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This paper presents a framework and solution concepts for predicting coalitions formation and payoff distribution in sidepayment games.
In economics and political science there are situations inwhich we would like to predict the coalitions that form and the payoffs agents receive for their cooperation. when there are many “profitable” potential coalitions and agent s are limited toparticipating in only one coalition at a time, the price each agent can command may depend on his opportunities in other coalitions. These prices the agents demand in turn determine which coalitions arelikely to form. For example, in coalitions production economies where there are many potentially profitable firms, the profit share an agent can command in each firm will depend on his opportunitieswithin others firms will actually form.
There situations are often modeled as characteristic function games with sidepayments. Many of the usual solution concepts for sidepayment games- including thecore[Gillies; Shapley (1953)], the Shapley value[Shapley], the nucleolus[ Schmeidler], the bargaining set [Aumann/Maschler] and the kernel [Davis/Maschler]- are not designed to predict coalitionformation. These solution concepts answer a fundamentally different question of how the coalition’s gain should be distributed given that the coalition of the whole( or another given coalition structure) hasformed.
The approach we take corresponds to the following intuitions on how the game is played. When the characteristic functions becomes known to the players, the players discuss in variouscoalitions how the payoff should be distributed within the coalitions. In the course of this discussions each player picks a price which are then likely to form, given the agent’s payoff demand, areprecisely those coalitions which can afford to pay these prices. In this way the prediction of which coalitions are likely to form flows naturally from the agent’s decision making on payoff demands....