Probabilistic allocation rules and single-dipped preferences

We consider the problem of allocating an infinitely divisible endowment among a group of agents with single-dipped preferences. A probabilistic allocation rule assigns a probability distribution over the set of possible allocations to every preference profile. We discuss characterizations of the classes of Pareto-optimal and strategy-proof probabilistic rules which satisfy in addition replacement-domination or no-envy. Interestingly, these results also apply to problems of allocating finitely many identical indivisible objects – to probabilistic and to deterministic allocation. Received: 23 November 1998/Accepted: 20 October 2000     

On the equal division core

The Equal Division Core (EDC) of a transferable utility cooperative game (TU game) is the set of efficient pay-off vectors for the grand coalition which are not blocked by the equal division allocation for any sub-coalition. Our objective is to provide an axiomatic characterization of the EDC as a solution of TU games.This is revised version of a part of Chapt. 3 of my Ph.D. dissertation. Beginning with suggesting the problem, my supervisor Bhaskar Dutta extended his unstinting help in every step of this pursuit without which this work could not have been possible. I have also much benefitted from the comments and suggestions from the responsible editor, two anonymous referees, Hervé Moulin and seminar participants at Bilkent and Bonn Universities (especially from the detailed comments of Reinhard Selten). Of course, the shortcomings remaining are mine. Somdeb Lahiri, Anjan Mukherji and T. Yamato have been kind enough to make certain literature accessible to me.Research fellowships from the Indian Statistical Institute and CNRS, France and hospitality at GEMMA, Universite de Caen are gratefully acknowledged.31 March 2000     

Fair Groves mechanisms

We study allocation problems in which a costly task is to be assigned and money transfers are used to achieve fairness among agents. We consider a series of fairness notions (k-fairness for where n is the number of agents) of decreasing restrictiveness that are based on Rawls’ maximin equity criterion and impose welfare lower bounds. These fairness notions were introduced by Porter et al. (J Econ Theory 118:209–228, 2004) who also introduced two classes of Groves mechanisms that are 1-fair and 3-fair, respectively, and generate deficits that are bounded above. We show that these classes are the largest such classes of Groves mechanisms. We generalize these mechanisms for each and show that the corresponding mechanisms generate the smallest deficit for each economy among all k-fair Groves mechanisms. The first draft of this paper was written while we were Ph.D. students at the University of Rochester. We are grateful to William Thomson for his guidance and advice. We also thank two referees and the associate editor for their comments.     

ENDOWMENTS,PERCEIVED SIMILARITY,AND DICTATOR GIVING

A common assumption of money is that it is fungible. An implication of this assumption is that the source of money does not affect economic decision making. We find evidence contradicting this fungibility assumption. Specifically, we explore how the perception of an endowment source influences amounts sent in a dictator game. We find perceived similarity to the endowment provider to be negatively correlated with dictator offers. Dictators who consider themselves relatively more similar to their endowment provider send significantly smaller amounts to their partners. Our results demonstrate that economic decision making can be influenced by the provider of income shocks. (JEL C78, C91, C99, D31, D64, D74)     

New variable-population paradoxes for resource allocation

We identify previously unnoticed ways in which agents can strategically distort allocation rules, by affecting the set of “active” agents. (i) An agent withdraws with his endowment. (ii) He gives control of his endowment to someone else and withdraws. (iii) He invites someone in and let him use some of his endowment. (iv) He pre-delivers to some other agent the net trade that the rule would assign to that second agent if that second agent had participated. In (i) and (ii), he and his co-conspirator may end up controlling resources that allow them to reach higher welfare levels than they otherwise would. In (iii) and (iv), he may end up with a bundle that he prefers to the one he would have been assigned had he not engaged in the manipulation. We show that (i) the Walrasian rule is not “withdrawing-proof”, nor “endowments-merging-proof, nor “endowments-splitting-proof”, but that it is “pre-delivery-proof”, and that (ii) canonical selections from the egalitarian-equivalence-in-trades solutions satisfy none of the properties.     

