Marginal cost price rule for homogeneous cost functions

Mirman and Tauman (1982) show that axioms of cost sharing, additivity, rescaling invariance, monotonicity, and consistency uniquely determine a price rule on the class of continuously differentiable cost problems as the Aumann-Shapley price mechanism. Here we prove that standard versions of these axioms determine uniquely the marginal cost price rule on the class of homogeneous and convex cost functions, which are, in addition, continuously differentiable. This result persists even if the cost functons are not required to be convex. Received: August 2001     

Inheritance of properties in communication situations

In this paper we consider cooperative games in which the possibilities for cooperation between the players are restricted because communication between the players is restricted. The bilateral communication possibilities are modeled by means of a (communication) graph. We are interested in how the communication restrictions influence the game. In particular, we investigate what conditions on the communication graph guarantee that certain appealing properties of the original game are inherited by the graph-restricted game, the game that arises once the communication restrictions are taken into account. We study inheritance of the following properties: average convexity, inclusion of the Shapley value in the core, inclusion of the Shapley values of a game and all its subgames in the corresponding cores, existence of a population monotonic allocation scheme, and the property that the extended Shapley value is a population monotonic allocation scheme. Received May 1998/Revised version January 2000     

Proper rationalizability in lexicographic beliefs

Proper consistency is defined by the property that each player takes all opponent strategies into account (is cautious) and deems one opponent strategy to be infinitely more likely than another if the opponent prefers the one to the other (respects preferences). When there is common certain belief of proper consistency, a most preferred strategy is properly rationalizable. Any strategy used with positive probability in a proper equilibrium is properly rationalizable. Only strategies that lead to the backward induction outcome are properly rationalizable in the strategic form of a generic perfect information game. Proper rationalizability can test the robustness of inductive procedures. Final version: December 2001     

The consistency principle and an axiomatization of the α-core

This paper examines the α-core of strategic games by means of the consistency principle. I provide a new definition of a reduced game for strategic games. And I define consistency (CONS) and two forms of converse consistency (COCONS and COCONS^*) under this definition of reduced games. Then I axiomatize the α-core for families of strategic games with bounded payoff functions by the axioms CONS, COCONS^*, weak Pareto optimality (WPO) and one person rationality (OPR). Furthermore, I show that these four axioms are logically independent. In proving this, I also axiomatize the α-individually rational solution by CONS, COCONS and OPR for the same families of games. Here the α-individually rational solution is a natural extension of the classical `maximin' solution. Received: June 1998/Final version: 6 July 2001     

Dominant strategies, superior information, and winner's curse in second-price auctions

In a general model of common-value second-price auctions with differential information, we show equivalence between the following characteristics of a bidder: (i) having a dominant strategy; (ii) possessing superior information; (iii) being immune from winner's curse. When a dominant strategy exists, it is given by the conditional expectation of the common value with respect to bidder's information field; if the dominant strategy is used, other bidders cannot make a profit. Final version November 2001     

A conflict between sequential rationality and consistency principles

It is shown that no solution concept that selects sequentially rational (perfect, proper, persistent, or members of some stable set of) equilibria satisfies the following consistency property. Suppose that in every solution of the game G, player i's action is a, and denote by G ^a the game in which player i is restricted to choose a. Then some player j≠i has an action c that is used with positive probability in both some solution of G and some solution of G ^a. This result illustrates a conflict between a mild consistency condition and sequential rationality. Received: January 2001/Final version: April 2002     

Negotiation-proof Nash equilibrium

This paper defines “negotiation-proof Nash equilibrium', a notion that applies to environments where players can negotiate openly and directly prior to the play of a noncooperative game. It recognizes the possibility that a group of self-interested players may choose, voluntarily and without binding agreement, to coordinate their choice of strategies and make joint objections; moreover, it takes the perfect foresight of rational players fully into account. The merit of the notion of negotiation-proof Nash equilibrium is twofold: (1) It offers a way to rectify the nestedness assumption and myopia embedded in the notion of coalition-proof Nash equilibrium. (2) The negotiation process is formalized by a “graph”, which serves as a natural extension to the approach that models preplay communication by an extensive game. Received: October 1998/Final version: May 2000     

