Cooperation in the commons

This paper delineates circumstances in which a first-best cooperative solution can be supported as a subgame perfect equilibrium in a dynamic common property renewable resource game. In a game with nonlinear resource stock effects on cost, we characterize a worst perfect equilibrium that supports cooperation for the widest range of parameter values for the discount rate, resource growth rate, harvest price, and the number of resource exploiters. The strategy profile that we propose is consistent with human behavior observed in experiments and common property resource case studies.We thank seminar participants at the University of Minnesota, the Heartland Environmental and Resource Economics Conference at Iowa State University, Keio University, and two anonymous referees for helpful comments.     

Nash Equilibrium and Welfare Optimality

If A is a set of social alternatives, a social choice rule (SCR) assigns a subset of A to each potential profile of individuals' preferences over A , where the subset is interpreted as the set of "welfare optima". A game form (or "mechanism") implements the social choice rule if, for any potential profile of preferences, (i) any welfare optimum can arise as a Nash equilibrium of the game form (implying, in particular, that a Nash equilibrium exists) and, (ii) all Nash equilibria are welfare optimal. The main result of this paper establishes that any SCR that satisfies two properties—monotonicity and no veto power—can be implemented by a game form if there are three or more individuals. The proof is constructive.     

An efficiency characterization of plurality social choice on simple preference domains

Summary. We consider a model of social choice dealing with the problem of choosing a subset from a set of objects (e.g. candidate selection, membership, and qualification problems). Agents have trichotomous preferences for which objects are partitioned into three indifference classes, goods, bads, and nulls, or dichotomous preferences for which each object is either a good or a bad. We characterize plurality-like social choice rules on the basis of the three main axioms, known as Pareto efficiency, anonymity, and independence.Received: 29 August 2003, Revised: 3 June 2004, JEL Classification Numbers: D70, D71, D72.Biung-Ghi Ju: I am grateful to William Thomson and Jianbo Zhang for their helpful comments and discussions. I also thank Brandon Dupont, the participants in seminars at Iowa State University, University of Kansas, and the Midwest Theory Meeting at University of Notre Dame. I thank an anonymous referee for detailed comments and suggestions that were very helpful in simplifying the proof of Theorem 1 and in revising the paper.     

Implementation with partial provability

We extend implementation theory by allowing the social choice function to depend on more than just the preferences of the agents and allowing agents to support their statements with hard evidence. We show that a simple condition on evidence is necessary for the implementation of a social choice function f when the preferences of the agents are state independent and sufficient for implementation for any preferences (including state dependent) with at least three agents if the social planner can perform small monetary transfers beyond those called for by f. If transfers can be large, f can be implemented in a game with perfect information when there are at least two players under a boundedness assumption. For both results, transfers only occur out of equilibrium. The use of evidence enables implementation which is robust in the sense that the planner needs little information about agents? preferences or beliefs and agents need little information about each others? preferences. Our results are robust to evidence forgery at any strictly positive cost.     

The probability approach to general equilibrium with production

We develop an alternative approach to the general equilibrium analysis of a stochastic production economy when firms’ choices of investment influence the probability distributions of their output. Using a normative approach we derive the criterion that a firm should maximize to obtain a Pareto optimal equilibrium: the criterion expresses the firm’s contribution to the expected social utility of output, and is not the linear criterion of market value. If firms do not know agents utility functions, and are restricted to using the information conveyed by prices then they can construct an approximate criterion which leads to a second-best choice of investment which, in examples, is found to be close to the first best. We are grateful to participants in the 2006 Public Economic Theory Conference, Hanoi, the 2007 CARESS/COWLES workshop on General Equilibrium at Yale University, the 2007 SAET Conference at Kos, Greece, the NSF/NBER 2007 Conference on General Equilibrium at Northwestern University, and seminars at Rice University, the University of Southern California, Indiana University, and U.C. Davis for helpful comments. We particularly thank Jacques Drèze and David Cass for stimulating discussions, and a referee for helpful suggestions for improving the paper.     

