One-deviation principle in coalition formation

2011

In a previous paper, we generalized to the mixed strategy case the c model of coalition formation (introduced by Hart and Kurz in Econometrica 51(4):1047-1064, 1983) for situations in which players have ambiguous expectations about the formation of the coalitions in which they are not involved; then we analyzed the corresponding evolutionary games. In this paper, we embody into the model rationality of the players; it follows that allowing for mixed strategies makes it impossible to construct unequivocally a von Neumann-Morgestein expected utility function coherent (in the sense of de Finetti B in Sul Significato Soggettivo della Probabilità, Fundamenta Mathematicae, T, vol XVIII, pp 298-329, 1931) to every strategy profile. We find out that if the multiplicity of coherent beliefs problem is approached by considering ''ambiguity loving'' players then existence results for classical static equilibria can be obtained in this model. Moreover, we provide conditions for the game to be dynamically playable and we find how the coalition structure beliefs might evolve coherently (according) to the evolution of the strategies.

2006

A natural,extension,of superadditivity,is not su¢ cient to imply that the grand,coalition is e¢ cient when,externalities are present. We provide a con- dition –analogous,to convexity–that,is su¢ cient for the grand coalition to be e¢ cient and show,that this also implies that the (appropriately de…ned) core is nonempty. Moreover, we propose a mechanism which implements the most e¢ cient partition for all coalition formation,games,and characterize the payo¤ division of the mechanism. JEL Classi…cation Numbers: C71, C72, D62 Keywords: Coalition formation, externalities, partition function games, Shapley value, implementation.

Lecture Notes in Computer Science, 2020

In a strategic form game a strategy profile is an equilibrium if no viable coalition of agents (or players) benefits (in the Pareto sense) from jointly changing their strategies. Weaker or stronger equilibrium notions can be defined by considering various restrictions on coalition formation. In a Nash equilibrium, for instance, the assumption is that viable coalitions are singletons, and in a super strong equilibrium, every coalition is viable. Restrictions on coalition formation can be justified by communication limitations, coordination problems or institutional constraints. In this paper, inspired by social structures in various real-life scenarios, we introduce certain restrictions on coalition formation, and on their basis we introduce a number of equilibrium notions. As an application we study our equilibrium notions in resource selection games (RSGs), and we present a complete set of existence and non-existence results for general RSGs and their important special cases.

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...

In the usual models of cooperative game theory, the outcome of a coalition formation process is either the grand coalition or a coalition structure that consists of disjoint coalitions. However, in many domains where coalitions are associated with tasks, an agent may be involved in executing more than one task, and thus may distribute his resources among several coalitions. To tackle such scenarios, we introduce a model for cooperative games with overlapping coalitions-or overlapping coalition formation (OCF) games. We then explore the issue of stability in this setting. In particular, we introduce a notion of the core, which generalizes the corresponding notion in the traditional (non-overlapping) scenario. Then, under some quite general conditions, we characterize the elements of the core, and show that any element of the core maximizes the social welfare. We also introduce a concept of balancedness for overlapping coalitional games, and use it to characterize coalition structures that can be extended to elements of the core. Finally, we generalize the notion of convexity to our setting, and show that under some natural assumptions convex games have a non-empty core. Moreover, we introduce two alternative notions of stability in OCF that allow a wider range of deviations, and explore the relationships among the corresponding definitions of the core, as well as the classic (non-overlapping) core and the Aubin core. We illustrate the general properties of the three cores, and also study them from a computational perspective, thus obtaining additional insights into their fundamental structure.

2020

We propose two versions of stable set as a solution concept that generalizes subgame perfection for dynamic coalition formation processes. Weakly stable set of paths (WSSP) and weakly conservative stable set of paths (WCSSP) is based on a dominance relationship which derives from a weak preference relation. The new solution concepts are closely related to OSSB and CSSB in the Theory of Social Situations. In game trees with single player moves, WSSP, like CSSB, selects paths that correspond to the set of perfect equilibrium paths. WCSSP, which is based on a more demanding dominance relation, refines this concept and eliminates paths that are dominated in the conventional (strategic) sense. Finally, we generalize WSSP drawing on Delver and Monsuur’s socially stable set, which always exists, and establish weakly socially stable set of paths (WSSSP). WSSSP, like WSSP, generalizes subgame perfection.

Social Choice and Welfare, 2006

This paper studies a class of NTU coalition formation game in which every player's payo® depends only on the members of her coalition. We provide three conditions under which the core of such games is non-empty. The three properties identi¯ed are called Union Responsiveness, Intersection Responsiveness, and Essentiality. All three are restrictions on individuals' preferences and stable allocations always exist under each of them.

Games

Coalition formation is often analysed in an almost non-cooperative way, as a two-stage game that consists of a first stage comprising membership actions and a second stage with physical actions, such as the provision of a public good. We formalised this widely used approach for the case where actions are simultaneous in each stage. Herein, we give special attention to the case of a symmetric physical game. Various theoretical results, in particular, for cartel games, are provided. As they are crucial, recent results on the uniqueness of coalitional equilibria of Cournot-like physical games are reconsidered. Various concrete examples are included. Finally, we discuss research strategies to obtain results about equilibrium coalition structures with abstract physical games in terms of qualitative properties of their primitives.

Games and Economic Behavior, 1996

We characterize the set of agreements that the players of a non-cooperative game may reach when they have the opportunity to communicate prior to play. We show that communication allows the players to correlate their actions. Therefore, we take the set of correlated strategies as the space of agreements. Since we consider situations where agreements are non-binding, they must not be subject to profitable self-enforcing deviations by coalitions of players. A coalition-proof equilibrium is a correlated strategy from which no coalition has an improving and self-enforcing deviation. A coalition-proof equilibrium exists when there is a correlated strategy which (i) has a support contained in the set of actions that survive the iterated elimination of strictly dominated strategies, and (H) weakly Pareto dominates every other correlated strategy whose support is contained in that set. Consequently, the unique equilibrium of a dominance solvable game is coalition-proof.

Working Papers, 2005

We provide an existence and a uniqueness result for coalitional equilibria of a game in strategic form. Both results are illustrated for a public good game and a homogeneous Cournot-oligopoly game.