INVESTMENT CHOICE ARCHITECTURE IN TRUST GAMES: WHEN “ALL‐IN” IS NOT ENOUGH

While many economic interactions feature “All‐or‐Nothing” options nudging investors towards going “all‐in,” such designs may unintentionally affect reciprocity. We manipulate the investor's action space in two versions of the “trust game.” In one version investors can invest either “all” their endowment or “nothing.” In the other version, they can invest any amount of the endowment. Consistent with our intentions‐based model, we show that “all‐or‐nothing” designs coax more investment but limit investors' demonstrability of intended trust. As a result, “all‐in” investors are less generously reciprocated than when they can invest any amount, where full investments are a clearer signal of trustworthiness. (JEL C72, C90, C91, D63, D64, L51)     

On monotonicity in economies with indivisible goods

We consider the problem of fair allocation in economies with indivisible objects that may or may not be desirable (for instance, activities that may or may not be pleasurable but have to be carried out unless there are not enough agents for that). We search for efficient solutions satisfying two additional properties. First, each agent should find his bundle at least as desirable as the bundle that would be assigned to him in the hypothetical economy in which all agents have preferences identical to his, under equal treatment of equals and efficiency. In a preliminary step, we show that there is no logical relation between this requirement and no-envy, and between it and egalitarian-equivalence. We also establish the existence of efficient allocations satisfying it. The second property, object monotonicity, says that the availability of additional objects either has a negative impact on everyone's welfare, or it has a positive impact on everyone's welfare. We show that there is no object-monotonic selection from the correspondence that associates with each economy its set of efficient allocations meeting an even weaker version of the bound.I am grateful to Atila Abdulkadiroglu, Koichi Tadenuma, and a referee for their very helpful comments.     

Strategy-proof division with single-peaked preferences and individual endowments

We consider the problem of (re)allocating the total endowment of an infinitely divisible commodity among agents with single-peaked preferences and individual endowments. We propose an extension of the so-called uniform rule and show that it is the unique rule satisfying Pareto optimality, strategy-proofness, reversibility, and an equal-treatment condition. The resulting rule turns out to be peaks-only and individually rational: the allocation assigned by the rule depends only on the peaks of the preferences, and no agent is worse off than at his individual endowment. Received: 8 September 1995/Accepted: 30 October 1996     

On the social stability of coalitional property rights regimes

We present a model of coalitional property rights (CPR) regimes– regimes in which ownership of a good is attributable to coalitions of various sizes. Specifically, for each good, we define a legal structure that specifies the legal coalitions of individuals that share a communal claim to that good. Generally, each legal coalition may use exclusionary rules to allocate its holdings internally. These rules allow eligible subcoalitions to recontract by expropriating some fraction of the legal coalition's endowment. We then ask: what types of CPR regimes are socially stable in the sense of having a nonempty core? We give conditions on the legal structure and the primitives of the economy that achieve social stability in this sense. We emphasize two cases of particular interest. ( I ) Unanimity. Unanimity is required for a legal coalition to recontract against (block) the status quo. In this case, the core is nonempty under standard assumptions. Each agent's ability to veto an alternative allocation allows a partial characterization in terms of the economies that are privatized by dividing up the communal endowment among the members of each legal coalition. We show that in some economies' collective vs private ownership matters in terms of social stability. ( II ) Exclusion. Many eligible subcoalitions can expropriate the legal coalition's entire endowment. An example is the collection of simple majorities. The presence of cycles can easily lead to social instability. We show that if endowment holdings are sufficiently “specialized” and each agent's “veto power” sufficiently large, then stability can be achieved despite the presence of cycles in some goods. Received: 30 June 1993/Accepted: 28 February 1998     

Toward general impossibility theorems in pure exchange economies

We study the possibility of strategy-proof and efficient mechanisms in pure exchange economies. In his remarkable paper, Zhou (1991) establishes an elegant impossibility result: there is no strategy-proof, efficient, and non-dictatorial mechanism in the two-agent case. He conjectures that there is no strategy-proof, efficient, and “non-inversely-dictatorial” mechanism in the case of three or more agents. However, we discover some counterexamples to his conjecture in the case of four or more agents. We present a new interesting open question: Is there any strategy-proof, efficient, and “non-alternately-dictatorial” mechanism? Received: 17 October 2000/Accepted: 20 April 2001     