On bargaining partner selection when communication is restricted

This paper analyzes the optimal selection of a bargaining partner when communication among players is restricted by an exogenously given graph. If players are equally patient, bargaining agreements are immune to players' locations, and the selection of a bargaining partner is not an issue. In contrast, when players differ in their discount factors, both location and impatience matter for bilateral agreements and partner selection becomes an issue. We show that selecting the most impatient neighbor is an equilibrium strategy whenever two players having a common neighbor share their most impatient neighbor. This condition is always satisfied by stratified graphs with no more than three strata. In the absence of this condition, cyclically-stratified graphs with no more than three strata also admit this equilibrium selection rule. Received: November 2000/Final version: January 2002     

Voting for voters: the unanimity case

We present a simplified model of the evolution of a society which is regulated by a formal unanimity voting procedure. We examine several protocols, which depend on whether admission or expulsion are permissible, and on the order with which they are implemented. Conditions which ensure the existence of pure-strategy perfect equilibrium profiles for some voting protocols, and counter examples for the existence of such profiles in other protocols are presented. Finally, we prove that, if the agents insist on perfect equilibrium strategy profiles in a one-stage play, the original founders would prefer a protocol in which expulsion precedes admission to protocols in which either admission precedes expulsion, or the two are treated simultaneously. The paper concludes with an overview and a discussion on the results and suggestions for further research. Received: December 2001 RID="*" ID="*"  The authors thank Salvador Barberà for his critical reading and his many suggestions. The authors are also grateful to the anonymous referee for many very useful suggestions. Support by a Natural Sciences and Engineering Research Council of Canada grant and by the Center for Rationality and Interactive Decision Theory of the Hebrew University of Jerusalem is gratefully acknowledged.     

First price auctions: Monotonicity and uniqueness

I study monotonicity and uniqueness of the equilibrium strategies in a two-person first price auction with affiliated signals. Existing results establish uniqueness within the class of non-decreasing bidding strategies. I show that there is an effectively unique Nash equilibrium within the class of piecewise monotone strategies. The main result is that in equilibrium, the strategies must be strictly increasing within the support of winning bids. This result provides the missing link for the analysis of uniqueness in two-person first price auctions. The analysis applies to asymmetric environments as well and does not require risk neutrality. Received: August 1997/Last revision: March 2000     

Axiomatizing the Harsanyi solution,the symmetric egalitarian solution and the consistent solution for NTU-games

The validity of the axiomatization of the Harsanyi solution for NTU-games by Hart (1985) is shown to depend on the regularity conditions imposed on games. Following this observation, we propose two related axiomatic characterizations, one of the symmetric egalitarian solution (Kalai and Samet, 1985) and one of the consistent solution (Maschler and Owen, 1992). The three axiomatic results are studied, evaluated and compared in detail.Revised October 2004We thank an anonymous referee and an associate editor for their helpful comments. Geoffroy de Clippel also thanks Professors Sergiu Hart, Jean-François Mertens and Enrico Minelli. Horst Zank thanks the Dutch Science Foundation NWO and the British Council for support under the UK-Netherlands Partnership Programme in Science (PPS 706). The usual disclaimer applies.     

A value for mixed action-set games

We extend the Aumann-Shapley value to mixed action-set games, i.e., multilevel TU games where there are simultaneously two types of players: discrete players that possess a finite number of activity levels in which they can join a coalition, and continuous players that possess a continuum of levels. Received February 1999/Final version October 2000     

The gamma-core and coalition formation

This paper reinterprets the γ-core (Chander and Tulkens in Int Tax Pub Financ 2:279–293, 1995; in Int J Game Theory 26:379–401, 1997) and justifies it as well as its prediction that the efficient coalition structure is stable in terms of the coalition formation theory. The problem of coalition formation is formulated as an infinitely repeated game in which the players must choose whether to cooperate or not. It is shown that a certain equilibrium of this game corresponds to the γ-core assumption that when a coalition forms the remaining players form singletons, and that the grand coalition is an equilibrium coalition structure. An earlier version of this paper was presented at the conference on Game Theory and Its Applications held in Mumbai in 2003 and was subsequently circulated as CORE Discussion Paper 2003/46.     

