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Endogenous community formation and collective provision – A procedurally fair mechanism
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Endogenous community formation and collective provision – A procedurally fair mechanism夽 Werner Güth ∗ Max Planck Institute of Economics, Jena, Germany
a r t i c l e
i n f o
Article history: Received 11 April 2013 Received in revised form 7 November 2013 Accepted 14 January 2014 Available online xxx
Keywords: Procedural fairness Mechanism design Equality axiom Public provision Collective action
a b s t r a c t A group of actors, individuals or firms, can engage in collectively providing projects which may be costly or generating revenues and which may benefit some and harm others. Based on requirements of procedural fairness, we derive a bidding mechanism determining endogenously who participates in collective provision, which projects are implemented, and the positive or negative payments due to the members as well as outsiders. The mechanism allows only for one community with more or less outsiders but not forming multiple communities. We justify procedural fairness but acknowledge that the outsider problem questions some of its desirable properties. Furthermore, we compare procedurally fair with optimal, e.g., welfaristic mechanism design (e.g. Myerson, 1979). © 2014 Elsevier B.V. All rights reserved.
JEL classification: D44 D46 D61 D62 D63 D71 D72 D73 D74
1. Introduction Via our residence, we usually become members of regional communities like municipalities and states. We propose a mechanism allowing community members to influence what is collectively provided in ways similar to private procurement. For communities with exogenously given membership Güth and Kliemt (2013) have suggested how to regulate public provision in procedurally fair ways. Their proposed mechanism has also been studied experimentally (Güth et al., 2014a) what will be briefly reported. Here we want to demonstrate how to extend this approach by allowing for endogenous community formation to determine what is collectively provided as well as its financing.
夽 The author gratefully acknowledges the constructive advice and encouragement of two anonymous referees how to revise the manuscript. ∗ Tel.: +49 3641 686 620; fax: +49 3641 686 623. E-mail address: [email protected] 0167-2681/$ – see front matter © 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jebo.2014.01.005
Please cite this article in press as: Güth, W., Endogenous community formation and collective provision – A procedurally fair mechanism. J. Econ. Behav. Organ. (2014), http://dx.doi.org/10.1016/j.jebo.2014.01.005
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Examples are sports clubs, private organizations like charities, political parties, non-profit organizations etc. for whom procedural fairness in regulating their activities is crucial – more crucial than optimality, e.g. allocative efficiency, dominating in welfaristic mechanism design, based on dominance solvability or the revelation principle. Whereas “optimal mechanism design” tries to achieve the best allocation results via eliciting private evaluations for each and every specific situation, our procedural fairness approach is generally applicable and much more in line with the legal tradition of justifying institutions by their properties rather than by their allocation results in an unforeseeable future. What procedural fairness rules out is arbitrary favoring of some of the parties involved. More specifically, this must be guaranteed with respect to all objectively verifiable and interpersonally comparable characteristics. A possible requirement would be, for example, envy-free net trades according to bids. The essential requirement of procedural fairness is an equality axiom (see Güth, 2011) which implies such envyfreeness. It does not mean to make unequals equal but rather postulates equal treatment when possibly unequal community members in overt behavior choose equally like when counting votes based on the “one person – one vote” principle. Imposing equal treatment based on interpersonally and objectively observable behavior renders our approach applicable across the board. We can allow for private information and question common knowledge and incentive compatibility constraints. In game theoretic terminology, what we derive is just a game form without appealing to commonly or privately known evaluations and beliefs concerning them. As a consequence our approach differs fundamentally from defining procedural fairness by symmetry of player roles in (Bayesian) games. Beside its procedural fairness its advantage is to be legally implementable. Obvious real-world examples of endogenously formed communities are private clubs whose activities also affect outsiders. Of course, also local communities are “formed”, e.g., due to migration, but their outsiders do not participate in bidding. When implementing the mechanism experimentally, private evaluations have to be added. But no commonly known beliefs concerning them as required by game theoretic equilibrium analysis, have to be experimentally induced or controlled. Compared to all-encompassing communities, endogenously formed communities like private clubs allow for outsiders who are exempted from procedural fairness enjoyed by community members. Although all individuals participate in the endogenous determination of the community, some of them might be excluded. It will be shown that this outsider problem questions some desirable properties which procedural fairness implies for all-encompassing communities. But, in our view, this is due to endogenous community formation and its outsider problem and not a drawback of the procedural fairness approach as such. In Section 2, we discuss the related literature. Section 3 derives the mechanism which is illustrated by the example in Section 4. How properties are questioned by outsiders is discussed in Section 5. Section 6 concludes by relating our approach to optimal, e.g. welfaristic mechanism design. 2. On the related literature Quite generally, one can distinguish between (i) fairness of allocations and (ii) fairness of procedures. The former topic (i) is extensively discussed by economists who partly argue that low and possibly unfair wages go along with larger profits, more investments and employment and partly propagate high wages which could crowd in intrinsic efficiency and reciprocity concerns of employees. More recently, experimentalists use distribution games featuring tradeoffs between fairness (more equal payoffs) and efficiency (measured by the payoff sum of all parties). Fairness of procedures, (ii), is neither necessary nor sufficient for (i): fair procedures can allow for unfair allocations and unfair procedures may yield fair allocations (see Roth, 1995, for an early survey of experimental findings). So what procedural fairness grants are equal chances but not necessarily equal well-being of the participating individuals. Since we want to focus on (ii), we will mostly neglect topic (i) in the following. Fair procedures, i.e., topic (ii), have a very long tradition of discourse in legal history and its religious forerunners as well as in sports contests. In “law and economics”, one partly views legal institutions as shaped by efficiency concerns (like, for example, the “new economic approach” to competition policy). This could be due to “legal evolution” as well as to institutional design based on likely allocation outcomes. But, at least traditionally, legal norms are not justified by their likely allocation effects,1 i.e., in a consequentialistic way, but by their desirable properties, e.g. fairness. One wants to rule out arbitrary (dis)favoring by guaranteeing equal treatment of all parties involved. In constitutional law the prominent principle of “one person – one vote” is why we propagate democracy rather than objecting to possibly intransitive majority voting and the ambiguity of allocation effects resulting from majority voting. In commercial law analogous norms rule out discrimination and insider trading, impose information disclosure, etc. Compared to this long legal tradition for which we partly provide an axiomatic foundation (see also Güth,forthcoming ), experimental studies of fair procedures, topic (ii), are rather recent. Partly the experimental findings of unfair procedures
1 Allocation efficiency is almost by definition desirable but is rather unpredictable when the future is not certain and when incentive compatibility (in weakly dominant) strategies is impossible, at least for actual implementability.
