 10 September 2019; Accepted 14 September 2019 Available online 31 January 2020 0921-8009/ © 2019 Elsevier B.V. All rights reserved.

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Because players are making decisions at the identity group level, whenever social fragmentation becomes more extensive, the probability of overuse increases while the welfare of community members decreases. This theory may help explain the inconsistent empirical record on social diversity. Even when social diversity fragments information sharing and joint-planning across social groups, this should not always cause externalities. Barriers to joint-planning are more likely to have environmental consequences when a resource management problem is sufficiently “complex,” because in these cases there would have been greater returns to intergroup collaboration. For example, the uncertainty that surrounds fish stock estimation (Begossi, 1996; Murawski, 2000) could indicate that identity diversity is more likely to cause problems in marine management than forest management. Moreover, within marine management, the problem might be less threatening for communities that harvest species with more predictable stock movements. I note several implications of this model for conservation policy. First, it suggests that prospects for sustainability may be poor in the aftermath of events like intercommunal conflict that prime intergroup tensions. Interventions that successfully bridge such divides may carry downstream sustainability benefits. Second, this research complements field evidence on the benefits of broad participation in co-management institutions that facilitate joint-planning among resource users. However, I also find that the benefits of these initiatives might vary significantly with the “difficulty” of the management problem these forums are designed to address. Finally, this research suggests that third-party interventions attempting to increase the amount of information available to resource consumers (e.g., by providing improved monitoring technology) may be more productive in communities where social tensions bleed over into resource use behavior. The next section overviews the literature on diversity and sustainability, as well as evidence in support of the theory that diversity threatens sustainability by interfering with joint-planning and information sharing across society. After this, I introduce my cooperative game theory model.

Other noteworthy studies, when taken together, also lead to nebulous conclusions (Bennett et al., 2001; Adhikari and Lovett, 2006a; Pomeroy et al., 2007; Naidu, 2009; Papyrakis, 2013; Torpey-Saboe et al., 2015). A possible reason for these inconsistencies is that studies have focused on the effects of diversity within management institutions, or on their creation. Yet, it should also be important to consider diversity’s influence over resource use patterns themselves. If diversity makes unsustainable collective use more likely, then diverse societies trying to create sustainable management institutions may face more pressing technical challenges than otherwise similar homogenous societies. A negative relationship could appear between diversity and resource governance for reasons that have nothing to do with management institutions per se. This also implies that successful institutions in homogenous societies may be different from the institutions needed to support sustainability in more diverse societies (recalling Andeweg, 2000). 2.2. The effect of social diversity on harvesting behavior The concerns I raise above are only noteworthy if social diversity does influence resource use patterns themselves. Available evidence suggests that this is sometimes the case. Consider work by Barnes et al. (2013, 2016a, 2016b). These authors collect social network data from most fishers working in Hawaii’s longline fishery. The fishery in question constitutes a multimillion-dollar industry, is highly regulated, and is often touted as a fishery management success story. Yet even here, Barnes et al. argue: (1) that ethnic differences lead to the emergence of homogenous information sharing networks; (2) that there is disincentive for fishers to act as information brokers between these ethnic networks; and (3) that this segregated information sharing increases shark bycatch rates. This work illustrates that when social divisions prevent information sharing or joint-planning among resource users, it can put the environment at risk. Other research supports that argument as well. Limits on information sharing and learning within a community due to weak social ties are thought to threaten sustainability (Alexander et al., 2017; Bodin, 2017), while vice versa interventions that facilitate broader social interaction can encourage more productive resource use practices (Matous and Todo, 2018). Gatewood (1984); Salas (2000); Rudd (2001), and Gezelius (2007) provide further examples of contexts where information sharing and joint-planning can potentially support efficient fishery use. I highlight two broad theoretical justifications for the importance of information sharing and joint-planning. First, consider seminal work discussing the “cooperation dilemmas” that plague resource management (Hardin, 1968; Ostrom et al., 1994). The idea is that a fear of acting sustainably alone and being taken advantage of prevents each member of a community from harvesting with restraint. Yet, if resource users can commit to making binding decisions as a group, the strategic uncertainty produced by this cooperation dilemma washes away.2 It follows that when social divisions prevent binding agreements across identity groups, it allows cooperation dilemmas to persist even when a community could otherwise resolve them. Another important source of strategic uncertainty is “coordination dilemmas,” wherein agents face multiple possible steady-state outcomes, and they must anticipate which one other agents will pursue. Of course, some of these steady-state outcomes may be more desirable for the community than others. While activities like sharing information or joint-planning make it easier to resolve such dilemmas, research illustrates that social diversity can make those activities more difficult (Kooij-de Bode et al., 2008; Chen and Chen, 2011; Chen et al., 2014; Larson and Lewis, 2017). This is especially true if social diversity limits face-to-face communication across groups (Hardin, 1995; Drolet and

