The Buck-Passing Game
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We consider a model where agents want to transfer the responsibility of doing a job to one of their neighbors in a social network. This can be considered a network variation of the public good model. The goal of the agents is to see the buck coming back to them as rarely as possible. We frame this situation as a game, called the buck-passing game, where players are the vertices of a directed graph and the strategy space of each player is the set of her out-neighbors. The cost that a player incurs is the expected long term frequency of times she gets the buck. We consider two versions of the game. In the deterministic one the players choose one of their out-neighbors. In the stochastic version they choose a probability vector that determines who of their out-neighbors is chosen. We use the finite improvement property to show that the deterministic buck-passing game admits a pure equilibrium. Under some conditions on the strategy space this is true also for the stochastic version. This is proved by showing the existence of an ordinal potential function. These equilibria are prior-free, that is, they do not depend on the initial distribution according to which the first player having the buck is chosen.
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