Resumen de Case-Based Coalition Formation
Xavier Vilá
We approach in this paper the analysis of coalition formation in a situation in which individual players have incomplete information with regards to the effective value that belonging to a specific group of people reports to him. For instance, firms involved in a merging project do not know in reality how their profits will be affected until the very moment in which the merging actually takes place. Also, countries discussing trading agreements do not actually know how their wealth might improved until a treaty is implemented. To our knowledge, this approach has not been found in the literature on the topic and we think that it deserves some attention.
To start with, we focus our attention on hedonic games, although some comments on future directions of research including more general frameworks are discussed in the conclusions. To deal with the fact that players do not know how valuable is to belong to a given coalition until the very moment such coalition is formed we use a derivative of Case-Based Theory by Gilboa and Schmeidler suited to our framework. Losely speaking, Case-Based Theory assumes that when evaluating unknown situations, players take into account the situations that they know, how �similar� are they to the unknown situation, and how �valuable� were. Our framework is a very simple dynamic coalition formation model. Starting with a given situation (configuration of coalitions), any player can decide at any moment whether to remain in the same group he currently belongs to, or joint one of the other coalitions that exist. If some of these �other coalitions that exist� is a group to which the player has never belonged to, he will evaluate the group by comparing it to �similar� groups he has belonged to at some point and, hence, knows the true value that such group had for him. In some sense, this model is close to the analysis by Konishi and Ray, with the only difference that they allow for coalitional moves (i.e., not only individual players can move at some point, but also existing coalitions may to merge or split), and that in their model players have perfect information on the value that each possible coalition has for them. Another key feature in our approach is that players are farsighted in a very week sense that will be specified. Briefly, if a player is considering to move to a coalition he had belonged to in the past and so happenned that such coalition was not stable (in the sense that some people departed from it or other people joined it), then the player will take this fact into consideration in his evaluation process. We model the underlying strategic situation as a stochastic game and characterize the set of Markov Perfect Equilibria of it.