2. Theoretical background 2.1. Social diversity in resource management institutions A priority of contemporary research on common-pool resource use is identifying characteristics of a resource or its harvesters’ social environment that undermine sustainability (Agrawal, 2001; Cox et al., 2010). Diversity among users appears to be one such factor (Adhikari and Lovett, 2006a). When a group is divided along lines such as religion or ethnicity, this social diversity may increase the risk of unsustainable resource use. That idea reflects a broader literature in political science and economics debating the consequences of ethnic diversity (Miguel, 1999; Alesina et al., 2003; Fearon and Laitin, 2003; Habyarimana et al., 2007). Social diversity can threaten resource management simply by implying economic or political inequalities (see: Baland and Platteau, 1999; Dayton-Johnson, 2000; Adhikari and Lovett, 2006a, 2006b). However, identity divisions themselves may also be problematic. Social diversity can interfere with management processes by generating incompatible policy interests, undermining intra-community trust, and making environmental policymaking more conflictual (Heckathorn, 1993; Banks, 2008; Adhikari and Lovett, 2006a; Wittayapak, 2008). Yet, some important questions remain unanswered. For instance, diversity will not always lead to policy disagreements (Habyarimana et al., 2007). Why does diversity undermine trust and induce conflict in some circumstances but not others (Bennett et al., 2001; Yamazaki et al., 2018)? Unanswered theoretical questions aside, the empirical record is also ambiguous. Two reviews of studies associated with the International Forestry Resources and Institutions (IFRI) initiative, Poteete and Ostrom (2004) and Varughese and Ostrom (2001), provide mixed findings on the relationship between diversity and resource management outcomes.

2 Of course, this raises the question of how and when resource users can accomplish this task. My game theoretic analysis below speaks to that question in detail.

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Morris, 2000) or prevents the establishment of shared behavioral expectations (Mehta et al., 1994; Weber, 2006; Jackson and Xing, 2014). In sum, we have an argument that social diversity is problematic when it prevents behaviors across identity groups that would help resolve cooperation and coordination dilemmas. Cooperation dilemmas are already a common explanation of degradation (Ostrom et al., 1994). A coordination dilemma, meanwhile, will appear in resource use any time there are multiple feasible combinations of different users’ behavior that would lead to a stable total harvest (again, some may be more desirable). This is a reasonable characterization of many real-world cases. For instance, Alvard et al. (2002) characterize the coordination dynamics of the Lamelara whale hunters in Indonesia, and review parallel work in biology on the importance of the concept of “mutualism.” See also Norr and Norr (1974) and Abraham (2006). Of course, some of the same evidence noted above also illustrates that joint-planning and information sharing are not a consistently important part of resource use behavior. Gatewood (1984), for instance, studies salmon fishers in Southeast Alaska, and notes that information sharing cliques only appear in face of fishery openings with a quota. Meanwhile, Salas (2000) notes that catch-sharing teams in the Yucatan only form when seasonal winds cause daily fish stocks to be more highly variant. Finally, Romani (2003) finds in a study of agriculture in Cote d'Ivoire that ethnic minorities shared information more frequently within their communities than farmers in majority groups, because they had to cope with a lack of access to extension services. Rather than back out explanations for the conditional importance of these behaviors on a post hoc basis, it is more productive to theoretically derive those conditions. This should make it easier for researchers to identify cases where the concerns raised by Barnes et al. (2013, 2016a, 2016b) are most compelling— cases where social diversity is most likely to increase the risk of overuse. I turn to this task in the next section, using the tools of cooperative game theory.

A second example is Diekert (2017), who uses a dynamic model to illustrate that even uncertain thresholds can in some cases still encourage sustainable economic behavior. In cases where the result of crossing the threshold is not quite destructive enough to entirely prevent increases in resource use, it may still encourage agents to engage in only limited experimentation (in that model, one round of increased resource use) before their behavior stabilizes. This initial increase and then leveling off is inefficient, but (presuming that it does not trip the threshold) it is still better than an alternative of indefinitely increasing pressure on the shared resource. As a final example, while Barrett (2013) and Diekert (2017) emphasize the role of uncertainty, Walker et al. (2015) emphasize a different source of variation in this disciplining effect. They utilize a dynamic model that builds on the seminal Great Fish Wars study by Levhari and Mirman (1980). They also find that catastrophic environmental thresholds can encourage responsibility, but only when players’ payoffs are evaluated exclusively in steady states. When deviations by players from large-scale coordinated arrangements leads to a transition phase instead of leading right into a catastrophic depletion state, the disciplining power of the catastrophic threshold is weakened. Moreover, they also emphasize that the threshold must be sufficiently catastrophic to be beneficial: the alternative must be depletion of the shared fishery.4 In addition to modeling joint-planning, I must also model the social fragmentation that interrupts it. To do so, I incorporate the ideas of scholars like Chalkiadakis et al. (2012), who suggest using social network structures to represent limits on players’ opportunities to collaborate with others. What should we make of the disciplining effect of catastrophic thresholds when large-scale collaboration is not possible, such as in the presence of inter-group hostilities? This is a novel feature of my study. Finally, note that like Barrett (2013) and Diekert (2017), I emphasize the essential conditioning effects of environmental uncertainty in all these processes.