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like dictatorial allocation or ultimatum bargaining reveal strong intrinsic concerns for allocational fairness (see Roth, 1995; Güth and Kocher, 2013), partly one implements fair procedures to explore, for example, • whether this crowds in monetary opportunism and • how (dis)functional such mechanisms are. Among the latter studies are Bolton et al. (2005) who focus on unbiased randomization as a fair procedure for allocating indivisible commodities and Chlaß et al. (2009) who compare game protocols differing in fairness but not in allocation effects. Of course, even when experimentally implementing fair procedures, the mentally perceived positions of the parties involved can differ dramatically. Actually, one robust experimental finding is that in spite of fair procedures experimentally induced asymmetry of interacting participants still triggers intrinsic other regarding concerns. Thus, fair procedures alone do not crowd in monetary opportunism across the board. 3. Requirements and derivation of mechanism Let i = 1, 2, . . . denote an arbitrary potential community member. Whether i will join the community aiming at collective provision of services and/or commodities, in short projects, depends endogenously on • the community formed • the projects provided by this community • the due payments of its members. For the formal definition of our requirements and the derivation of the mechanism, we introduce the following notation: ∅: the status quo with no community formed and no provision, evaluated by each i with 0 in terms of net improvement (0-payoffs) /˝ ˝ = {p1 , p2 , . . .} : the non-empty set of possible projects p ∈ ˝ with ∅ ∈ C(p) ∈ R for all p ∈ ˝ : known “cost” of project p bi (p) ∈ R : i’s monetary bid for project p ∈ ˝ bi = ((bi (p))p ∈ ˝ ) = (bi (p1 ), bi (p2 ), . . .) : i’s bid b = ((bi )i=1,2,... ) : bid vector p(b) ∈ ˝ ∪ {∅} : the collective project as selected by b ci (p(b), b) ∈ R : i’s payment when becoming a member of the community providing p(b) according to bid vector b Let us briefly comment on this very general setup of collective provision: “costs” can be negative, i.e., we allow for projects generating revenue. Furthermore, each project p ∈ ˝ may be a subset of several collective tasks what would then require to justify its “cost” C(p) via the “costs” of these tasks. Assuming that all C(p) are known avoids conditional bids for different random realizations of C(p). Similarly, bids can be negative and actually should be negative when individuals suffer rather than gain from collective provision. The rules must specify for all bid vectors b whether a project p(b) ∈ ˝ will be implemented and, if so, the payments ci (p(b), b) of all community members i or whether the status quo ∅ with 0 payoffs is maintained. Altogether this illustrates that what we want to derive is a game form and not a Bayesian game what would require commonly or privately known evaluations of projects p ∈ ˝ and, in case of private information, beliefs concerning them. We first consider the easier case of exogenously given communities N = 1, . . ., n with n≥2, i.e., of coercive membership as in most cases of regional communities. The following requirements will be illustrated by an example in Section 4 and motivated more thoroughly in Section 5: (i) The status quo ∅ is maintained if for all possible projects p ∈ ˝ the bid sum does not cover the possibly negative cost of project p, i.e., if b (p) − C(p) < 0 for all p ∈ ˝. In that case all net improvements for i = 1, 2, . . . are nil (0 payoffs). i∈N i ∗ ∗ ∗ (ii) Otherwise, ∅ is substituted and the chosen∗ project p ∗(b) ∈ ˝ with non-negative bid surplus i ∈ N bi (p (b)) − C(p (b)) maximizes the bid surplus, i.e., b (p (b)) − C(p (b))≥ i ∈ N bi (p) − C(p) for all p ∈ ˝. In case of ties one of the i∈N i maximizing projects is selected by an unbiased chance move. (iii) For all community members i ∈ N the bid payoff bi (• ) − ci (• ) is equal. ∗ c (p∗ (b), b) = C(p∗ (b)). (iv) In case of p (b) ∈ ˝ : i∈N i (iii) is satisfied in case of ∅ being maintained. If therefore p∗ (b) = / ∅ it follows from (iii) and (iv) that ci (p∗ (b), b) = Obviously ∗ ∗ ∗ b (p (b)) − C(p (b)) /n for all i = 1, . . ., n. Because of requirement (ii), no bidder can – according to his bid bi (p (b)) − i∈N i – prefer another’s net trade. Furthermore, no bidder ever has to pay more than his bid. Especially when bidding negatively, one is compensated and when doing this excessively, one can veto provision. Altogether the mechanism clearly rules out arbitrary discrimination. However, although it is overbidding proof, it invites strategic underbidding (of true evaluations). Please cite this article in press as: Güth, W., Endogenous community formation and collective provision – A procedurally fair mechanism. J. Econ. Behav. Organ. (2014), http://dx.doi.org/10.1016/j.jebo.2014.01.005
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If not all bidders i in N are needed for collective provision, it could be that several disjoint communities are formed. Here this is avoided: the non-included bidders are “outsiders” who do not engage in collective tasks themselves but only experience the effects of public provision by the endogenously formed community.2 We do not deny that “outsiders” can collectively act as well but consider the case of only one subcommunity as a natural first step in the study of endogenous community formation. Let us now adapt the four requirements in order to allow for an endogenously formed community providing possibly some project p ∈ ˝. In the following, K denotes an arbitrary non-empty subgroup of potential community members i = 1, 2, . . . and K ∗ (b) the endogenously formed community providing some project p∗ (b) ∈ ˝ as implied by the bid vector b. This obviously excludes that the group N of bidders splits up in several disjoint subgroups. All bidders, not included in the only subgroup, are outsiders who cannot engage in collective action. The adapted axioms are: (i ) The status quo ∅ is maintained with K ∗ (b) as the empty set, i.e., no community is formed with 0 payoffs for all i = 1, 2, . . ., b (p) < C(p). if for all p ∈ ˝ and all sets K the K sum of bids does not cover the costs, i.e., i∈K i (ii ) Otherwise, ∅ is substituted by the chosen project p∗ (b) ∈ ˝ with formation of community K ∗ (b); the bid surplus for this ∗ ∗ ∗ community K (b) is maximal, i.e., b (p (b)) − C(p (b))≥ i ∈ K bi (p) − C(p) for all non-empty sets K and all p ∈ ˝. In i ∈ K ∗ (b) i case of ties, one of the maximizing projects is selected by an unbiased chance move. (iii ) In case of p∗ (b) ∈ ˝ the bid payoff bi (p∗ (b)) − ci (p∗ (b), b) is equal for all i ∈ K ∗ (b). (iv ) In case of p∗ (b) ∈ ˝:
ci (p∗ (b), b) = C(p∗ (b)).
i ∈ K ∗ (b)
Let n(K ∗ (b)) denote the number of members of community K ∗ (b). From (iii ) follows for p∗ (b) ∈ ˝: bj (p∗ (b)) − cj (p∗ (b), b) =: for j ∈ K ∗ (b) and thus, due to (iv ), also b (p∗ (b)) − C(p∗ (b)) = n(K ∗ (b)), respectively j ∈ K ∗ (b) j
=
b (p∗ (b)) − C(p∗ (b)) j ∈ k∗ (b) j (≥0). n(K ∗ (b))
Inserting this above, finally implies
∗
∗
ci (p (b), b) = bi (p (b)) −
b (p∗ (b)) − C(p∗ (b)) j ∈ K ∗ (b) j n(K ∗ (b))
for all i ∈ K ∗ (b).
