Stable Outcomes for Contract Choice Problems

2007

Abstract Coalition formation is a problem of great interest in AI, allowing groups of autonomous, individually rational agents to form stable teams. Automating the negotiations underlying coalition formation is, naturally, of special concern. However, research to date in both AI and economics has largely ignored the potential presence of uncertainty in coalitional bargaining.

SSRN Electronic Journal, 2013

In this paper we introduce the concept of quasi-building set that may underlie the coalitional structure of a cooperative game with restricted communication between the players. Each feasible coalition, including the set of all players, contains a nonempty subset called the choice set of the coalition. Only players that are in the choice set of a coalition are able to join to feasible subcoalitions to form the coalition and to obtain a marginal contribution. We demonstrate that all restricted communication systems that have been studied in the literature take the form of a quasi-building set for an appropriate set system and choice set. Every quasi-building set determines a nonempty collection of maximal strictly nested sets and each such set induces a rooted tree satisfying that every node of the tree is a player that is in the choice set of the feasible coalition that consists of himself and all his successors in the tree. Each tree corresponds to a marginal vector of the underlying game at which each player gets as payoff his marginal contribution when he joins his successors in the tree. As solution concept of a quasi-building set game we propose the average marginal vector (AMV) value, being the average of the marginal vectors that correspond to the trees induced by all maximal strictly nested sets of the quasi-building set. Properties of this solution are also studied. To establish core stability we introduce appropriate convexity conditions of the game with respect to the underlying quasi-building set. For some specifications of quasi-building sets, the AMV-value coincides with solutions known in the literature, for example, for building set games the solution coincides with the gravity center solution and the Shapley value recently defined for this class. For graph games it therefore differs from the well-known Myerson value. For a full communication system the solution coincides with the classical Shapley value.

The two main questions in coalition games are 1) what coalitions should form and 2) how to distribute the value of each coalition between its members. When a game is not superadditive, other coalition structures (CSs) may be more attractive than the grand coalition. For example, if the agents care about the total payoff generated by the entire society, CSs that maximize utilitarian social welfare are of interest. The search for such optimal CSs has been a very active area of research. Stability concepts have been defined for games with coalition structure, under the assumption that the agents agree first on a CS, and then the members of each coalition decide on how to share the value of their coalition. An agent can refer to the values of coalitions with agents outside of its current coalition to argue for a larger share of the coalition payoff. To use this approach, one can find the CS s★ with optimal value and use one of these stability concepts for the game with s★. However, it m...

Mathematical Social Sciences, 2007

In this paper we study the restriction, to the class of bargaining problems with coalition structure, of several values which have been proposed on the class of non-transferable utility games with coalition structure. We prove that all of them coincide with the solution independently studied in Chae and Heidhues [Chae, S., Heidhues, P., 2004. A group bargaining solution. Mathematical Social Sciences 48, 37–53] and Vidal-Puga [Vidal-Puga, J.J., 2005a. A bargaining approach to the Owen value and the Nash solution with coalition structure. Economic Theory 25, 679–701]. Several axiomatic characterizations and two non-cooperative mechanisms are proposed.

Economics Letters, 2020

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Economics …, 2011

Lecture Notes in Economics and Mathematical Systems, 2001

in Aix-en-Provence, and particularly Hideo Konishi for comments and suggestions that greatly improved the exposition of this work are gratefuly acknowledged. Part of this work was done while I was visiting the Institute of Mathematical Economics at Bielefeld University under the European research programme "Game-theoretic approaches to cooperation and exchange of information, with economic applications." Financial support from the European Commission, contract number HPMF-CT-1999-00284, is gratefuly acknowledged. All remaining errors are mine.

Artificial Intelligence, 1999

Coalition formation is a key topic in multiagent systems. One may prefer a coalition structure that maximizes the sum of the values of the coalitions, but often the number of coalition structures is too large to allow exhaustive search for the optimal one. Furthermore, finding the optimal coalition structure is NP-complete. But then, can the coalition structure found via a partial search be guaranteed to be within a bound from optimum?

Journal of Economic Theory, 1987

In Bernheim, Peleg, and Whinston ("Coalition-Proof Equilibria. I. Concepts." J. Econ. Theory 42 (1987), l-12) we proposed the notion of Coalition-Proof Nash equilibrium and Perfectly Coalition-Proof Nash equilibrium as solution concepts for strategic environments in which players can freely discuss their strategies, but cannot make binding commitments. This paper undertakes applications to several economic problems, including the behavior of Cournot oligopolists, oligopolistic entry deterrence, cooperation in finite horizon games, and social choice rule implementation.

Homo Oeconomicus, 2016

We consider here pure bargaining problems endowed with a coalition structure such that each union is given its own utility. In this context we use the Shapley rule in order to assess the main options available to the agents: individual behavior, cooperative behavior, isolated unions behavior, and bargaining unions behavior. The latter two respectively recall the treatment given by Aumann-Drèze and Owen to cooperative games with a coalition structure. A numerical example illustrates the procedure. We provide criteria to compare any pair of behaviors for each agent, introduce and axiomatically characterize a modified Shapley rule, and determine its natural domain, that is, the set of problems where the bargaining unions behavior is the best option for all agents.