Coalitional stability under perfect foresight (original) (raw)
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SSRN Electronic Journal, 2002
Stable Coalitions* This Paper examines recent theoretical developments in the theory of coalition stability. It focuses on the relationship between the incentives to defect from a coalition, the size of the resulting equilibrium coalition structure and the different assumptions on membership rules, coalition behaviour, players' conjectures, etc. The Paper considers several cases. Simultaneous versus sequential moves, linear versus circular order of moves, Nash versus rational conjectures, open versus exclusive membership, monotonic versus nonmonotonic pay-off functions and orthogonal versus non-orthogonal reaction functions. The profitable and stable coalition will be derived for each possible configuration of the rules of the game, the pay-off functions and the membership rules. The results show that the size of the profitable and stable coalition highly depends on the chosen configuration and that the equilibrium outcome ranges from a small coalition with a few signatories to full cooperation. The Paper explores under which conditions a large stable coalition is likely to emerge, and identifies the institutional setting that favours the emergence of such coalition.
A Theory of Gradual Coalition Formation
The Review of Economic Studies, 1998
We study noncooperative multilateral bargaining games, based on underlying TU games, in which coalitions can renegotiate their agreements. We distinguish between models in which players continue to bargain after implementing agreements (''reversible actions'') and models in which players who implement agreements must leave the game (''irreversible actions''). We show that renegotiation always results in formation of the grand coalition if actions are reversible, but that the process may otherwise end with smaller coalitions. On the other hand, we show that the grand coalition cannot form in one step if the core of the game is empty, irrespective of the reversibility of actions. 1. The classic reference is Henderson (1939). 2. Consequently, we do not study committee problems in which there are winning coalitions smaller than the grand coalition. Political scientists have long recognized the importance of GCF in such problems, but have not provided a theoretical explanation. (See Riker (1962).) 3. Chatterjee et al. (1993) and Okada (1996) prove a related result for games without renegotiation in which the discount factor is close to, but less than 1: the grand coalition can only form if the egalitarian outcome is in the core.
An Experimental Study of Self-Enforcing Coalitions
Games
We study a model in which agents endowed with power compete for a divisible resource by forming coalitions with other agents. The coalition with the greatest power wins the resource and divides it among its members via proportional sharing. We conduct an economic experiment using this model to investigate possible behavioral factors that may explain deviations from theoretical predictions. The main findings show that agents display rational behavior when forming coalitions, especially when they know that a large proportion of their opponents play myopic strategies from the outset. Over time, however, agents learn to behave more strategically and even more rationally, thus enabling agents to display more of the behavior predicted by the coalition formation model with farsighted agents.
Evolution in time of Farsightedly Stable Coalitions: An Application of FUND
2008
Game theory is used to analyze the formation and stability of coalitions for environmental protection. The paper extends further our previous research on farsightedly stable coalitions and preferred farsightedly stable coalitions . The integrated assessment model FUND provides data for different time horizons as well as the cost-benefit function of pollution abatement. This allows for analysis of the evolution in time of farsightedly stable coalitions and their improvement to environment and welfare. Considering multiple farsightedly stable coalitions, the participation in coalitions for environmental protection is significantly increased, which is a positive result of the game theoretical approach. However, the farsighted behavior cannot be sustained for a long term which implies there are no big coalitions for environmental protection even in "a farsighted world". ). The usual approach of non-cooperative game theory to stable IEAs is based on the idea developed for cartel stability and requires so-called internal and external stability. Internal stability means that a country does not have an incentive to leave the coalition, while external stability means that a country does not have an incentive to join the coalition. This part of the literature reaches the conclusion that the size of a stable coalition is typically very small, thus representing a pessimistic view of global environmental goods. At the first level, the link between the economic activity and the physical environment is established in order to generate the integrated-assessment model. This link is established through a social welfare function. The social welfare function captures the difference between the profit from pollution and the environmental damage. The Climate Framework for Uncertainty, Negotiation and Distribution (FUND, see Section ??) model provide the social-welfare functions. Following this approach, countries play a two stage-game. In the first stage, each country decides to join the IEA or not, and in the second stage, a country decides on emissions. The main body of literature examining the formation of IEA within a two stage framework uses a