Thus, the four requirements (i ), (ii ), (iii ), (iv ) uniquely determine via the bid vector b: • whether or not the status quo (∅) is maintained • if not, which p∗ (b) ∈ ˝ is provided by which community K ∗ (b), • which payments ci (p∗ (b), b) are due to the community members i ∈ K ∗ (b) Due to (iii ) equal treatment is restricted to community members i ∈ K ∗ (b) what allows for non-equal bid payoffs in the sense of bi (p∗ (b)) = / bj (p∗ (b)) of two outsiders i, j ∈ / K ∗ (b) as well as for inequality of community members i and outsiders ∗ ∗ ∗ / bi (p (b)) − ci (p (b), b) for some j ∈ / K ∗ (b) and some i ∈ K ∗ (b). As a consequence envy-free net trades with j, i.e., bj (p (b)) = respect to bids are restricted to members only. Furthermore, overbidding proofness is lost when allowing for outsiders. This obviously questions basic advantages of the bidding mechanism. But in our view, this is due to the outsider problem and not to our procedural fairness approach. 4. An example For the sake of simplicity, let N = {1, 2},
˝ = {x, y} and assume commonly known evaluations v2 (x) < v2 (y) < 0 <
v1 (y) < v1 (x) and costs such that v1 (y) + v2 (y) − C(y)≥v1 (x) − C(x) > 0.
2
This is related to cartels or rings with a competitive fringe in the literature of industrial organization.
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This features bidder 2 as the outsider candidate who, however, may want to prevent project x which is worse for him. We will demonstrate that this is possible by equilibrium overbidding. For an equilibrium preventing that x is provided by {1}, it must hold that b2 (y) > 0 and (∗) b1 (y) + b2 (y) − C(y) = v1 (x) − C(x) where we assume the left-hand side to be marginally larger (to avoid a tie). Now when {1,2} provides y, bidder 2 earns
v2 (y) − b2 (y) +
v1 (x) − C(x) 2
what must be at least as good as being an outsider, confronting x provided by {1}. An equilibrium therefore requires
v2 (y) − v2 (x) +
v1 (x) − C(x) 2
≥b2 (y).
For bidder 1, in turn, provision of y by {1,2} should not be worse than v1 (x) − C(x), i.e., provision of x by {1}. The condition guaranteeing this is
v1 (y) − b1 (y)≥
v1 (x) − C(x) 2
.
Now equality (*) above allows to substitute b1 (y) by b2 (y) via b1 (y) = v1 (x) + C(y) − C(x) − b2 (y). We thus obtain a second requirement for b2 (y), namely
v1 (y) −
v1 (x) − C(x) 2
≥v1 (x) + C(y) − C(x) − b2 (y)
or 3 b2 (y)≥ [v1 (x) − C(x)] + C(y) − v1 (y). 2 Altogether one must therefore satisfy
v2 (y) − v2 (x) +
v1 (x) − C(x) 2
≥b2 (y) > max
3 2
[v1 (x) − C(x)] + C(y) − v1 (y), 0
.
This is generically possible if
v2 (y) − v2 (x) > max{v1 (x) − v1 (y) + C(y) − C(x), 0}. A generic numerical example for which this inequality holds is, for instance, given by v2 (x) = −50, v2 (y) = −10, v1 (y) = 30, v1 (x) = 50, C(y) = 6 and C(x) = 46 implying the restriction 42≥b2 (y) > 0 for 2’s bid b2 (y) according to an equilibrium implementing project y by {1,2}. The example illustrates how the mechanism can be completed numerically in order to yield a well-defined game, here one with complete information. It also demonstrates that, due to the outsider problem, the overbidding proofness of the mechanism for all encompassing communities is lost. According to one of the many equilibria, bidder 2 can prevent project x which he considers worse by strategically overbidding for project y, i.e., by b2 (y) > v2 (y). 5. The outsider problem Non-equal treatment outside the community and when comparing members and outsiders had to be expected. One can view this outsider problem as the price one has to pay for voluntary community formation. If outsiders would complain, one could argue that their too low bids are responsible for not qualifying as community members. Only community members i ∈ K ∗ (b) will be monetarily compensated when bidding negatively for p∗ (b), i.e., in case of bi (p∗ (b)) < 0, and only community members i ∈ K ∗ (b) with bi (p∗ (b)) > 0 can be asked for positive payments ci (p∗ (b), b). Since , introduced in Section 3, is non-negative, no community member i ∈ K ∗ (b) has ever to pay more than the own bid bi (p∗ (b)). Conversely, this means that by bidding sufficiently low, one can prevent p∗ (b) to be implemented and/or becoming a community member. However, an outsider j with bj (p∗ (b)) < 0 and j ∈ / K ∗ (b) is not monetarily compensated. This illustrates again that equal treatment does not apply to community outsiders. A further requirement (see Güth, 1986) of procedural fairness is that according to his bid no community member i ∈ K ∗ (b) should prefer another community member’s net trade to his own one. We mention this here only since this envyfreeness according to bids is guaranteed by the equality axiom (iii), respectively (iii ). Of course, again this does not extend to community outsiders or to no envy between outsiders and insiders. When wanting to explore the mechanism game theoretically, one has to complement it by adding
Please cite this article in press as: Güth, W., Endogenous community formation and collective provision – A procedurally fair mechanism. J. Econ. Behav. Organ. (2014), http://dx.doi.org/10.1016/j.jebo.2014.01.005
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• the true evaluations vi (p) ∈ R for all p ∈ ˝ and all potential community members i which they can misrepresent by bi (p) = / vi (p) or reveal, bi (p) = vi (p), for some or all p ∈ ˝ and, • in case of privately known true evaluations, the beliefs of others j = / i concerning vi (p), for all p ∈ ˝ and all i, j with i = / j. If vi (p) < 0 for some p ∈ ˝, individual i would suffer from public provision. Thus, our setup allows for public goods but also for collective projects harming some or more. For exogenously given all-encompassing communities, it never pays to overbid, no bidder i will prefer bi (p) > vi (p) for some p ∈ ˝ to bidding truthfully, bi (p) = vi (p), i.e., the mechanism is overbidding proof.3 However, there are strong incentives for strategic underbidding. in case of commonly true eval Actually, known b (p∗ (b)) = C(p∗ (b)) what for v (p∗ (b)) > C(p∗ (b)) uations, equilibrium bidding implies cost balancing in the sense of i i i i allows for many equilibria, based on strategic underbidding. Thus, for exogenously given all-encompassing communities, the mechanism is overbidding proof but not incentive compatible (requiring over-as well as underbidding proofness). But even overbidding proofness is lost when allowing for endogenous community formation since potential outsiders can have an incentive to overbid strategically as illustrated by the example in section 4. The mechanism as such only respects overt and interpersonally observable behavioral input, summarized by the bid vector. There is no speculation about the true and usually only privately known evaluations and the beliefs concerning them. Furthermore, there is no common knowledge assumption concerning true evaluations and the corresponding beliefs. What has to be known is the behavior, here the bid vector, and this is elicited and thus a readily available input of the mechanism. For our analysis above we have assumed known costs C(p) ∈ R for all projects p ∈ ˝. If these costs are at best stochastically predictable, for example, in the sense of C(p|z) where z denotes one of several possible random events, then one might ask b (p|z) = C(p|z) for all z and for bids bi (p|z) for all possible random events z and require cost balancing in the sense of i i implement a project p ∈ ˝ only if its bid surplus is non-negative for all z and maximal for at least one z or, when probabilities exist for all random events z, maximizing the expected bid surplus. One may object to our mechanism that it rules out provision of several projects p ∈ ˝. This is, however, no restriction since bundling several projects can be captured as a further project of set . Actually, one may view the different projects in as different subsets of a set of single projects (see Cicognani et al., 2012). One then would have to argue whether the costs of such subsets are just the sums of the costs of its individual projects or whether bundling of single projects increases or decreases the cost of the whole bundle. Here we have avoided this by focusing on alternative projects p ∈ ˝ of which at most one can be implemented. Cost balancing, as captured by (iv), respectively (iv ) is natural but not necessary at all. One can allow for subsidies to cover the cost C(p∗ (b)) as well as for taxing collective provision (see Güth et al., 2014b). One just adds a constant to the cost in the balancing requirement where the constant can be positive (taxing) or negative (subsidizing). In our analysis it has been assumed that community members will accept their due payments. For exogenously given communities the justification is that one can prevent unwelcome projects by bidding sufficiently low for them. There is some sort of veto power and unanimity principle in the background which should make it easy for all community members i = 1, 2, . . . to participate in the bidding and to submit to the rules of the mechanism. In case of endogenous community formation individual veto rights are much weaker and one may even prefer to be part of the community providing something bad to prevent an even worse project. Axioms (i ) and (ii ) can be described as efficiency conditions in view of bids: if according to bids the status quo is preferable, it should be maintained where we, however, did not allow to bid for ∅, the status quo. It is giving up the status quo what has to be justified by efficiency according to bids. Similarly, (ii ) asks for the most efficient project p ∈ ˝ according to bids when giving up the status quo. Thus, via bidding, community members determine whether ∅ is maintained and, if not, which community K ∗ (b) provides which project p∗ (b) ∈ ˝. The procedural fairness of our mechanism is due to the equality requirement (iii), respectively (iii ). It essentially rules out any arbitrary (dis)favoring of specific community members although it may treat community outsiders quite unequally. Rather than viewing this as a drawback of our mechanism, one can consider this as a reason to enter the community and enjoy its procedural fairness. But, of course, some may not be welcome since they bid negatively and thus question every community including them. If this is not sufficiently comforting, one would have to argue for compulsory membership of all potential community members i = 1, 2, . . . for which requirements (i), (ii), (iii), (iv), guarantee general procedural fairness. In our view, since both mechanisms, the one for exogenously given communities based on (i), (ii), (iii), (iv) and the one for endogenously formed communities based on (i ), (ii ), (iii ), (iv ) rely on similar procedural requirements, one can easily recognize the advantage of compulsory membership, i.e., of not allowing to opt out of the community, formed for the purpose of collective provision. 6. Conclusions What we consider are rules for endogenously determined collective provision by endogenously formed communities to select and finance collective projects. In our view, the requirements characterizing the mechanism are rather obvious and
3
Overbidding might imply a loss which would be prevented by bidding truthfully, i.e., every bid bi with overbidding is weakly dominated.
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intuitive when wanting to apply the mechanism to possibly many future situations about which hardly anything can be known when implementing the mechanism. It is in this sense that our approach can be claimed to be in line with the legal tradition (of institutional design) what has been discussed in more detail elsewhere (Güth, forthcoming). The factual implementability has so far been checked only experimentally but under varying conditions for: • projects favoring each and everybody competing with more efficient projects harming some, vi (p) < 0, and favoring others, vj (p) > 0 • projects generating revenues, C(p) < 0, competing with more efficient but costly ones, C(p) > 0 (Güth et al., 2014a) • commonly known evaluations and no information at all concerning the true evaluations by others (Cicognani et al., 2012). Altogether the mechanism is functioning surprisingly well, at least in the lab environment.4 There is reliable collective provision and mostly of the truly most efficient project. One bias, according to the preliminary evidence so far, is that participants implement projects with negative costs, even when they are not the most efficient ones. How does optimal, e.g. welfaristic mechanism design differ from our procedural fairness approach? Whereas we justify our mechanism by its procedural properties, i.e., by arguing that what we want is to guarantee these properties when acting collectively, optimal mechanisms are justified by their allocative implications (e.g. Myerson, 1979). The idea is to induce truth telling in bidding what then allows to derive the allocation effects and to evaluate them according to these true evaluations rather than according to bids as in our procedural fairness approach. The method is either dominance solvability, i.e., bidding truthfully is the only weakly undominated behavior, what does not require any kind of common knowledge since each bidder has a best choice irrespective of the others’ behavior. This relies on similarly weak assumptions as our approach but is, unfortunately, hardly ever applicable. Whereas for auctions the second-price rule is incentive compatible, no such price rule exists when the bidders collectively own the auctioned commodity and share the price (Güth, 1986) Additionally,the incentive campatible second-price rule invites ring formation. Thus incentive compatibility is more often than not either undesirable or impossible. The other method is the revelation principle (e.g. Myerson, 1979) assuming common knowledge as required by game theoretic equilibrium analysis. One derives an allocation equivalent revelation mechanism (for which general truthful bidding is an equilibrium) for each equilibrium of each well defined (Bayesian) game. This is suitable for exploring allocational possibilities via the limited class of revelation mechanisms but not at all for mechanism design when confronting an uncertain future with all sorts of situations, mostly ill-defined in the game theoretic sense. References Bolton, G.E., Brandts, J., Ockenfels, A., 2005. Fair procedures: evidence from games involving lotteries. The Economics Journal 115, 1054–1076. Chlaß, N., Güth, W., Miettinen, T., 2009. Beyond Procedural Equity and Reciprocity. Jena Economic Research Paper Series #2009-069. Cicognani, S., D’Ambrosio, A., Güth, W., Pfuderer, S., Ploner, M., 2012. Community Projects: An Experimental Analysis of a Fair Implementation Process. Jena Economic Research Paper Series #2012-015. Güth, W., 1986. Auctions, public tenders, and fair division games: an axiomatic approach. Mathematical Social Sciences 11, 283–294. Güth, W., 2011. Rules (of bidding) to generate equal stated profits: an axiomatic approach. Journal of Institutional and Theoretical Economics 167 (4), 608–612. Güth, W., 2014. In: Parisi, F. (Ed.), Mechanism Design and the Law. Oxford Handbook of Law and Economics. Oxford University Press (forthcoming). Güth, W., Kliemt, H., 2013. Fairness that money can buy: procedural egalitarianism in practice. Rationality, Markets and Morals 4, 20–30. Güth, W., Kocher, M., 2013. More than thirty years of ultimatum bargaining experiments: Motives, variations, and a survey of the recent literature. Jena Economic Research Paper Series #2013-035. Güth, W., Kliemt, H., Koukoumelis, A., Levati, V., Ploner, M., 2014a. Procedurally fair collective provision: its requirements and experimental functionality. In: Stadler, M., et al. (Eds.), Proceedings Volume Ottobeuren. (forthcoming). Güth, W., Levati, V., Montinari, N., 2014b. Ranking alternatives by a fair bidding rule: a theoretical and experimental analysis. European Journal of Political Economy (forthcoming). Myerson, R.B., 1979. Incentive compatibility and the bargaining problem. Econometrica 47 (1), 61–73. Roth, A., 1995. Bargaining experiments. In: Kagel, J., Roth, A. (Eds.), Handbook of Experimental Economics. Princeton University Press, Princeton.
4 A new experiment of Güth, Krügel, Levati and Ploner with focus on endogenous community formation has already been run in the lab. Its results are, however, not yet analyzed.