2.3. Formal models of catastrophic thresholds

3. Modeling resource use with social fragmentation

To formally represent the potential benefits of joint-planning arrangements, I employ a cooperative coalition theory model. In short, these models let players make the binding decisions to work as a group if they feel that it serves their own self-interest. There are many such models I could use as a basis for my own. Funaki and Yamato (1999), for instance, already discuss some conditions under which large-scale decision-making is sustainable for players in a more classic CPR dilemma. However, I argue that it is most poignant to illustrate negative effects of social diversity in a strategic dilemma where there are factors that could render efficient resource use especially easy. Therefore, I study a dilemma in which players are threatened by the total depletion of a shared resource if they do not limit their net extraction levels. Previous work illustrates that the threat of catastrophe can have a disciplining effect on environmental behavior. However, the strength of this disciplining appears to vary. For one example, Barrett (2013) outlines a one-shot environmental collective action problem in which the benefits of avoiding a catastrophic climate threshold can sometimes be much higher than the costs of doing so. In those cases, and when the location of the threshold is certain, players face a straightforward coordination problem that joint-planning arrangements are ideal to help solve even without enforcement power.3 However, when the location of the threshold becomes uncertain, it is no longer as useful a focal point for coordination. In effect, joint-planning arrangements are less likely to be effective (see also Barrett and Dannenberg, 2014).

The model below shows that, under some conditions, joint-planning is not necessary for a community of resource consumers. However, in other cases rationally self-interested individuals may have an incentive to work together in a Pareto-improving way that limits pressure on their shared resource. If social divisions prevent this joint-planning, it should have consequences for the welfare of the community and the sustainability of the resource itself. 3.1. The base resource dilemma game I build upon the Resource Dilemma (RD) game originally used in the psychology field (Rapoport and Suleiman, 1992; Budescu et al., 1995). As opposed to Common-Pool Resource (CPR) appropriation games (Ostrom et al., 1994), in which overuse imposes an externality cost, the RD presumes the existence of catastrophic threshold for net community use of a resource. When net use of the resource is above this level, the resource deteriorates, and all players receive a payoff of 0.5 Consider a set N of players sharing access to a resource with value X , and indexed by i {1, 2, …, n} . Each player makes a continuous request x i : x i > 0 . If x i > X, the resource is depleted, and each player receives a payoff of 0. Otherwise, players receive their requests. An important complication is that players do not know X precisely. They know that it is determined by a random draw from the uniform funif ( , ) . In other words, players know that X is at distribution: X

3

First, note that there is also a non-cooperative Nash equilibrium in which players fail to avoid tripping the threshold. Second, note that when the benefits of avoiding catastrophe are only moderately higher than the mitigation costs, we instead see a middle range where credible enforcement mechanisms are more necessary.

4 In most cases, these authors focus on the potential for joint-planning across all players. Miller and Nkuiya (2016) are noteworthy for emphasizing mixed coalition structures in similar dynamic resource management models. 5 For an integration of these approaches see Walker and Gardner (1992).

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least and at most β, while every number within this range has an equal chance of being the true value.6 The RD model was initially developed to explore how environmental uncertainty undermines sustainability (Budescu et al., 1992; Roch and Samuelson, 1997; Gustafsson et al., 1999; Rapoport and Au, 2001). The degree of environmental uncertainty can be manipulated by increasing or decreasing β − α. A player’s utility is given by (Suleiman and Rapoport, 1988; Rapoport and Suleiman, 1992):

