David Wettstein

Bidding For The Surplus: A Non-Cooperative Approach To The Shapley Value

We consider zero-monotonic environments with transferable utility and propose a simple non-cooperative game to determine how the surplus generated by cooperation is to be shared. First, the players bid for the right to propose a sharing of the surplus. Second, after the winner pays the bids, she makes a proposal to each of the other players. If the proposal is rejected, the rest of the players will play the same game again with the proposer left out. If her proposal is accepted, she forms the grand coalition, keeping its value for herself in exchange for the proposed payments to the rest of the players. We show that the final outcome of any subgame perfect equilibrium of this mechanism always coincides with the vector of the Shapley value payoffs. Finally, we extend our results to implement the weighted Shapley values.

Sharing the surplus: An extension of the Shapley value for environments with externalities

Economic activities, both on the macro and micro level, often entail wide-spread externalities. This in turn leads to disputes regarding the compensation levels to the various parties affected. We propose a method of deciding upon the distribution of the gains (costs) of cooperation in the presence of externalities when forming the grand coalition is efficient. We show that any sharing rule satisfying efficiency, linearity, dummy player and a strong symmetry axioms can be obtained through an average game. Adding an additional axiom, we identify one unique rule satisfying these properties.

Feasible and Continuous Implementation

There has been a great deal of research in recent years investigating the question of whether or not there exist institutions (game forms) for which the set of equilibria will coincide with the set of Walrasian equilibria. In this paper we show the existence of a game form that is feasible, both for equilibrium and disequilibrium strategies, continuous, and for which the set of Nash equilibria coincides with the set of (constrained) Walrasian equilibria for all pure exchange economies. The game form allows agents to behave strategically both with respect to their preferences and their initial endowments.

All-Pay Auctions with Variable Rewards

We study all-pay auctions with variable rewards under incomplete information. In standard models, a reward depends on a bidders privately known type; however, in our model it is also a function of his bid. We show that in such models there is a potential for paradoxical behavior where a reduction in the rewards or an increase in costs may increase the expected sum of bids or alternatively the expected highest bid. Copyright 2002 by Blackwell Publishing Ltd

Innovative Activity and Sunk Cost

We analyze a patent race where the first innovator receives a time-dependent reward while all firms incur costs. When firms are identical, there is a unique, symmetric, mixed-strategy equilibrium that yields zero expected profits for all firms. Furthermore, the expected innovation time is an increasing function of the number of firms and a decreasing function of the size of the reward. When one firm has a higher reward than another, it is more likely to win. Although similar to an all-pay auction, our approach may yield both similar and qualitatively different behavior.

Choosing Wisely: A Multibidding Approach

Reaching decisions about the location of noxious facilities, such as dump sites, environmentally hazardous plants, nuclear power generators and the like, is a highly contentious issue. For instance, in February 2000, the U.S. Senate decided that nationwide nuclear waste would be shipped to the Yucca mountain site in Nevada (conditional to it being approved as a high-level nuclear waste repository). Despite the attractive compensation package, the State of Nevada voiced vehement opposition. President Clinton vetoed the bill, and in May 2000 the Senate failed to overturn it. As such, the major problem facing the U.S. nuclear industry on where to site a high-level radioactive waste repository remains virtually unresolved. Neither are decisions about the location of desirable events easily solvable. Every two years, the International Olympic Committee selects hosts for the summer and winter games, a procedure that is constantly under review and revision in order to bring about the “best possible” outcome. Until about a year ago, the decision was made by a vote based on bids and plans submitted by candidate cities. However, the recent controversy surrounding the choice of Salt Lake City to host the 2002 winter games culminated in the design of a new procedure for choosing the host of the 2006 winter games. This procedure called for the selection of two finalist cities (in this case, Turin and Sion), immediately after which the host was selected by secret ballot (in this case, Turin). Another similar issue is currently the subject of heated debate in Spain. The Spanish government, both on the national and local level, has recently been discussing various possible projects for transferring water from rivers in the north of Spain to the arid southern regions. The parties involved have conflicting interests with regard to several aspects of the projects proposed. Particularly, the water-rich regions are hesitant to give up parts of their water resources. The parties involved have still not agreed upon the choice of a transport mode or the size of the transfer payments that would compensate the localities that are relinquishing part of the water supply. These and several other cases belong to a class of problems in which a group of agents has to choose one out of several projects. A project is efficient if it maximizes the aggregate welfare of the group members. Reaching an efficient outcome is trivial when the designer has all the relevant information. However, it is often the case that the parties concerned possess much more information than the designer. Hence, the designer faces a nontrivial problem if she wishes to optimally choose one of the projects. Moreover, from a normative point of view, even if the designer has all the information, it is easier to justify the use of a fixed procedure to reach a decision than to modify the procedure for various cases in light of information disclosed or already available to the designer. Several well-known methods are available for the problem of choosing one out of a set of alternatives. One class of methods consists of various voting schemes, such as majority voting or the Borda rule. The outcomes generated by these methods need not be efficient due to strategic behavior on the part of the agents. Another class of methods consists of VickreyClarke-Groves mechanisms. For this class, “truthtelling” is a dominant strategy that always results in the choice of an efficient alternative. However, these mechanisms are not budgetbalanced and the payments collected from the * Perez-Castrillo: Department of Economics & CODE, Universitat Autonoma de Barcelona, 08193 Bellatera (Barcelona), Spain; Wettstein: Department of Economics, BenGurion University of the Negev, Monaster Center for Economic Research, Beer-Sheva 84105, Israel. We thank Herve Moulin for his helpful suggestions; Suresh Mutuswami who encouraged us to check for strong Nash equilibria, and Francis Bloch, Mark Gradstein, Moshe Justman, Jordi Masso, and two anonymous referees for their useful comments. Perez-Castrillo gratefully acknowledges financial support from BEC2000-0172 and 2000SGR-00054.

Bidding for the surplus: realizing efficient outcomes in economic environments

In this paper, we consider two classes of economic environments. In the first type, agents are faced with the task of providing local public goods that will benefit some or all of them. In the second type, economic activity takes place via formation of links. Agents need both to both form a network and decide how to share the output generated. For both scenarios, we suggest a bidding mechanism whereby agents bid for the right to decide upon the organization of the economic activity. The subgame perfect equilibria of this game generate efficient outcomes.

Efficient Bidding with Externalities

We implement a family of efficient proposals to share benefits generated in environments with externalities. These proposals extend the Shapley value to games with externalities and are parametrized through the method by which the externalities are averaged. We construct two slightly different mechanisms: one for environments with negative externalities and the other for positive externalities. We show that the subgame perfect equilibrium outcomes of these mechanisms coincide with the sharing proposals.

Implementation of Bargaining Sets via Simple Mechanisms

Abstract We propose two simple mechanisms that implement two bargaining sets in super-additive environments. The first bargaining set is a close variation of the one proposed by L. Zhou (1994, Games Econom. Behav. 6 , 512–526), and the second is the Pareto optimum payoffs of the A. Mas-Colell (1989, J. Math. Econom. 18 , 129–139) bargaining set. We adopt a simple framework in which the cooperative outcomes are realized as non-cooperative subgame perfect equilibria in pure strategies of a two-stage game played by an auxiliary set of individuals competing over the cooperative agents. Journal of Economic Literature Classification Numbers: C71, C72.

Equivalence between Bargaining Sets and the Core in Simple Games

We investigate the equivalence between several notions of bargaining sets which occur in the literature and the core of simple games.