The Shapley Value of a Patent Licensing Game: the Asymptotic Equivalence to Non-cooperative Results

We consider a game in characteristic form played by firms and an outside patent holder of a cost-reducing innovation. The worth of a coalition of players is the total Cournot profit the coalition can guarantee to obtain when it operates an optimal number of its firms while the complement operates any number of its firms as to minimize the profit of the coalition. Only firms in a coalition with the patent holder are allowed to use the efficient technology. We prove that when the number of firms is large, the Shapley value of the patent holder approximates the payoff he obtains in the non-cooperative auction game traditionally studied in the literature.We thank an anonymous referee for very helpful comments that significantly improved the paper. The second author is being partially supported by the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Grant-in-Aid for 21 Century COE Program. He wishes to thank his advisor Yair Tauman and co-advisor Pradeep Dubey for their intellectual guidance, Akira Okada and Haruo Imai for their encouragement, and Shigeo Muto for his helpful comments to the first draft of this paper at the autumn meeting of the Japanese Economic Association in 2003.     

Recommended play and correlated equilibria: an experimental study

This study reports a laboratory experiment wherein subjects play a hawk–dove game. We try to implement a correlated equilibrium with payoffs outside the convex hull of Nash equilibrium payoffs by privately recommending play. We find that subjects are reluctant to follow certain recommendations. We are able to implement this correlated equilibrium, however, when subjects play against robots that always follow recommendations, including in a control treatment in which human subjects receive the robot “earnings.” This indicates that the lack of mutual knowledge of conjectures, rather than social preferences, explains subjects’ failure to play the suggested correlated equilibrium when facing other human players. We are grateful for financial support provided by the Purdue University Faculty Scholar program and the Asociación Méxicana de Cultura, as well as for the valuable research assistance provided by Shakun Datta and Marikah Mancini. We received helpful comments from Shurojit Chatterji, David Cooper, Arthur Schram, Ricard Torres, an anonymous referee, and from conference and seminar participants at Royal Holloway, the University of Amsterdam, Purdue University, the Economic Science Association and the Society for the Advancement of Economic Theory.     

Robustness of simple menus of contracts in cost-based procurement

We consider a model of cost-based procurement in which the principal faces Knightian uncertainty about the agent's preferences for cost reduction. We show that a particularly simple incentive scheme—a menu comprising a fixed-price contract and a cost-reimbursement contract—minimizes the maximum expected payment, where this maximum is taken over the set of possible agent preferences. For some parameters of the problem, a range of alternative incentive schemes also satisfy this criterion. We show that the simple incentive scheme is not weakly dominated by any of the alternatives: there does not exist an alternative mechanism for which the expected payment is no higher for all realizations of the agent's preferences and strictly lower for some realization.     

Characterization of the extreme core allocations of the assignment game

A characterization of the extreme core allocations of the assignment game is given in terms of the reduced marginal worth vectors. For each ordering in the player set, a payoff vector is defined where each player receives his or her marginal contribution to a certain reduced game played by his or her predecessors. This set of reduced marginal worth vectors, which for convex games coincide with the usual marginal worth vectors, is proved to be the set of extreme points of the core of the assignment game. Therefore, although assignment games are hardly ever convex, the same characterization of extreme core allocations is valid for convex games.     

Existence and efficiency of a stationary subgame-perfect equilibrium in coalitional bargaining models with nonsuperadditive payoffs

We provide the existence theorem of stationary subgame-perfect equilibrium (SSPE) in a noncooperative coalitional bargaining game model with random proposers. Our model contains a bargaining situation where the coalitional game is nonsuperadditive. We also provide a necessary and sufficient condition for the existence of a pure-strategy SSPE satisfying the efficiency property when the discount factor is close to one. Furthermore, we provide examples where the delay in agreement occurs, even in a random-proposers model, when the game is nonsuperadditive. I am grateful to Akira Okada and an anonymous referee for their useful comments and helpful suggestions.     

Strategy-Proofness and the Tops-Only Property

A social choice function satisfies the tops‐only property if the chosen alternative only depends on each person's report of his most‐preferred alternatives on the range of this function. On many domains, strategy‐proofness implies the tops‐only property provided that the range of the social choice function satisfies some regularity condition. The existing proofs of this result are model specific. In this paper, a general proof strategy is proposed for showing that a strategy‐proof social choice function satisfies the tops‐only property when everyone has the same set of admissible preferences.     