xi , xi + x i (xi + x i )] , < xi + x

xi [

E (u i ) =

Ostrom, 2005), we could already answer the research questions I pose. Under enough uncertainty, when a society fragments into more identity groups this will increase the total number of decision-makers and increase the risk of over use. But when will a similar result appear if players can choose to coordinate within groups? 3.2. The coalition-theory resource dilemma I modify the RD game by introducing concepts from “coalitiontheory,” or cooperative game theory. Assume the community is made up of some number of coalitions (groups of players), each denoted by Sj , and indexed by j {1,2, …, k } . We then have a coalition structure k , which is the set {S1, Sj , …, Sk } . This coalition structure is contained in the set of all possible structures . By assumption, every coalition contains at least one player, and no player is in two coalitions. Every player could be their own coalition ( k would be a set of singletons). In a cooperative game, players commit to merge into coalitions of various sizes, and each coalition then takes whatever action maximizes the sum of its members’ collective utilities (imagine that a coalition elects a representative to make decisions for everyone in the group based on their collective best interest; Hart and Kurz, 1983). To make my discussion simpler, I assume earnings are divided equally within each coalition (i.e., symmetry within coalitions). Note that “coalition” does not neccesarily refer to a social identity group, but simply a set of players that act as a unit. Also, note that it is standard in cooperative game theory to assume that the decision to join a coalition is binding (Huang and Sjöström, 2003). Once a coalition has formed, there are mechanisms (perhaps simply reputational; Gatewood, 1984) that prevent players from defecting. This simplifies the process of establishing dominance relations. For a non-cooperative coalition approach to resource dilemmas, see Pintassilgo (2003). A vector of payoffs {p1 , … pi , … pn } z and the coalition structure that produces it represent a stable outcome if they are in “the core;” if they are weakly undominated by any possible imputation (Kóczy, 2007). That is easiest to establish in transferrable utility (TU) games (or CFGs, which stands for “characteristic function games”), where outcomes within a coalition are independent of what happens outside it. But here, for any coalition Sj N , decisions of outsiders influence the payoffs that accrue to Sj . This means that the coalition-theory Resource Dilemma is a game in “partition function” form: Sj ’ s welfare depends on k . In partition function games (PFGs), there is no universally correct or unambiguous way to define a dominance relation that identifies core outcomes (Hart and Kurz, 1983; Immorlica et al., 2010; Bloch and Van den Nouweland, 2014). Presume members of coalition Sj are weighing their expected utility under some core outcome (z, ck) against an alternative (z , Sj N \Sj ) wherein they diverge from it. Players must pre-assess their expected utility in each case (Hart and Kurz, 1983; Huang and Sjöström, 2003). Let the value function v (Sj ) represent the pre-assessment process. This function assigns expected utilities to players in a coalition based on the coalition structure it is embedded within. Pre-assessing the value of divergence, though, requires pinning down N \ Sj . Many approaches to solving PFGs assume that players do this using a specific expectation rule (Kóczy, 2007; Bloch and Van den Nouweland, 2014). These rules essentially transform a PFG so that it resembles a simpler TU game (Funaki and Yamato, 1999). Utilizing this approach requires justifying (or assuming) an equivalence between: (1) the core of the simplified (transformed) game; and (2) the core of the PFG itself under that expectation rule. I discuss this further below. The simplest and most common expectation rules— representing opposite extremes— posit that N \ Sj reacts in the best possible way for Sj (an optimistic rule, used when analyzing the optimistic core of a PFG), or the worst possible way (a pessimistic or

i

0, else Based on this, the symmetric Nash equilibrium request is as follows:7

x i* =

(n + 1) n

, if n >

, if n

(n + 1)

(n + 1)

The logic of this result is important. The first potential equilibrium request, , appears by following the standard procedure of maximizing (n + 1)

E (u i ) and determining where symmetric players’ best-response functions overlap. The resulting total request at the community-level is then n , (n + 1) which is less than or equal to the lower bound of the resource when n (n + 1). In such a case, rational players would instead elect to each request in a symmetric equilibrium, which they receive with certainty. n This is the reason for the conditional equilibrium above. In some situations, then, environmental uncertainty and the number of players (a source of strategic uncertainty) are low enough that players pursue their self-interest by safely requesting as a group rather than risking overextraction. Increases in the number of players or environmental unin equilibrium. certainty will make it more likely that players request n+1 Consider also the symmetric Pareto efficient outcome in this game (Budescu et al., 1995):

x iPE =

2n n

, if

, if

>2 2

When environmental uncertainty is high enough that > 2 , it is Pareto efficient for the community as a group to risk over extraction and make a net request greater than . Yet, when environmental uncertainty is lower, it is Pareto efficient for the community to request . The Nash equilibrium in this game shown above is therefore only sometimes inefficient. When environmental uncertainty is low enough, players in a symmetric equilibrium will not risk over-extracting, and will instead make what is the Pareto efficient request in that parameter space.8 If we assumed that players always operate as a unit within their identity groups (perhaps by force of social norms: Hardin, 1995; 6 While each player in this model is subject to the same uncertainty, Lindahl (2012) provides an interesting illustration of how an unequal distribution of environmental uncertainty influences resource use dilemmas. 7 In this game, there are an infinite number of non-symmetric equilibria, which presents an extra coordination problem as players must form beliefs about which steady state they expect others to pursue. Moreover, under enough environmental uncertainty, these non-symmetric equilibria could imply a higher net request than those I outline above. While those complications are interesting, I set them aside to simplify the discussion in this section. I focus on symmetric equilibria to avoid introducing theoretical moving parts that are not strictly necessary for my argument in later sections. Inequality in the RD game is worth treating as an object of study in its own right. 8 Both optima discussed in this section are derived elsewhere. However, I also justify them in the Appendix.

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cautious rule, used for the pessimistic core).9 The optimistic core is more conservative, because it is the most likely to encourage divergence from an analyst’s outcome of interest (Hafalir, 2007; Bloch and Van den Nouweland, 2014). I consider both rules in my analysis below.

some coalition of players considers diverging from any focal outcome (z, ck) .