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Endogenous community formation and collective provision – A procedurally fair mechanism夽 Werner Güth ∗ Max Planck Institute of Economics, Jena, Germany
a r t i c l e
i n f o
Article history: Received 11 April 2013 Received in revised form 7 November 2013 Accepted 14 January 2014 Available online xxx
Keywords: Procedural fairness Mechanism design Equality axiom Public provision Collective action
a b s t r a c t A group of actors, individuals or firms, can engage in collectively providing projects which may be costly or generating revenues and which may benefit some and harm others. Based on requirements of procedural fairness, we derive a bidding mechanism determining endogenously who participates in collective provision, which projects are implemented, and the positive or negative payments due to the members as well as outsiders. The mechanism allows only for one community with more or less outsiders but not forming multiple communities. We justify procedural fairness but acknowledge that the outsider problem questions some of its desirable properties. Furthermore, we compare procedurally fair with optimal, e.g., welfaristic mechanism design (e.g. Myerson, 1979). © 2014 Elsevier B.V. All rights reserved.
JEL classification: D44 D46 D61 D62 D63 D71 D72 D73 D74
1. Introduction Via our residence, we usually become members of regional communities like municipalities and states. We propose a mechanism allowing community members to influence what is collectively provided in ways similar to private procurement. For communities with exogenously given membership Güth and Kliemt (2013) have suggested how to regulate public provision in procedurally fair ways. Their proposed mechanism has also been studied experimentally (Güth et al., 2014a) what will be briefly reported. Here we want to demonstrate how to extend this approach by allowing for endogenous community formation to determine what is collectively provided as well as its financing.
夽 The author gratefully acknowledges the constructive advice and encouragement of two anonymous referees how to revise the manuscript. ∗ Tel.: +49 3641 686 620; fax: +49 3641 686 623. E-mail address: [email protected] 0167-2681/$ – see front matter © 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jebo.2014.01.005
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Examples are sports clubs, private organizations like charities, political parties, non-profit organizations etc. for whom procedural fairness in regulating their activities is crucial – more crucial than optimality, e.g. allocative efficiency, dominating in welfaristic mechanism design, based on dominance solvability or the revelation principle. Whereas “optimal mechanism design” tries to achieve the best allocation results via eliciting private evaluations for each and every specific situation, our procedural fairness approach is generally applicable and much more in line with the legal tradition of justifying institutions by their properties rather than by their allocation results in an unforeseeable future. What procedural fairness rules out is arbitrary favoring of some of the parties involved. More specifically, this must be guaranteed with respect to all objectively verifiable and interpersonally comparable characteristics. A possible requirement would be, for example, envy-free net trades according to bids. The essential requirement of procedural fairness is an equality axiom (see Güth, 2011) which implies such envyfreeness. It does not mean to make unequals equal but rather postulates equal treatment when possibly unequal community members in overt behavior choose equally like when counting votes based on the “one person – one vote” principle. Imposing equal treatment based on interpersonally and objectively observable behavior renders our approach applicable across the board. We can allow for private information and question common knowledge and incentive compatibility constraints. In game theoretic terminology, what we derive is just a game form without appealing to commonly or privately known evaluations and beliefs concerning them. As a consequence our approach differs fundamentally from defining procedural fairness by symmetry of player roles in (Bayesian) games. Beside its procedural fairness its advantage is to be legally implementable. Obvious real-world examples of endogenously formed communities are private clubs whose activities also affect outsiders. Of course, also local communities are “formed”, e.g., due to migration, but their outsiders do not participate in bidding. When implementing the mechanism experimentally, private evaluations have to be added. But no commonly known beliefs concerning them as required by game theoretic equilibrium analysis, have to be experimentally induced or controlled. Compared to all-encompassing communities, endogenously formed communities like private clubs allow for outsiders who are exempted from procedural fairness enjoyed by community members. Although all individuals participate in the endogenous determination of the community, some of them might be excluded. It will be shown that this outsider problem questions some desirable properties which procedural fairness implies for all-encompassing communities. But, in our view, this is due to endogenous community formation and its outsider problem and not a drawback of the procedural fairness approach as such. In Section 2, we discuss the related literature. Section 3 derives the mechanism which is illustrated by the example in Section 4. How properties are questioned by outsiders is discussed in Section 5. Section 6 concludes by relating our approach to optimal, e.g. welfaristic mechanism design. 2. On the related literature Quite generally, one can distinguish between (i) fairness of allocations and (ii) fairness of procedures. The former topic (i) is extensively discussed by economists who partly argue that low and possibly unfair wages go along with larger profits, more investments and employment and partly propagate high wages which could crowd in intrinsic efficiency and reciprocity concerns of employees. More recently, experimentalists use distribution games featuring tradeoffs between fairness (more equal payoffs) and efficiency (measured by the payoff sum of all parties). Fairness of procedures, (ii), is neither necessary nor sufficient for (i): fair procedures can allow for unfair allocations and unfair procedures may yield fair allocations (see Roth, 1995, for an early survey of experimental findings). So what procedural fairness grants are equal chances but not necessarily equal well-being of the participating individuals. Since we want to focus on (ii), we will mostly neglect topic (i) in the following. Fair procedures, i.e., topic (ii), have a very long tradition of discourse in legal history and its religious forerunners as well as in sports contests. In “law and economics”, one partly views legal institutions as shaped by efficiency concerns (like, for example, the “new economic approach” to competition policy). This could be due to “legal evolution” as well as to institutional design based on likely allocation outcomes. But, at least traditionally, legal norms are not justified by their likely allocation effects,1 i.e., in a consequentialistic way, but by their desirable properties, e.g. fairness. One wants to rule out arbitrary (dis)favoring by guaranteeing equal treatment of all parties involved. In constitutional law the prominent principle of “one person – one vote” is why we propagate democracy rather than objecting to possibly intransitive majority voting and the ambiguity of allocation effects resulting from majority voting. In commercial law analogous norms rule out discrimination and insider trading, impose information disclosure, etc. Compared to this long legal tradition for which we partly provide an axiomatic foundation (see also Güth,forthcoming ), experimental studies of fair procedures, topic (ii), are rather recent. Partly the experimental findings of unfair procedures
1 Allocation efficiency is almost by definition desirable but is rather unpredictable when the future is not certain and when incentive compatibility (in weakly dominant) strategies is impossible, at least for actual implementability.
