Sequential Formation of Coalitions through Bilateral Agreements

Journal of Economic Theory, 2011

We study coalition formation processes of Konishi and Ray (2003) [27]. It is shown that an absorbing and deterministic process of coalition formation that also forms an equilibrium – satisfies a coalitional one-deviation property – does exist if one allows the process to be history dependent. All such dynamic equilibrium processes of coalition formation are characterized. Absorbing outcomes of dynamic equilibrium processes are also identified. It is shown that they always constitute a subset of the largest consistent set of Chwe (1994) [11]. A procedure that identifies a dynamic equilibrium process of coalition formation in finite time is constructed.

Games and Economic Behavior, 2000

2003

This paper proposes a model of coalitional bargaining based on strategic interaction across coalitions, where players endogenously choose whether to exit. This formulation is general enough to study the formation of coalitions and the distribution of gains from cooperation in a wide variety of economic models with externalities and outside options. We show that when outside options are independent of the actions of other players, the Markov Perfect Equilibria of the coalitional bargaining game converge to e¢cient outcomes when the players become perfectly patient. On the other hand, we show through an example than in a model with negative externalities where players' outside options depend on the action of other players, the outcome may be ine¢cient, as players choose to exit before they extract all gains from cooperation.

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.

Journal of Economic Theory, 2013

We study a model of sequential bargaining in which, in each period before an agreement is reached, a proposer is randomly selected, the proposer suggests a division of a pie of size one, each other agent either approves or rejects the proposal, and the proposal is implemented if the set of approving agents is a winning coalition for the proposer. We show that stationary equilibrium outcomes of a coalitional bargaining game are unique. This generalizes Eraslan insofar as: (a) there are no restrictions on the structure of sets of winning coalitions; (b) different proposers may have different sets of winning coalitions; (c) there may be a positive probability that no proposer is selected. Running Title: Coalitional Bargaining J ournal of Economic Literature Classification Number D71.

Journal of Economic Theory, 2007

If agents negotiate openly and form coalitions, can they reach efficient agreements? We address this issue within a class of coalition formation games with externalities where agents' preferences depend solely on the coalition structure they are associated with. We derive Ray and Vohra's [Equilibrium binding agreements, J. Econ. Theory 73 (1997) 30-78] notion of equilibrium binding agreements using von Neumann and Morgenstern [Theory of Games and Economic Behavior, Princeton University Press, Princeton, 1944] abstract stable set and then extend it to allow for arbitrary coalitional deviations (as opposed to nested deviations assumed originally). We show that, while the extended notion facilitates the attainment of efficient agreements, inefficient agreements can nevertheless arise, even if utility transfers are possible.

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.

Many multiagent settings require a collection of agents to partition themselves into coalitions. In such cases, the agents may have conflicting preferences over the possible coalition structures that may form. We investigate a noncooperative bargaining game to allow the agents to resolve such conflicts and partition themselves into non-overlapping coalitions. The game has a finite horizon and is played over discrete time periods. The bargaining agenda is defined exogenously. An important element of the game is a parameter 0 ≤ δ ≤ 1 that represents the probability that bargaining ends in a given round. Thus, δ is a measure of the degree of democracy (ranging from democracy for δ = 0, through increasing levels of authoritarianism as δ approaches 1, to dictatorship for δ = 1). For this game, we focus on the question of how a player's position on the agenda affects his power. We also analyse the relation between the distribution of the power of individual players, the level of democracy, and the welfare efficiency of the game. Surprisingly, we find that purely democratic games are welfare inefficient due to an uneven distribution of power among the individual players. Interestingly, introducing a degree of authoritarianism into the game makes the distribution of power more equitable and maximizes welfare.

This paper provides a su¢ cient condition for the non-emptiness of the core in coalition formation such as the formation of clubs, partnerships, …rms, business alliances, and jurisdictions voting on public goods. The condition is formulated for settings in which agents …rst form coalitions and then each coalition realizes a payo¤ pro…le from the set of available alternatives via mechanisms such as various games, bargaining, and sharing rules. In these settings, the core is non-empty for all preference pro…les induced by the mechanisms if and only if the preferences of agents over proper coalitions are pairwise aligned. The agents'preferences over proper coalitions are pairwise aligned if any two agents in the intersection of any two proper coalitions prefer the same one of the two coalitions. For instance, there exists a core coalition structure if the payo¤s are determined in the Tullock rent-seeking, and Nash, egalitarian, and Rawlsian bargaining solutions. In these cases, there is generically a unique core coalition structure and the grand coalition does not necessarily form. The core might be empty if the payo¤s are determined by the Kalai-Smorodinsky bargaining solution or Shapley value. The paper also determines the class of linear sharing rules and regular Pareto optimal mechanisms for which there are core coalition structures.

The Manchester School, 2014

In this paper we review a number of coalitional solution concepts for the analysis of the stability of cartels and mergers under oligopoly. We show that, although so far the industrial organization and the cooperative game-theoretic literature have proceeded somehow independently on this topic, the two approaches are highly inter-connected. We …rst consider the basic problem of the stability of the whole industry association of …rms under oligopoly and, for this purpose, we introduce the concept of core in games with externalities. We show that di¤erent assumptions on the behaviour as well as on the timing of the coalitions of …rms yield very di¤erent results on the set of allocations which are core-stable. We then consider the stability of associations of …rms organized in coalition structures di¤erent from the grand coalition. To this end, various coalition formation games recently introduced by the so called endogenous coalition formation literature are critically reviewed. Again, di¤erent assumptions concerning the timing and the behaviout of …rms are shown to yield a wide range of di¤erent results.