A labor market with heterogeneous firms and workers

A labor market where firms and workers are heterogeneous and may form more than one partnership is considered. A natural concept of core for such markets, different from the concept used by Thompson (1977), is defined. We show that the core is non-empty and is, in general, strictly greater than Thompson's core. Unlike Thompson, we found several dissimilarities between our model and the well known one-to-one case studied in Shapley and Shubik (1972). Received April 2001/Revised July 2002  This work was partially supported by FIPE-S?o Paulo and CNPq-Brazil.?I am in debt to David Gale and an anonymous referee and associate editor of IJGT whose comments and suggestions contributed for the improvement of this paper.     

Arithmetic families of smooth surfaces and equisingularity of embedded schemes

This article deals with the foundations of a theory of equisingularity for families of zero-dimensional sheaves of ideals on smooth algebraic surfaces, in the arithmetic context, i.e., where one works with schemes defined over Dedekind rings. Here, different equisingularity conditions are analyzed and compared, based on one of the following requirements: 1) each member of the the family has the same desingularization tree, 2) the family admits a simultaneous desingularization, 3) a naturally associated family of curves is equisingular. Similar conditions had been investigated, in the context of Complex Local Analytic Geometry, by J. J. Risler. Received: 17 November 1997 / Revised version: 19 April 1999     

Farsighted Stability in an n-Person Prisoner’s Dilemma

Farsighted stability is examined in an n-person prisoner’s dilemma. It is shown that any individually rational and Pareto efficient outcome is a farsighted stable set and no other farsighted stable set exists; it is further shown that the largest consistent set consists of all individually rational outcomes.     

A stratification of Hilbert schemes by initial ideals and applications

We show that the set of the homogeneous saturated ideals with given initial ideal in a fixed term-ordering is locally closed in the Hilbert scheme, and that it is affine if the initial ideal is saturated. Then, Hilbert schemes can be stratified using these subschemes. We investigate the behaviour of this stratification with respect to some properties of the closed points. As application, we describe the singular locus of the component of Hilb^{4 z +1} _ℙ4 containing the ACM curves of degree 4. Received: 30 November 1998 / Revised version: 16 September 1999     

Two-person repeated games with finite automata

We study two-person repeated games in which a player with a restricted set of strategies plays against an unrestricted player. An exogenously given bound on the complexity of strategies, which is measured by the size of the smallest automata that implement them, gives rise to a restriction on strategies available to a player.  We examine the asymptotic behavior of the set of equilibrium payoffs as the bound on the strategic complexity of the restricted player tends to infinity, but sufficiently slowly. Results from the study of zero sum case provide the individually rational payoff levels. Received February 1997/revised version March 2000     

私募基金规模、申购赎回机制与动态道德风险

运用动态合约理论与实物期权理论研究了私募基金最优激励相容合约的一般特征,考察了基金规模与申购赎回机制对缓解道德风险的作用。结论表明,私募基金最优激励相容合约由投资人的最大预期收益与管理者的最大预期回报共同决定,且购买私募基金类似于做多一种特殊期权,该期权标的资产价格由管理者后续值度量;投资人为激励管理者努力工作而付出的激励成本随基金初始规模或再申购比例递增,而最优基金规模由其边际激励成本与预期边际业绩决定;赎回成本影响投资人的最大预期收益,但对缓解道德风险不具显著作用;适当的业绩抽成可降低道德风险,且业绩抽成与私募基金初始规模或再申购比例在缓解道德风险方面存在一定的替代性。