3.3. Adding social fragmentation

Proof. The two most extreme reactions are N Sj acting as a unit in response to divergence by Sj , or N \ Sj splintering into a coalition structure of singletons. Proposition A in the Appendix illustrates that Sj has a higher expected utility under the former than the latter given 2 . ◼

Lemma 1. Consider Γ1 and let q = |N \ Sj |. Players using v p (Sj ) i Sj , and players using v o (Sj ) presume N \ Sj = {i1, …, i q } i Sj . presume N \ Sj = {i1 i2 … i q }

The goal of this study is to determine the consequences of social diversity when it prevents joint-planning and information sharing. I refer to that effect as “social fragmentation.” Note that it is possible to have an ethnically diverse society that is not socially fragmented in this way, or an ethnically homogenous society that is fragmented on some other dimension. To introduce social fragmentation, I draw on the suggestions of Chalkiadakis et al. (2012). I treat the degree of social fragmentation as an exogenous parameter in this study (see the Discussion and Conclusion). Consider a network graph, G, wherein each player is a node, and the ties between players indicate whether it is possible for them to merge together into a coalition. Fig. 1 provides an example. In this figure, there is a community of eight people broken up into two identity groups that will not make decisions with out-group members. In graph theory terminology, the social network is complete within groups, but not across them. I denote any fully complete network structure as G1, and any other network structure as Gh, where the integer h is the smallest number of coalitions that can form. Social fragmentation becomes more extensive as h rises. Therefore, I increase fragmentation by increasing h, which decreases the possible extent of joint-planning. Any assumption about the network structure within these identity groups would be arbitrary. Absent further theoretical guidance, I assume each identity group constitutes a complete graph.

Lemma 1 argues that any coalition evaluating a divergence from (z, ck) using a pessimistic value function will assume the rest of the coalition structure is going to break up into singletons as a result. Meanwhile, optimistic players will assume that the rest of the coalition structure responds by merging together into one unit. Next, I turn to identifying the most efficient outcome. In Γ1, it is uniquely efficient for every player to merge into one “grand” coalition. Result 1. In the PFG Γ1 defined by the quintuple (N , , {v } , G1, 2) , the grand coalition is the unique Pareto efficient outcome. Proof. Other studies establish x iPE (defined in subsection 3.1) as the efficient symmetric outcome with non-cooperative players. A community there makes a net request equivalent to the decision of a unitary player under 2 (Suleiman and Rapoport, 1988; Rapoport and Suleiman, 1992; Budescu et al., 1995). Since the grand coalition is a unitary player and, under 2 , no other coalition structure results in this efficient request (per Proposition B in the Appendix), the claim stands. Moreover, a typical source of inefficiency in the grand coalition is negative externalities (Pintassilgo, 2003; Hafalir, 2007), which do not appear in this game (see Proposition B). ◼

3.4. Stability of maximal coordination under high environmental uncertainty

The efficiency of the grand coalition (everyone making decisions together) is important in the next Lemma. Below, CoPFG , p refers to the core (optimistic or pessimistic) of a partition-function game itself, and C TU (v o, p ( )) refers to the core when either an optimistic or pessimistic expectation formation rule is used to transform the game into a simpler TU form. Doing so renders the PFG easier to solve by imposing an assumption about how players expect others outside their coalition to respond to their coalition’s behavior. Lemma 2 establishes that the core of the simpler game is equivalent to the core of the PFG for game Γ1. This equivalence means that assessing the simpler C TU (v o, p ( )) also provides an assessment of the more complex CoPFG ,p .

I explore results under two parameter spaces, to illustrate two of the patterns of play that can appear in this game.10 The first parameter 2 and n > 1, with n space— 1 — corresponds to a case where (n + 1) . The non-cooperative equilibrium here defined such that n is x i*1 = n . Second, I consider 2 , where > 2 , n > 1, and therefore

x i*2 = . Under this parameter space, there is an inefficient symn+1 metric equilibrium in non-cooperative play. Below, I identify the conditions that drive players to engage in mutually beneficial joint-planning, and go on to discuss the consequences when social fragmentation restricts that cooperation. I produce these results assuming symmetry within coalitions, and symmetry across coalitions of the same size. , G1, 2) , where Consider a cooperative PFG Γ1= (N , , {v } N is the set of all players, is the set of all possible coalition structures, {v } is a value function that determines the worth of a coalition based on its partition structure and any other structure containing it, G1 is a graph representing a society with no fragmentation (no restrictions on merges), and 2 is defined as above. I begin my discussion by pinning down how coalitions using optimistic and pessimistic valuations expect the rest of the coalition structure to behave. Assume

Lemma 2. Given Γ1, CoPFG = C TU (v o ( )) and CpPFG = C TU (v p ( )) . Proof. Funaki and Yamato (1999) and Chalkiadakis et al. (2012) discuss the equivalence between the core of a PFG under optimistic or pessimistic expectation rules and the core of the transformed TU game when the unique, efficient outcome of a PFG is the grand coalition. Result 1 establishes the unique efficiency of the grand coalition for Γ1, so this equivalence follows.11 ◼ With this justification for my solution approach in hand, next I argue that the grand coalition is in the core of Γ1 under a pessimistic rule, but not an optimistic rule. This recalls the findings of Funaki and Yamato (1999) and Hafalir (2007).

