Abstract
The relationship between coalition-proof (Nash) equilibria in a normal-form game and those in its subgame is examined. A subgame of a normal-form game is a game in which the strategy sets of all players in the subgame are subsets of those in the normal-form game. In this paper, focusing on a class of aggregative games, we provide a sufficient condition for the aggregative game under which every coalition-proof equilibrium in a subgame is also coalition-proof in the original normal-form game. The stringency of the sufficient condition means that a coalition-proof equilibrium in a subgame is rarely a coalition-proof equilibrium in the whole game.
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