certain set of assumptions. The essential assumptions are mentioned below: decisions are simultaneous in both stages, countries can form a single coalition; stability of IEA's is based on the ideas developed for cartel stability and requires so-called internal and external stability; internal stability means that a country does not have an incentive to leave the coalition while external stability means that a country does not have an incentive to join the coalition; when defecting from coalition, a country assumes that all other countries remain in the coalition (this is a consequence of the myopic stability concept , which allows only singleton movements and myopia); within the coalition, players play cooperatively and maximize their joint welfare, while the coalition and single countries compete in a non cooperative way. Non-cooperative game theory draws a pessimistic picture of the prospect of successful cooperation between countries. It claims that a large coalition of signatories is hardly stable, and that the free-rider incentive is strong. The model explains the problems of international cooperation in the attendance of environmental spillovers, but cannot explain IEAs with high membership such as the Montreal Protocol on Ozone Depleting Substances. This calls for a modification of the standard assumptions. Following, I mention some of the modifications. and allow more than one IEA to be formed. They reach the conclusion that two IEA's can perform better than one IEA in regional environmental problems but not in global ones. Sartzetakis (2002), Eyckmans (2003) and Osmani and Tol (2009a,b) use the farsighted stability concept instead of myopic stability. The farsighted stability is, firstly, introduced by Chwe (1994). The idea of farsightedness means that one should check for multi-step stability by comparing the profits of a coalition member after a series of deviations has come to an end. This research develops further our previous work (Osmani and Tol, 2009b) on farsightedly stable coalitions and preferred farsightedly stable coalitions. In our previous paper, we show that multiple preferred farsightedly stable coalitions include two thirds of countries and improve significantly the welfare and environment which are optimistic results. Here the discussion is extended on the issue, which farsightedly stable coalitions are more likely to form in different time horizons and how much improvements they bring to welfare and environment. I raise the question if the farsightedly stable coalitions can be maintained for a long-term period. The improvements in welfare and abatement levels of full non-cooperative behavior (atom structure) and grand coalition are considered also. The benefit-cost functions come from the Climate Framework for Uncertainty, Negotiation and Distribution (FUND) model, which is described in section two. The next section presents the game-theoretic model, and a discussion on single farsightedly stable coalitions. The preferred and 2 dominated farsightedly stable coalitions are considered in section four. In section four multiple preferred farsightedly stable coalitions are taken into account. The following section examines, why are preferred farsightedly stable coalitions varying in different time horizons? Section eight provides the conclusions. I discuss in Appendix the winners and losers from participation in coalitions for environmental protection for different year horizons. 2 The Game, Direct and Indirect Domination Similarly to Chwe (1994), a game Γ is defined as, Γ = (N, O, {≺ i } i∈N , {→ C } C⊂N,C =∅ ) where N is the set of players, O is the set of all coalition structures (which are also outcomes), N = ∅, O = ∅ ; {≺ i } i∈N are the strong preference relation of players defined on O. Before explaining further the game, let define the coalition structure: Definition 2.1 A coalition structure a = {C 1 , C 2 , ..., C m } is a partition of the set of players N = {1, 2, ..., n} : S i ∩ S j = ∅ where i=1:m C i = N .
Coalitions, agreements and efficiency
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.
Bargaining and Coalition Formation
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.
On the stability of an Optimal Coalition Structure
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...
Coalition formation in the presence of continuing conflict
International Journal of Game Theory, 2009
This paper studies endogenous coalition formation in a rivalry environment where continuing conflict exists. A group of heterogeneous players compete for a prize with the probability of winning for a player depending on his strength as well as the distribution of strengths among his rivals. Players can pool their strengths together to increase their probabilities of winning as a group through coalition formation. The players in the winning coalition will compete further until one individual winner is left. We show that in any equilibrium there are only two coalitions in the initial stage of the contest. In the case of three players, the equilibrium often has a coalition of the two weaker players against the strongest. The equilibrium coalition structure with four players mainly takes one of the two forms: a coalition of the three weaker players against the strongest or a coalition of the weakest and strongest players against a coalition of the remaining two. Our findings imply that the rivalry with the possibility of coalition formation in our model exhibits a pattern of two-sidedness and a balance of power. We further study the impact of binding agreements by coalition members on equilibrium coalition structures. Our analysis sheds some light on problems of temporary cooperation among individuals who are rivals by nature.