9 There are expectation formation rules that fall between these two extremes (Huang and Sjöström, 2003; Kóczy, 2007). Bloch and Van den Nouweland (2014) overview the relative merits of these rules. 10 Although it is sometimes possible for there to be a shift between these spaces based on players’ decisions, I set that situation aside for this study. It does not work against my primary conclusions, and simply presents a more complicated middle case to analyze. For instance, it is possible to have a modification of parameter space two, where suboptimal play among a coalition of singletons would only appear if the number of players is above some threshold. If merges are allowed here, they would eventually cause a shift to parameter space one.

Result 2. In the PFG Γ1 defined by the quintuple (N , , {v } , G1, 2) , the grand coalition is in the pessimistic core of Γ1, but not the optimistic core. 11

When the grand coalition is not uniquely efficient, the core of the TU game simplified through an optimistic expectation rule may not be in the core of the PFG itself (Chalkiadakis et al., 2012). Under pessimistic expectations, it could indicate that there are additional outcomes in the pessimistic core of the PFG besides the TU result. 5

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Fig. 1. An example network with eight players, broken up into two social groups that can form coalitions within their group but not across groups. Here, we have the graph G2.

Proof. I must show that the grand coalition is undominated in C TU (v p ( )) but not C TU (v o ( )) . Proposition C in the Appendix shows that the grand coalition is more valuable to a pessimistic subset of players Sj than acting apart from it and facing a set N \ Sj of singletons. However, given optimistic expectations about the reactions of \ Sj , individual players or small coalitions can gain by choosing not to join the grand coalition. The grand coalition is only undominated against deviations of a relatively large subset of optimistic players. ◼

the expectations of optimistic and pessimistic players. Optimistic players expect that if they diverge from some focal outcome, everyone outside their own coalition will merge into one residual coalition. Pessimistic players presume that the rest of the players will splinter and act non-cooperatively. Result 1 establishes that the grand coalition (all players merging) is the unique efficient coalition structure. Given this, Lemma 2 defends my solution approach. Using that solution approach, Result 2 then shows that when players are pessimistic and merging is unrestricted, the grand coalition is a stable outcome (“in the core”). Finally, Results 3 and 4 establish that when merging is restricted, it is instead in the core for pessimistic players to merge as much as possible within their groups.

As in other studies, pessimism about the behavior of non-coalition members— here, a fear that they will splinter and act separately— motivates joint-planning at the highest possible level (“maximal coordination”). Absent this fear, there is simply less demand for jointplanning. Therefore, I set aside optimism, and treat pessimism as a scope condition (see the Discussion and Conclusion). The following Results highlight why the grand coalition is stable in the game above, and then generalize to games where fragmentation blocks the grand coalition. In short, Result 3 argues that merging as much as possible is uniquely efficient in the presence of social fragmentation, while Result 4 argues that this outcome is therefore in the pessimistic core. Result 3. For Γ2 = (N , , {v } unique efficient outcome.

, G h < n,

2),

the pair (z,

h)

3.5. Considering low environmental uncertainty Consider now the other parameter space 1, where environmental uncertainty and the number of players (i.e., strategic uncertainty) are low enough that a community of singletons will use a shared resource efficiently in a non-cooperative equilibrium. Some results above break down. First, the grand coalition is no longer the unique efficient coalition structure. A set of singletons will also make Pareto efficient choices in this parameter space (Budescu et al., 1995). This lack of unique efficiency may render Lemma 1’s equivalence theorem unreliable (see footnote 11). More importantly, observe that the logic justifying maximal coordination alone in C TU (v p ( )) no longer holds. Here, a pessimistic singleton remaining outside the grand coalition given G1 expects the exact same utility they would have received from working with everyone else in their community. In effect, per the Result below, atomistic play and the grand coalition are each in C TU (v p ( )) . Moreover, when social fragmentation blocks the grand coalition, then the only outcome in C TU (v p ( )) is a coalition structure of singletons. Pessimistic players under 1 do not expect to gain by forming coalitions different from the grand coalition or atomistic play. If players merge at all in C TU (v p ( )) it would be to form the grand coalition (when possible)

is the

Proof. Presume we have some maximally coordinated outcome (z, h) that is not Pareto efficient. For this to be true, there must be some possible Pareto improving change in the coalition structure. But further concentration is impossible by assumption, and I show in Proposition D of the Appendix that any fracturing of the coalition structure will decrease the sum of the expected utilities of every player. There is no possible Pareto improvement. ◼ Result 4. For the PFG Γ2 = (N , , {v } coordination is in the pessimistic core.

, G h < n,

2),

maximal

Proof. Per Lemma 1, pessimistic expectations lead players in some coalition Sj to presume that the alternative is facing a set N \ Sj of singletons if they make merge below the level permitted by their social structure. Per Result 3, this maximal coordination is efficient. Result 4 follows if this efficient outcome is more valuable to any potentially diverging set of players than facing a set of singletons. Proposition E of the Appendix argues that this is the case. ◼

Result 5. Consider the PFGs Γ3 = , and Γ4 = (N , , {v } , G h < n, 1) . The grand coalition and atomistic play TU are each in C (v p ( )) of Γ3, and atomistic play is in C TU (v p ( )) of Γ4. Proof. Per Proposition F in the Appendix, the outcome pairs (z , k) and (z , 1) that respectively represents singleton play and the grand coalition under 1 are undominated by any outcome with a coalition structure Sj N \Sj under pessimistic expectations. Each outcome is in the pessimistic core of either transformed TU game, when feasible. ◼