A characterization of optimal feasible tax mechanism

If the provision of public good is financed by property (wealth or endowment) taxes, what is the optimal tax mechanism when agents have private information about his own endowment? Employing the state-dependent implementation model, under incentive compatibility and feasibility constraints, we provide the full characterization of an optimal tax mechanism with two agents and its properties. Some interesting comparative statics analyses are also provided. For the general n-agent case, some partial characterization results are obtained. In addition, we fully characterize the optimal tax mechanism for the corresponding infinitely large economy.     

Trust between individuals and groups: Groups are less trusting than individuals but just as trustworthy

We compare the behavior of groups and individuals in a two-person trust game. The first mover in this game, the sender, receives an endowment and can send any part of it to the responder; the amount sent is tripled, and the responder can then return to the sender any portion of the tripled sum. In a 2 × 2 design, the players in the roles of sender and responder are either individuals or groups of three players (who conduct face-to-face discussions to decide on a collective group strategy). We find that groups in the role of sender send smaller amounts than individuals, and expect lower returns. In particular, groups send nothing more often than individuals do (and are even more likely to do so when the responder is another group). Groups and individuals in the role of responder return on average the same fraction of the amount sent. Hence, we conclude that groups are less trusting than individuals, but just as trustworthy.     

Welfare-domination under preference-replacement: A survey and open questions

The objective of this paper is to describe various applications of a requirement of solidarity pertaining to situations in which the preferences of some of the agents may change. It says that the welfares of all agents whose preferences are fixed should be affected in the same direction: they should all weakly gain, or they should all weakly lose. We show how this condition, which we name “welfare-domination under preference-replacement”, can help in evaluating allocation rules. We discuss it in several contexts: private good allocation in classical economies, public good decision, binary choice with quasi-linear preferences, economies with indivisible goods, economies with single-peaked preferences, both in the private good case and in the public good case, and economies with time. For some of these models the implications of the property are well understood. For others, we state a number of open problems. Received: 2 January 1997/Accepted: 26 February 1998     

An arbitration game and the egalitarian bargaining solution

We analyze a simple arbitration procedure which is a multi-stage variant of Nash's demand game. In the absence of discounting, all Nash equilibria of the game yield the egalitarian solution in the first stage. The crucial feature of our arbitration procedure is that, in the case of incompatible demands, the game is allowed to continue and the player who demands the higher gain over the disagreement point is penalized by restricting her or his feasible demands in the following stage. Suitable modifications of the arbitration game yield the lexicographic extension of the egalitarian solution, resp. the proportional solutions. Journal of Economic Literature Classification Numbers: C72, C78.Financial support through grants from the Social Sciences and Humanities Research Council of Canada and the University of Waterloo is gratefully acknowledged. Earlier versions of the paper were presented at McMaster University and Brock University. The authors thank Nejat Anbarci, Michele Piccione, Venkatraman Sadanand, an editor, and the referees for their useful comments.     

Strategy-proof allocation mechanisms for economies with an indivisible good

We consider economies with a single indivisible good and money. We characterize the set of mechanisms that satisfy strategy-proofness, individual rationality, equal compensation, and demand monotonicity. There are three types of mechanisms which have the following properties: (i) they determine the allocation of monetary compensation depending on who receives the indivisible good; (ii) they allocate the indivisible good to one of the pre-specified (one or two) agent(s); and (iii) they disregard preferences of agents other than the pre-specified agent(s). This result implies that the presence of an indivisible good induces serious asymmetry in mechanisms. Received: 26 March 1996 / Accepted: 23 September 1997     

