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Handbook of Game Theory by Shmuel Zamir, Petyon Young

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6.5.3 The volunteer's dilemma

So far the public good games discussed have involved a coordination problem of “no provision” versus “provision.” In the payoff structure given in [6.29], this requires m ≥ 2. When m = 1 the game is a volunteer's dilemma. It takes one, and only one, player to contribute toward the production of the public good in order for it to be successfully provided. So long as the maintained assumption that vi >ci for all i continues to hold, there are n (pure) Nash equilibria, each involving zi = 1 for precisely one player i, and zj = 0 for all ji. There is no equilibrium in Z0 any longer, as (any) single player would wish to deviate and receive vici > 0. Thus all the (pure) equilibria lie in the first layer, Z1. The ...

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