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like dictatorial allocation or ultimatum bargaining reveal strong intrinsic concerns for allocational fairness (see Roth, 1995; Güth and Kocher, 2013), partly one implements fair procedures to explore, for example, • whether this crowds in monetary opportunism and • how (dis)functional such mechanisms are. Among the latter studies are Bolton et al. (2005) who focus on unbiased randomization as a fair procedure for allocating indivisible commodities and Chlaß et al. (2009) who compare game protocols differing in fairness but not in allocation effects. Of course, even when experimentally implementing fair procedures, the mentally perceived positions of the parties involved can differ dramatically. Actually, one robust experimental finding is that in spite of fair procedures experimentally induced asymmetry of interacting participants still triggers intrinsic other regarding concerns. Thus, fair procedures alone do not crowd in monetary opportunism across the board. 3. Requirements and derivation of mechanism Let i = 1, 2, . . . denote an arbitrary potential community member. Whether i will join the community aiming at collective provision of services and/or commodities, in short projects, depends endogenously on • the community formed • the projects provided by this community • the due payments of its members. For the formal definition of our requirements and the derivation of the mechanism, we introduce the following notation: ∅: the status quo with no community formed and no provision, evaluated by each i with 0 in terms of net improvement (0-payoffs) /˝ ˝ = {p1 , p2 , . . .} : the non-empty set of possible projects p ∈ ˝ with ∅ ∈ C(p) ∈ R for all p ∈ ˝ : known “cost” of project p bi (p) ∈ R : i’s monetary bid for project p ∈ ˝ bi = ((bi (p))p ∈ ˝ ) = (bi (p1 ), bi (p2 ), . . .) : i’s bid b = ((bi )i=1,2,... ) : bid vector p(b) ∈ ˝ ∪ {∅} : the collective project as selected by b ci (p(b), b) ∈ R : i’s payment when becoming a member of the community providing p(b) according to bid vector b Let us briefly comment on this very general setup of collective provision: “costs” can be negative, i.e., we allow for projects generating revenue. Furthermore, each project p ∈ ˝ may be a subset of several collective tasks what would then require to justify its “cost” C(p) via the “costs” of these tasks. Assuming that all C(p) are known avoids conditional bids for different random realizations of C(p). Similarly, bids can be negative and actually should be negative when individuals suffer rather than gain from collective provision. The rules must specify for all bid vectors b whether a project p(b) ∈ ˝ will be implemented and, if so, the payments ci (p(b), b) of all community members i or whether the status quo ∅ with 0 payoffs is maintained. Altogether this illustrates that what we want to derive is a game form and not a Bayesian game what would require commonly or privately known evaluations of projects p ∈ ˝ and, in case of private information, beliefs concerning them. We first consider the easier case of exogenously given communities N = 1, . . ., n with n≥2, i.e., of coercive membership as in most cases of regional communities. The following requirements will be illustrated by an example in Section 4 and motivated more thoroughly in Section 5: (i) The status quo ∅ is maintained if for all possible projects p ∈ ˝ the bid sum does not cover the possibly negative cost of project p, i.e., if b (p) − C(p) < 0 for all p ∈ ˝. In that case all net improvements for i = 1, 2, . . . are nil (0 payoffs). i∈N i ∗ ∗ ∗ (ii) Otherwise, ∅ is substituted and the chosen∗ project p ∗(b) ∈ ˝ with non-negative bid surplus i ∈ N bi (p (b)) − C(p (b)) maximizes the bid surplus, i.e., b (p (b)) − C(p (b))≥ i ∈ N bi (p) − C(p) for all p ∈ ˝. In case of ties one of the i∈N i maximizing projects is selected by an unbiased chance move. (iii) For all community members i ∈ N the bid payoff bi (• ) − ci (• ) is equal. ∗ c (p∗ (b), b) = C(p∗ (b)). (iv) In case of p (b) ∈ ˝ : i∈N i (iii) is satisfied in case of ∅ being maintained. If therefore p∗ (b) = / ∅ it follows from (iii) and (iv) that ci (p∗ (b), b) = Obviously ∗ ∗ ∗ b (p (b)) − C(p (b)) /n for all i = 1, . . ., n. Because of requirement (ii), no bidder can – according to his bid bi (p (b)) − i∈N i – prefer another’s net trade. Furthermore, no bidder ever has to pay more than his bid. Especially when bidding negatively, one is compensated and when doing this excessively, one can veto provision. Altogether the mechanism clearly rules out arbitrary discrimination. However, although it is overbidding proof, it invites strategic underbidding (of true evaluations). Please cite this article in press as: Güth, W., Endogenous community formation and collective provision – A procedurally fair mechanism. J. Econ. Behav. Organ. (2014), http://dx.doi.org/10.1016/j.jebo.2014.01.005
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If not all bidders i in N are needed for collective provision, it could be that several disjoint communities are formed. Here this is avoided: the non-included bidders are “outsiders” who do not engage in collective tasks themselves but only experience the effects of public provision by the endogenously formed community.2 We do not deny that “outsiders” can collectively act as well but consider the case of only one subcommunity as a natural first step in the study of endogenous community formation. Let us now adapt the four requirements in order to allow for an endogenously formed community providing possibly some project p ∈ ˝. In the following, K denotes an arbitrary non-empty subgroup of potential community members i = 1, 2, . . . and K ∗ (b) the endogenously formed community providing some project p∗ (b) ∈ ˝ as implied by the bid vector b. This obviously excludes that the group N of bidders splits up in several disjoint subgroups. All bidders, not included in the only subgroup, are outsiders who cannot engage in collective action. The adapted axioms are: (i ) The status quo ∅ is maintained with K ∗ (b) as the empty set, i.e., no community is formed with 0 payoffs for all i = 1, 2, . . ., b (p) < C(p). if for all p ∈ ˝ and all sets K the K sum of bids does not cover the costs, i.e., i∈K i (ii ) Otherwise, ∅ is substituted by the chosen project p∗ (b) ∈ ˝ with formation of community K ∗ (b); the bid surplus for this ∗ ∗ ∗ community K (b) is maximal, i.e., b (p (b)) − C(p (b))≥ i ∈ K bi (p) − C(p) for all non-empty sets K and all p ∈ ˝. In i ∈ K ∗ (b) i case of ties, one of the maximizing projects is selected by an unbiased chance move. (iii ) In case of p∗ (b) ∈ ˝ the bid payoff bi (p∗ (b)) − ci (p∗ (b), b) is equal for all i ∈ K ∗ (b). (iv ) In case of p∗ (b) ∈ ˝:
ci (p∗ (b), b) = C(p∗ (b)).
i ∈ K ∗ (b)
Let n(K ∗ (b)) denote the number of members of community K ∗ (b). From (iii ) follows for p∗ (b) ∈ ˝: bj (p∗ (b)) − cj (p∗ (b), b) =: for j ∈ K ∗ (b) and thus, due to (iv ), also b (p∗ (b)) − C(p∗ (b)) = n(K ∗ (b)), respectively j ∈ K ∗ (b) j
=
b (p∗ (b)) − C(p∗ (b)) j ∈ k∗ (b) j (≥0). n(K ∗ (b))
Inserting this above, finally implies
∗
∗
ci (p (b), b) = bi (p (b)) −
b (p∗ (b)) − C(p∗ (b)) j ∈ K ∗ (b) j n(K ∗ (b))
for all i ∈ K ∗ (b).
Thus, the four requirements (i ), (ii ), (iii ), (iv ) uniquely determine via the bid vector b: • whether or not the status quo (∅) is maintained • if not, which p∗ (b) ∈ ˝ is provided by which community K ∗ (b), • which payments ci (p∗ (b), b) are due to the community members i ∈ K ∗ (b) Due to (iii ) equal treatment is restricted to community members i ∈ K ∗ (b) what allows for non-equal bid payoffs in the sense of bi (p∗ (b)) = / bj (p∗ (b)) of two outsiders i, j ∈ / K ∗ (b) as well as for inequality of community members i and outsiders ∗ ∗ ∗ / bi (p (b)) − ci (p (b), b) for some j ∈ / K ∗ (b) and some i ∈ K ∗ (b). As a consequence envy-free net trades with j, i.e., bj (p (b)) = respect to bids are restricted to members only. Furthermore, overbidding proofness is lost when allowing for outsiders. This obviously questions basic advantages of the bidding mechanism. But in our view, this is due to the outsider problem and not to our procedural fairness approach. 4. An example For the sake of simplicity, let N = {1, 2},
˝ = {x, y} and assume commonly known evaluations v2 (x) < v2 (y) < 0 <
v1 (y) < v1 (x) and costs such that v1 (y) + v2 (y) − C(y)≥v1 (x) − C(x) > 0.
