Using the aspiration Core to Predict Coalition Formation

This work uses the defining principles of the core solution concept to determine not only payoffs but also coalition formation. Given a cooperative transferable utility (TU) game, we propose two noncooperative procedures that in equilibrium deliver a natural and nonempty core extension, the aspiration core, together with the supporting coalitions it implies. As expected, if the cooperative game is balanced, the grand coalition forms. However, if the core is empty, other coalitions arise. Following the aspiration literature, not only partitions but also overlapping coalition configurations are allowed. Our procedures interpret this fact in different ways. The first game allows players to participate with a fraction of their time in more than one coalition, while the second assigns probabilities to the formation of potentially overlapping coalitions. We use the strong Nash and subgame perfect Nash equilibrium concepts.

[1]  E. Bennett.  The aspiration approach to predicting coalition formation and payoff distribution in sidepayment games , 1983 .

[2]  Juan Camilo Gómez.  An Extension of the Core solution Concept , 2003 .

[3]  Lloyd S. Shapley,et al.  On balanced sets and cores , 1967 .

[4]  Roger Guesnerie,et al.  On economic games which are not necessarily superadditive: Solution concepts and application to a local public good problem with few a agents , 1979 .

[5]  Lin Zhou,et al.  A New Bargaining Set of an N-Person Game and Endogenous Coalition Formation , 1994 .

[6]  J. Cross.  Some theoretic characteristics of economic and political coalitions , 1967 .

[7]  Robert J. Aumann,et al.  Chapter 1. A Survey of Cooperative Games Without Side Payments , 1967 .

[8]  T. E. S. Raghavan,et al.  Chapter 20 Zero-sum two-person games , 1994 .

[9]  R. Aumann.  Lectures On Game Theory , 2019 .

[10]  Stef Tijs,et al.  Strategic claim games corresponding to an NTU-game , 1992 .

[11]  Zaifu Yang,et al.  Competitive Outcomes and Endogenous Coalition Formation in an N-Person Game , 2004 .

[12]  Kim C. Border,et al.  Fixed point theorems with applications to economics and game theory: Fixed point theorems for correspondences , 1985 .

[13]  Joseph Greenberg,et al.  Chapter 37 Coalition structures , 1994 .

[14]  R. Selten.  A Noncooperative Model of Characteristic-Function Bargaining , 1988 .

[15]  R. Selten.  Reexamination of the perfectness concept for equilibrium points in extensive games , 1975, Classics in Game Theory.

[16]  Walter Trockel,et al.  Integrating the Nash program into mechanism theory , 2002 .

[17]  H. Peyton Young,et al.  Cost allocation, demand revelation, and core implementation , 1998 .

[18]  HANS KEIDING,et al.  The Extended Core of a Cooperative NTU Game , 2010, IGTR.

[19]  John Duggan,et al.  An Implementation-Theoretic Approach to Non-cooperative Foundations , 1999 .

[20]  S. Hart,et al.  On the endogenous formation of coalitions , 1983 .

[21]  Yakar Kannai,et al.  The core and balancedness , 1992 .

[22]  J. Pérez-Castrillo,et al.  Cooperative Outcomes through Noncooperative Games , 1994 .

[23]  Elaine Bennett,et al.  Multilateral Bargaining Problems , 1997 .

[24]  Ehud Kalai,et al.  A group incentive compatible mechanism yielding core allocations , 1979 .

[25]  William R. Zame,et al.  Bargaining in cooperative games , 1988 .

[26]  Maria Montero,et al.  The demand bargaining set: general characterization and application to majority games , 2003, Games Econ. Behav..