Preference for flexibility in the absence of learning: the risk attitude effect

Individuals’ preferences over opportunity sets may display “preference for flexibility” which prescribes to gradually eliminate alternatives from a given set until a final choice is made. One rationale for this preference for flexibility is individuals’ incentive to postpone the final choice in order to better learn their underlying preferences over basic alternatives. In this paper we show that even in the absence of learning, preference for flexibility arises if individuals are risk-averse or, at least, are not very risk-seeking. Thus, individual’s attitude towards risk provides yet another rationale for preference for flexibility. One of our results is that in the absence of learning, risk-neutral as well as risk-averse individuals display the same, maximal preference for flexibility. We thank Han Bleichrodt, Robert Dur, Chaim Fershtman, Maarten Janssen, Peran van Reeven, Peter Wakker, and Timothy van Zandt for helpful comments to and inspiring discussions. We are very grateful to the anonymous referee for very constructive comments and suggestions.     

Coalitional manipulation and the Pareto rule

This paper examines aggregation procedures that map profiles of individual preferences into choice sets. An aggregation procedure is said to be “manipulable by a coalition” if there is a group of individuals, and a preference profile, such that every member of the group prefers the choice set obtained when they are misrepresenting their preferences, to the one obtained when they are honest. We show that the Pareto rule, which is an aggregation procedure that maps profiles of individual preferences into corresponding sets of Pareto optima, is not manipulable by any coalition of individuals under various behavioural assumptions which relate preferences over choice sets to preferences over alternatives. The non-manipulability of the Pareto rule by a single individual follows as a special case under these behavioural assumptions.     

Implementing cooperative solution concepts: a generalized bidding approach

This paper provides a framework for implementing and comparing several solution concepts for transferable utility cooperative games. We construct bidding mechanisms where players bid for the role of the proposer. The mechanisms differ in the power awarded to the proposer. The Shapley, consensus and equal surplus values are implemented in subgame perfect equilibrium outcomes as power shifts away from the proposer to the rest of the players. Moreover, an alternative informational structure where these solution concepts can be implemented without imposing any conditions of the transferable utility game is discussed as well. The authors thank Yukihiko Funaki, Andreu Mas-Colell, David Pérez-Castrillo and Jana Vyrastekova for helpful discussions. We also appreciate the comments from the seminar and conference participants at Keele University, Tilburg University, University of Haifa, University of Warwick, CORE at Louvain-la-Neuve, Catholic University Leuven, Pablo de Olavide University in Seville, University of Vigo, the 2006 Annual Conference of the Israeli Mathematical Union in Neve Ilan, Israel, and the 61st European Meeting of the Econometric Society in Vienna, Austria in 2006. In particular, we are grateful to the associate editor and an anonymous referee. Their valuable comments and constructive suggestions contributed to a significant improvement of the paper. Wettstein acknowledges the financial support of the Pinchas Sapir Center for Development in Tel Aviv University.     

Double implementation in Nash and undominated Nash equilibria in social choice environments

Summary Jackson [1] and Yamato [12] constructed game forms which implement social choice correspondences in Nash and undominated Nash equilibria simultaneously in exchange economies. In this paper, I deal with social choice environments and construct a game form which implements social choice correspondences satisfying monotonicity, no veto power and having at least three agents in Nash and undominated Nash equilibria under the existence of an alternative called a holocaust. The game form constructed in this paper includes an integer game but satisfies the boundedness condition introduced by Jackson [1].I am grateful to Professors Tatsuyoshi Saijo and Stephen Turnbull, and to an anonymous referee for their helpful comments and suggestions. However all remaining errors are mine. An earlier version of this paper was presented at the 1991 Annual Meeting of the Japan Association of Economics and Econometrics at Hokkaido University.After this paper was submitted toEconomic Theory I became aware of the work of Jackson, Palfrey, and Srivastava [2] who have obtained a similar result to mine as a by-product of their main result.     