2
This is related to cartels or rings with a competitive fringe in the literature of industrial organization.
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This features bidder 2 as the outsider candidate who, however, may want to prevent project x which is worse for him. We will demonstrate that this is possible by equilibrium overbidding. For an equilibrium preventing that x is provided by {1}, it must hold that b2 (y) > 0 and (∗) b1 (y) + b2 (y) − C(y) = v1 (x) − C(x) where we assume the left-hand side to be marginally larger (to avoid a tie). Now when {1,2} provides y, bidder 2 earns
v2 (y) − b2 (y) +
v1 (x) − C(x) 2
what must be at least as good as being an outsider, confronting x provided by {1}. An equilibrium therefore requires
v2 (y) − v2 (x) +
v1 (x) − C(x) 2
≥b2 (y).
For bidder 1, in turn, provision of y by {1,2} should not be worse than v1 (x) − C(x), i.e., provision of x by {1}. The condition guaranteeing this is
v1 (y) − b1 (y)≥
v1 (x) − C(x) 2
.
Now equality (*) above allows to substitute b1 (y) by b2 (y) via b1 (y) = v1 (x) + C(y) − C(x) − b2 (y). We thus obtain a second requirement for b2 (y), namely
v1 (y) −
v1 (x) − C(x) 2
≥v1 (x) + C(y) − C(x) − b2 (y)
or 3 b2 (y)≥ [v1 (x) − C(x)] + C(y) − v1 (y). 2 Altogether one must therefore satisfy
v2 (y) − v2 (x) +
v1 (x) − C(x) 2
≥b2 (y) > max
3 2
[v1 (x) − C(x)] + C(y) − v1 (y), 0
.
This is generically possible if
v2 (y) − v2 (x) > max{v1 (x) − v1 (y) + C(y) − C(x), 0}. A generic numerical example for which this inequality holds is, for instance, given by v2 (x) = −50, v2 (y) = −10, v1 (y) = 30, v1 (x) = 50, C(y) = 6 and C(x) = 46 implying the restriction 42≥b2 (y) > 0 for 2’s bid b2 (y) according to an equilibrium implementing project y by {1,2}. The example illustrates how the mechanism can be completed numerically in order to yield a well-defined game, here one with complete information. It also demonstrates that, due to the outsider problem, the overbidding proofness of the mechanism for all encompassing communities is lost. According to one of the many equilibria, bidder 2 can prevent project x which he considers worse by strategically overbidding for project y, i.e., by b2 (y) > v2 (y). 5. The outsider problem Non-equal treatment outside the community and when comparing members and outsiders had to be expected. One can view this outsider problem as the price one has to pay for voluntary community formation. If outsiders would complain, one could argue that their too low bids are responsible for not qualifying as community members. Only community members i ∈ K ∗ (b) will be monetarily compensated when bidding negatively for p∗ (b), i.e., in case of bi (p∗ (b)) < 0, and only community members i ∈ K ∗ (b) with bi (p∗ (b)) > 0 can be asked for positive payments ci (p∗ (b), b). Since , introduced in Section 3, is non-negative, no community member i ∈ K ∗ (b) has ever to pay more than the own bid bi (p∗ (b)). Conversely, this means that by bidding sufficiently low, one can prevent p∗ (b) to be implemented and/or becoming a community member. However, an outsider j with bj (p∗ (b)) < 0 and j ∈ / K ∗ (b) is not monetarily compensated. This illustrates again that equal treatment does not apply to community outsiders. A further requirement (see Güth, 1986) of procedural fairness is that according to his bid no community member i ∈ K ∗ (b) should prefer another community member’s net trade to his own one. We mention this here only since this envyfreeness according to bids is guaranteed by the equality axiom (iii), respectively (iii ). Of course, again this does not extend to community outsiders or to no envy between outsiders and insiders. When wanting to explore the mechanism game theoretically, one has to complement it by adding
Please cite this article in press as: Güth, W., Endogenous community formation and collective provision – A procedurally fair mechanism. J. Econ. Behav. Organ. (2014), http://dx.doi.org/10.1016/j.jebo.2014.01.005
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• the true evaluations vi (p) ∈ R for all p ∈ ˝ and all potential community members i which they can misrepresent by bi (p) = / vi (p) or reveal, bi (p) = vi (p), for some or all p ∈ ˝ and, • in case of privately known true evaluations, the beliefs of others j = / i concerning vi (p), for all p ∈ ˝ and all i, j with i = / j. If vi (p) < 0 for some p ∈ ˝, individual i would suffer from public provision. Thus, our setup allows for public goods but also for collective projects harming some or more. For exogenously given all-encompassing communities, it never pays to overbid, no bidder i will prefer bi (p) > vi (p) for some p ∈ ˝ to bidding truthfully, bi (p) = vi (p), i.e., the mechanism is overbidding proof.3 However, there are strong incentives for strategic underbidding. in case of commonly true eval Actually, known b (p∗ (b)) = C(p∗ (b)) what for v (p∗ (b)) > C(p∗ (b)) uations, equilibrium bidding implies cost balancing in the sense of i i i i allows for many equilibria, based on strategic underbidding. Thus, for exogenously given all-encompassing communities, the mechanism is overbidding proof but not incentive compatible (requiring over-as well as underbidding proofness). But even overbidding proofness is lost when allowing for endogenous community formation since potential outsiders can have an incentive to overbid strategically as illustrated by the example in section 4. The mechanism as such only respects overt and interpersonally observable behavioral input, summarized by the bid vector. There is no speculation about the true and usually only privately known evaluations and the beliefs concerning them. Furthermore, there is no common knowledge assumption concerning true evaluations and the corresponding beliefs. What has to be known is the behavior, here the bid vector, and this is elicited and thus a readily available input of the mechanism. For our analysis above we have assumed known costs C(p) ∈ R for all projects p ∈ ˝. If these costs are at best stochastically predictable, for example, in the sense of C(p|z) where z denotes one of several possible random events, then one might ask b (p|z) = C(p|z) for all z and for bids bi (p|z) for all possible random events z and require cost balancing in the sense of i i implement a project p ∈ ˝ only if its bid surplus is non-negative for all z and maximal for at least one z or, when probabilities exist for all random events z, maximizing the expected bid surplus. One may object to our mechanism that it rules out provision of several projects p ∈ ˝. This is, however, no restriction since bundling several projects can be captured as a further project of set . Actually, one may view the different projects in as different subsets of a set of single projects (see Cicognani et al., 2012). One then would have to argue whether the costs of such subsets are just the sums of the costs of its individual projects or whether bundling of single projects increases or decreases the cost of the whole bundle. Here we have avoided this by focusing on alternative projects p ∈ ˝ of which at most one can be implemented. Cost balancing, as captured by (iv), respectively (iv ) is natural but not necessary at all. One can allow for subsidies to cover the cost C(p∗ (b)) as well as for taxing collective provision (see Güth et al., 2014b). One just adds a constant to the cost in the balancing requirement where the constant can be positive (taxing) or negative (subsidizing). In our analysis it has been assumed that community members will accept their due payments. For exogenously given communities the justification is that one can prevent unwelcome projects by bidding sufficiently low for them. There is some sort of veto power and unanimity principle in the background which should make it easy for all community members i = 1, 2, . . . to participate in the bidding and to submit to the rules of the