Efficiency in coalition games with externalities (original) (raw)
Related papers
E ciency in Coalition Games with Externalities
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.
An Almost Ideal Sharing Scheme for Coalition Games with Externalities
SSRN Electronic Journal, 2000
We propose a class of sharing schemes for the distribution of the gains from cooperation for coalition games with externalities. In the context of the partition function, it is shown that any member of this class of sharing schemes leads to the same set of stable coalitions in the sense of d' Aspremont et al. (1983). These schemes are "almost ideal" in that they stabilize these coalitions which generate the highest global welfare among the set of "potentially stable coalitions". Our sharing scheme is particularly powerful for economic problems that are characterized by positive externalities from coalition formation and which therefore are likely to suffer from severe free-riding.
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...
Top responsiveness and stable partitions in coalition formation games
2005
Top responsiveness is introduced by Alcalde and Revilla [Journal of Mathematical Economics 40 (2004) 869-887] as a property which induces a rich domain on playerss preferences in hedonic games, and guarantees the existence of core stable partitions. We strengthen this observation by proving the existence of strict core stable partitions, and when a mutuality condition is imposed as well, the
Cooperative Games with Overlapping Coalitions Georgios Chalkiadakis Evangelos Markakis
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.
Core in a simple coalition formation game
Social Choice and Welfare, 2001
We analyze the core of a class of coalition formation game in which every player's payo¨depends only on the members of her coalition. We ®rst consider anonymous games and additively separable games. Neither of these strong properties guarantee the existence of a core allocation, even if additional strong properties are imposed. We then introduce two top-coalition properties each of which guarantee the existence. We show that these properties are independent of the Scarf-balancedness condition. Finally we give several economic applications.
Strategy-proof coalition formation
International Journal of Game Theory, 2009
We analyze coalition formation problems in which a group of agents is partitioned into coalitions and agents' preferences only depend on the identity of the members of the coalition they are members of. We study rules that associate to each profile of agents' preferences a partition of the society. We are interested in rules that never provide incentives for the agents to misrepresent their preferences. Hence, we analyze strategy-proof rules and we focus on restricted domains of preferences, as the domain of additively representable or separable preferences.
Competitive outcomes and endogenous coalition formation in an n-person game
Journal of Mathematical Economics, 2008
We extend the analysis of competitive outcomes in TU market games of Competitive outcomes in the cores of market games. International Journal of Game Theory 4, 229-237] in two ways. First, our representing economies are coalition production economies. Second, and more importantly, our analysis holds for arbitrary TU games. By adopting the C-stable set of Guesnerie and Oddou [Guesnerie, R., Oddou, C., 1979. On economic games which are not necessarily superadditive. Economics Letters 3, 301-306], renamed c-core in our paper, we are able to characterize competitive outcomes even in games with empty core. As competitive outcomes are associated with specific coalition structures, our main result provides an endogenous determination of coalition building and shows that the c-core of any TU game coincides with the set of competitive outcomes of the corresponding coalition production economy.
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.
Cooperative games with overlapping coalitions
Journal of Artificial Intelligence Research, 2010
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.