Fully sincere voting

In a general social choice framework where the requirement of strategy-proofness may not be sensible, we call a social choice rule fully sincere if it never gives any individual an incentive to vote for a less-preferred alternative over a more-preferred one and provides an incentive to vote for an alternative if and only if it is preferred to the default option that would result from abstaining. If the social choice rule can depend only on the number of votes that each alternative receives, those rules satisfying full sincerity are convex combinations of the rule that chooses each alternative with probability equal to the proportion of the vote it receives and an arbitrary rule that ignores voters' preferences. We note a sense in which the natural probabilistic analog of approval voting is the fully sincere rule that allows voters maximal flexibility in expressing their preferences and gives these preferences maximal weight.     

Fully sincere voting

In a general social choice framework where the requirement of strategy-proofness may not be sensible, we call a social choice rule fully sincere if it never gives any individual an incentive to vote for a less-preferred alternative over a more-preferred one and provides an incentive to vote for an alternative if and only if it is preferred to the default option that would result from abstaining. If the social choice rule can depend only on the number of votes that each alternative receives, those rules satisfying full sincerity are convex combinations of the rule that chooses each alternative with probability equal to the proportion of the vote it receives and an arbitrary rule that ignores voters' preferences. We note a sense in which the natural probabilistic analog of approval voting is the fully sincere rule that allows voters maximal flexibility in expressing their preferences and gives these preferences maximal weight.     

Equilibria in a dynamic global game: the role of cohort effects

Summary. We introduce strategic waiting in a global game setting with irreversible investment. Players can wait in order to make a better informed decision. We allow for cohort effects, which arise endogenously in technology adoption problems with positive contemporaneous network effects. Formally, cohort effects lead to intra-period network effects being greater than inter-period network effects. Depending on the nature of the cohort effects, our game may or may not satisfy dynamic increasing differences. If it does, our model has a unique rationalizable outcome. Otherwise, multiple equilibria may exist as players want to invest at the same point in time others do.Received: 13 July 2004, Revised: 20 May 2005, JEL Classification Numbers: C72, C73, D82, D83.We thank George-Marios Angeletos, Helmut Bester, Andreas Blume, Estelle Cantillon, Frank Heinemann, Christian Hellwig, Larry Karp, Tobias Kretschmer, In Ho Lee, Robin Mason and an anonymous referee for helpful comments. We also thank seminar participants at the EEA-meeting in Stockholm 2003, ESRC Workshop in Warwick 2004, Free University Berlin, IAE (Barcelona), Keele, MIT, Southampton, University of Pittsburgh, and at a CEPR-conference in Brussels 2002 for comments, and the European Union for providing financial support through the TMR network on network industries (Contract number FMRX-CT98-0203). This paper was completed while the first author visited the Department of Economics at MIT, whose hospitality he gratefully acknowledges.     

A glove-market partitioned matrix related to the assignment game

To any assignment market we associate the unique exact assignment game defined on the same set of agents and with a core that is a translation of the core of the initial market. As it happens with the core, the kernel and the nucleolus of an assignment game are proved to be the translation of the kernel and the nucleolus of its related exact assignment game by the vector of minimum core payoffs. Agents on each side of the market are classified by means of an equivalence relation and, when agents on the same class are ordered to be consecutive, the related exact assignment market is defined by a partitioned matrix, each block of the partition being a glove market.     

The communication requirements of social choice rules and supporting budget sets

The paper examines the communication requirements of social choice rules when the (sincere) agents privately know their preferences. It shows that for a large class of choice rules, any minimally informative way to verify that a given alternative is in the choice rule is by verifying a “budget equilibrium”, i.e., that the alternative is optimal to each agent within a “budget set” given to him. Therefore, any communication mechanism realizing the choice rule must find a supporting budget equilibrium. We characterize the class of choice rules that have this property. Furthermore, for any rule from the class, we characterize the minimally informative messages (budget equilibria) verifying it. This characterization is used to identify the amount of communication needed to realize a choice rule, measured with the number of transmitted bits or real variables. Applications include efficiency in convex economies, exact or approximate surplus maximization in combinatorial auctions, the core in indivisible-good economies, and stable many-to-one matchings.