Pessimism drives any potential sub-coalition of N to assume that if they act outside the efficient coalition structure, they must make requests against a coalition structure of singletons. This establishes the grand coalition in the pessimistic core of Γ1, since it is more valuable to each of them than that alternative. The same is true in Γ2 when social fragmentation blocks the grand coalition, so long as some amount of joint-planning is still feasible (as long as making decisions together at some higher level is superior to the worst-case alternative). Therefore, under high enough environmental uncertainty, self-interested players will stably merge as much as the identity divisions in their society allow if they are pessimistic about the result of failing to do so. I conclude by summarizing the above findings, which together describe steady-state behavior under 2 (high uncertainty). Lemma 1 characterizes

The equivalence theorem that applies this Result to the PFG itself has limitations now: there may be additional outcomes in the core of the PFG that I do not describe above. This limits my ability to characterize coalition formation in the core under 1. However, from a strictly conservation perspective, the result is immaterial— at the community-level, these hypothetical additional core outcomes must lead to the same net request.12 Therefore, while I cannot pin down 12 Presume there is some other outcome in the pessimistic core of the PFG itself here besides singleton play and the grand coalition. While this alternative

6

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every PFG core outcome in this space with certainty, I posit that they share the same welfare and conservation implications as those noted in Result 5: the community as a whole requests , and there is no risk of over extraction.

environmental uncertainty becomes high enough, we might see that social fragmentation increases the probability of over-use. I show this by: first, establishing that players under high uncertainty will choose to merge together as much as the structure of society allows in a steady state outcome, leading to a RD game played at the social group level (Results 14); and second, establishing that games at the social group level become worse for both the environment and the players when the social structure of a community fragments (Result 6). However, this finding only appears under potentially limiting scope conditions, which helps point to circumstances in which diversity is more likely to explain resource use behavior. First, many of the results described above assume players are pessimistic about the behavior of others with whom they are not planning. Optimistic players will be more confident that merging at the highest level is unnecessary to protect their welfare, and so coalition-forming behavior may be harder to predict. Note that there are many possible expectation rules between these extremes (Bloch and Van den Nouweland, 2014). My results should hold under a less extreme pessimistic rule as long resource users predict that merging as much as possible is better than the likely alternative. This leaves an important role for focal events that prime a community’s fear of resource collapse (or optimism about sustainability). It would be interesting in future research to allow players’ expectations about non-coalition members to differ depending on whether they share an identity group (Weber, 2006; Jackson and Xing, 2014). Second, this model treats social fragmentation as exogenously emerging from social diversity. This avoids the question of why social diversity leads to fragmentation in some societies but not others, simply because it is beyond the scope of this analysis. Moreover, it means that this model applies to cases where the source of fragmentation is not resource conflicts themselves. I argue that this is plausible (e.g., in Hawaii’s longline fishery, ethnic tensions between Vietnamese, Korean, and European Americans likely had other sources and predated fishing interactions), but it would be interesting to develop a model that endogenizes the emergence of fragmentation. Third, this model assumes that the coalition-formation process is costless. Moreover, I do not propose a specific model of coalition-formation. Changing either of these features and introducing further complications may produce different substantive lessons (Goyal and Vega-Redondo, 2005; Hafalir, 2007), but in the case of coalition-formation processes it would be a tradeoff between gaining more generality in a subset of real-world cases that match the specific coalitionforming process while losing generality in all other cases. Fourth and finally, by assuming symmetry within coalitions and across coalitions of the same size, I assume away the presence of distributional conflicts, as well as some coordination problems that could result from the presence of non-symmetric equilibria (especially in subsection 3.1). On one hand, it is possible that these distributional conflicts would not significantly change the community-level results with which this model is concerned. On the other hand, if distributional conflicts are relevant for sustainability itself, it is possible to speculate how without introducing more analyses. Consider that players commit to a coalition merge when they feel that doing so is better for their expected utility than the likely alternative. If distributional conflicts threaten coordination, this would be because players expect to be taken advantage of by their own coalitions, and so merging would seem less worthwhile.13 The findings of this model make a useful contribution to the literature on diversity and environmental management, because they help clarify the circumstances in which a negative environmental consequence of intergroup tensions is more likely to appear. Empirical

3.6. Substantive consequences of increasing social fragmentation I have just argued that under 1, while social fragmentation may interfere with the coalition forming process, it will not influence the community’s steady state welfare or the risk of depletion. On the other hand, given 2 , pessimistic players will merge as much as possible given the restrictions posed by social fragmentation (subsection 3.4). What material consequences does social fragmentation have when it does limit the scope of mutually beneficial joint-planning?