mechanism. In case of endogenous community formation individual veto rights are much weaker and one may even prefer to be part of the community providing something bad to prevent an even worse project. Axioms (i ) and (ii ) can be described as efficiency conditions in view of bids: if according to bids the status quo is preferable, it should be maintained where we, however, did not allow to bid for ∅, the status quo. It is giving up the status quo what has to be justified by efficiency according to bids. Similarly, (ii ) asks for the most efficient project p ∈ ˝ according to bids when giving up the status quo. Thus, via bidding, community members determine whether ∅ is maintained and, if not, which community K ∗ (b) provides which project p∗ (b) ∈ ˝. The procedural fairness of our mechanism is due to the equality requirement (iii), respectively (iii ). It essentially rules out any arbitrary (dis)favoring of specific community members although it may treat community outsiders quite unequally. Rather than viewing this as a drawback of our mechanism, one can consider this as a reason to enter the community and enjoy its procedural fairness. But, of course, some may not be welcome since they bid negatively and thus question every community including them. If this is not sufficiently comforting, one would have to argue for compulsory membership of all potential community members i = 1, 2, . . . for which requirements (i), (ii), (iii), (iv), guarantee general procedural fairness. In our view, since both mechanisms, the one for exogenously given communities based on (i), (ii), (iii), (iv) and the one for endogenously formed communities based on (i ), (ii ), (iii ), (iv ) rely on similar procedural requirements, one can easily recognize the advantage of compulsory membership, i.e., of not allowing to opt out of the community, formed for the purpose of collective provision. 6. Conclusions What we consider are rules for endogenously determined collective provision by endogenously formed communities to select and finance collective projects. In our view, the requirements characterizing the mechanism are rather obvious and
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Overbidding might imply a loss which would be prevented by bidding truthfully, i.e., every bid bi with overbidding is weakly dominated.
Please cite this article in press as: Güth, W., Endogenous community formation and collective provision – A procedurally fair mechanism. J. Econ. Behav. Organ. (2014), http://dx.doi.org/10.1016/j.jebo.2014.01.005
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intuitive when wanting to apply the mechanism to possibly many future situations about which hardly anything can be known when implementing the mechanism. It is in this sense that our approach can be claimed to be in line with the legal tradition (of institutional design) what has been discussed in more detail elsewhere (Güth, forthcoming). The factual implementability has so far been checked only experimentally but under varying conditions for: • projects favoring each and everybody competing with more efficient projects harming some, vi (p) < 0, and favoring others, vj (p) > 0 • projects generating revenues, C(p) < 0, competing with more efficient but costly ones, C(p) > 0 (Güth et al., 2014a) • commonly known evaluations and no information at all concerning the true evaluations by others (Cicognani et al., 2012). Altogether the mechanism is functioning surprisingly well, at least in the lab environment.4 There is reliable collective provision and mostly of the truly most efficient project. One bias, according to the preliminary evidence so far, is that participants implement projects with negative costs, even when they are not the most efficient ones. How does optimal, e.g. welfaristic mechanism design differ from our procedural fairness approach? Whereas we justify our mechanism by its procedural properties, i.e., by arguing that what we want is to guarantee these properties when acting collectively, optimal mechanisms are justified by their allocative implications (e.g. Myerson, 1979). The idea is to induce truth telling in bidding what then allows to derive the allocation effects and to evaluate them according to these true evaluations rather than according to bids as in our procedural fairness approach. The method is either dominance solvability, i.e., bidding truthfully is the only weakly undominated behavior, what does not require any kind of common knowledge since each bidder has a best choice irrespective of the others’ behavior. This relies on similarly weak assumptions as our approach but is, unfortunately, hardly ever applicable. Whereas for auctions the second-price rule is incentive compatible, no such price rule exists when the bidders collectively own the auctioned commodity and share the price (Güth, 1986) Additionally,the incentive campatible second-price rule invites ring formation. Thus incentive compatibility is more often than not either undesirable or impossible. The other method is the revelation principle (e.g. Myerson, 1979) assuming common knowledge as required by game theoretic equilibrium analysis. One derives an allocation equivalent revelation mechanism (for which general truthful bidding is an equilibrium) for each equilibrium of each well defined (Bayesian) game. This is suitable for exploring allocational possibilities via the limited class of revelation mechanisms but not at all for mechanism design when confronting an uncertain future with all sorts of situations, mostly ill-defined in the game theoretic sense. References Bolton, G.E., Brandts, J., Ockenfels, A., 2005. Fair procedures: evidence from games involving lotteries. The Economics Journal 115, 1054–1076. Chlaß, N., Güth, W., Miettinen, T., 2009. Beyond Procedural Equity and Reciprocity. Jena Economic Research Paper Series #2009-069. Cicognani, S., D’Ambrosio, A., Güth, W., Pfuderer, S., Ploner, M., 2012. Community Projects: An Experimental Analysis of a Fair Implementation Process. Jena Economic Research Paper Series #2012-015. Güth, W., 1986. Auctions, public tenders, and fair division games: an axiomatic approach. Mathematical Social Sciences 11, 283–294. Güth, W., 2011. Rules (of bidding) to generate equal stated profits: an axiomatic approach. Journal of Institutional and Theoretical Economics 167 (4), 608–612. Güth, W., 2014. In: Parisi, F. (Ed.), Mechanism Design and the Law. Oxford Handbook of Law and Economics. Oxford University Press (forthcoming). Güth, W., Kliemt, H., 2013. Fairness that money can buy: procedural egalitarianism in practice. Rationality, Markets and Morals 4, 20–30. Güth, W., Kocher, M., 2013. More than thirty years of ultimatum bargaining experiments: Motives, variations, and a survey of the recent literature. Jena Economic Research Paper Series #2013-035. Güth, W., Kliemt, H., Koukoumelis, A., Levati, V., Ploner, M., 2014a. Procedurally fair collective provision: its requirements and experimental functionality. In: Stadler, M., et al. (Eds.), Proceedings Volume Ottobeuren. (forthcoming). Güth, W., Levati, V., Montinari, N., 2014b. Ranking alternatives by a fair bidding rule: a theoretical and experimental analysis. European Journal of Political Economy (forthcoming). Myerson, R.B., 1979. Incentive compatibility and the bargaining problem. Econometrica 47 (1), 61–73. Roth, A., 1995. Bargaining experiments. In: Kagel, J., Roth, A. (Eds.), Handbook of Experimental Economics. Princeton University Press, Princeton.
4 A new experiment of Güth, Krügel, Levati and Ploner with focus on endogenous community formation has already been run in the lab. Its results are, however, not yet analyzed.
Please cite this article in press as: Güth, W., Endogenous community formation and collective provision – A procedurally fair mechanism. J. Econ. Behav. Organ. (2014), http://dx.doi.org/10.1016/j.jebo.2014.01.005