Axiomatization of ratio equilibria in public good economies

Using consistency properties, we characterize the cost-sharing scheme arising from the ratio equilibrium concept for economies with public goods. The characterization turns out to be surprisingly simple and direct. In contrast to most axiomatic characterizations based on reduced games and consistency properties, our characterization requires that in the reduced game, the players take as given the proportions of the costs paid by the members of the complementary player set, rather than their utility levels. Received: 4 July 1996/Accepted: 28 March 2001     

Equal factor equivalence in economies with multiple public goods

We reconsider the problem of provision and cost-sharing of multiple public goods. The efficient equal factor equivalent allocation rule makes every agent indifferent between what he receives and the opportunity of choosing the bundle of public goods subject to the constraint of paying r times its cost, where r is set as low as possible. We show that this rule is characterized in economies with a continuum of agents by efficiency, a natural upper bound on everyone's welfare, and a property of solidarity with respect to changes in population and preferences. Received: 3 August 1995 / Accepted : 29 April 1997     

Natural implementation in public goods economies

In this paper, we identify necessary and sufficient conditions for social choice correspondences to be Nash implemented by “natural” mechanisms in economies with arbitrary numbers of private and public goods. We find that when there exist only one public good and an arbitrary number of private goods, the Lindahl correspondence is implementable by a natural quantity mechanism in which each agent announces his own consumption bundle of private goods and input vectors for public goods. However, regardless of the numbers of private and public goods, the Pareto correspondence is not implementable even by any natural price ⁿ -quantity mechanism in which each agent reports a price vector of private goods and all agents’ personalized price vectors of public goods, in addition to his own consumption bundle of private goods and input vectors for public goods.     

The possibility of efficient provision of a public good in voluntary participation games

In this study, we provide the conditions for efficient provision of a public good in a participation game in which a non-negative integer number of units of the public good can be provided. In the case in which at most one unit of the public good can be provided, we provide refinements of Nash equilibria at which agents choose only a Nash equilibrium with an efficient allocation and provide sufficient conditions for cost-sharing rules that guarantee the existence of a Nash equilibrium with an efficient allocation. In the case of a multi-unit public good, we provide a necessary and sufficient condition for the existence of a Nash equilibrium with an efficient allocation and prove that Nash equilibria are less likely to support efficient allocations if the participation of many agents is needed for efficient provision of the public good in the case of identical agents. I would like to thank Koichi Tadenuma, Yukihiro Nishimura, Toshiyuki Fujita, John Weymark, Tatsuyoshi Saijo, Takehiko Yamato, Toshiji Miyakawa, Motohiro Sato, Takashi Shimizu, Nobue Suzuki, and Dirk T. G. Rübbelke for helpful comments and suggestions. I also thank the anonymous referees for detailed comments and suggestions. This research was supported by the Japanese Economic Research Foundation and the Grand-in-Aid for Young Scientists (Start-up) from the Japan Society for the Promotion of Science. Any remaining errors are my own.     

LINKING WEALTH AND PUNISHMENT EFFECTIVENESS: PUNISHMENT AND COOPERATION UNDER CONGRUENT HETEROGENEITIES

Global and local cooperation in supplying global public goods is often insufficient. In this respect, laboratory experiments show that peer punishment is an effective cooperation-enhancing instrument. However, it is unclear whether peer punishment would facilitate cooperation and public good provision even under congruent heterogeneities in wealth and punishment effectiveness. To this end, we experimentally study the effect of peer punishment under joint heterogeneities, where either the richest or the poorest member is also the most effective punisher. We compare these joint heterogeneities to treatments with single heterogeneities in either endowment or punishment effectiveness and to a baseline symmetry treatment with homogeneous parties. We find that heterogeneity in punishment effectiveness does not matter for cooperation, whereas endowment heterogeneity reduces cooperation compared to symmetry. This is because rich members contribute a lower portion of their endowment to the public good than their poorer counterparts. We also observe that cooperation is higher under joint heterogeneities in endowment and punishment effectiveness than under endowment heterogeneity (with no differences than under symmetry). This holds even when the rich party gains less from cooperation and is the most effective punisher. (JEL C92, D74, H41)