, G h*, 2) , where Result 6. Consider the PFG Γ5 = (N , , {v } there are four potential network graphs with hn > h > h > h1. Also, let Pr ( k) represent the probability that x i > X given k . I claim that:

(

• Pr ( •

hn )

xi > X|

> Pr ( hn)

> (

h)

> Pr (

h' )

xi > X |

h)

> Pr ( > (

h1)

xi > X |

h')

> (

xi > X |

h1)

Proof. I demonstrate both points in Proposition G of the Appendix. ◼ In simpler language, the comparative statics in Result 6 show that as social fragmentation becomes more extensive, two other things increase: (1) the steady state amount that the community requests in total; and (2) the probability that the community will over-use their shared resource. This establishes the potential conservation implications of social fragmentation under assumptions of high environmental uncertainty and pessimistic strategic decision-makers. The potential welfare implications of social fragmentation follow from that point as well. Proposition H in the Appendix illustrates that as social fragmentation worsens and the probability of over-extraction rises, the expected utility to every player (or every coalition) decreases. In sum, tensions across identity groups can lead to negative environmental consequences by preventing mutually beneficial joint-planning. However, when uncertainty is low enough, joint-planning is less important for welfare or conservation purposes. Meanwhile, when players are optimistic about decision-makers outside their joint-planning groups, they may be less likely to consider the benefits of large-scale collaboration. In those cases, barriers to interaction across identity groups may be less useful predictors of resource use behavior. 4. Discussion and conclusion Human societies sometimes fragment into identity groups that will not or cannot share information and plan economic activities with outgroup members. Could this influence how those societies choose to harvest natural resources? To answer that question, I develop a cooperative coalition-theory model and identify conditions that would drive resource users to act in a way that resembles the findings of scholars like Barnes et al. (2013, 2016a, 2016b). Because my results characterize the behavior of rationally self-interested decision-makers, they demonstrate how strategic considerations alone can lead social fragmentation to have environmental consequences. Result 5 above and subsection 3.5 in general argue that when environmental uncertainty is low enough, even with extensive social fragmentation, efficient use of a shared resource is still the stable outcome. Social fragmentation there should not influence the probability of destructive over-use, even if it does influence coalition formation patterns themselves. Per my other Results and Lemmas though, when

13 This is a different condition than “pessimism.” Pessimism speaks to expectations about non-coalition members, whereas distributional conflicts refer to expectations about coalition members.

(footnote continued) outcome may exist, per the citation in footnote 12 it is in addition to those established by the simplified TU game. Therefore, it cannot be superior to them. 7

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work already underlines that this can problem can plague even wellmanaged resources, and my conclusions parallel the findings of prominent environmental organizations that degradation can result from communication and planning failures (Greenpeace, 2017). Moreover, this study makes a few more general theoretical contributions as well. First, I provide a unique integration two different strains of the cooperative coalition theory literature: research on how network structure can restrict coalition-formation patterns (Chalkiadakis et al., 2012); and research on how catastrophic (and perhaps uncertain) state shifts influence coalition-formation behavior (Barrett, 2013; Barrett and Dannenberg, 2014; Walker et al., 2015; Diekert, 2017). Somewhat like Diekert (2017), I show that in my model an uncertain threshold can still discipline the behavior of resource users. In my case, it is because players with the opportunity to plan their extraction decisions together respond to the uncertain threshold by planning as a group. A different result appears in the strategic dilemma studied by Barrett (2013). There, an uncertain climate tipping point may render even large-scale joint-planning less effective without the addition of cooperative enforcement mechanisms.14 However, note that the disciplining effect I observe weakens as we restrict the amount of collaboration in which players can engage. A second contribution is to illustrate from a new strategic setting that pessimism and optimism have different influences on collective environmental behavior (Funaki and Yamato, 1999). A compelling risk of depletion appears to drive pessimistic (but perhaps not optimistic) resource users in different contexts to all recognize the benefits of large-scale decision-making. In conclusion, I reiterate several cautious policy implications. Firstly, analysts should pay more attention to events that prime feelings of pessimism or optimism about long term productivity among users of a shared resource, especially for resources subject to extensive environmental uncertainty. Events that prime inter-group tensions are concerning in the same contexts. Secondly, interventions that set up joint-planning forums or provide resource users with more sophisticated monitoring technology should see a larger return-on-investment in the presence of environmental uncertainty and tensions across identity groups. Consideration of these issues may help scholars unpack the relationship between diversity and environmental outcomes more carefully in the future.

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Funding This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Declaration of Competing Interest None. Acknowledgements I am indebted to feedback from Eric Coleman, Robert Carroll, Jens Großer, Christopher Reenock, Kimberly Fruge, Jordan Holsinger, and Joseph Bommarito. I am also indebted to the excellent advice of several anonymous reviewers, and attendees to a panel at the 2018 Southern Political Science Association conference. This work would have been impossible without all of the guidance I received. Any errors are my own. 14 In other respects, my findings resemble some of Barrett (2013)’s. In my model, the benefits of avoiding catastrophe are always large, and I show that in such a case, depending on features of the wider environment (e.g., uncertainty), mutually beneficial joint-planning can either be easy or difficult to maintain. The point above where our results differ is likely an artifact of the different strategic dilemmas we study.

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