Handbook of Game Theory

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 v_i >c_i for all i continues to hold, there are n (pure) Nash equilibria, each involving z_i = 1 for precisely one player i, and z_j = 0 for all j ≠ i. There is no equilibrium in Z₀ any longer, as (any) single player would wish to deviate and receive v_i − c_i > 0. Thus all the (pure) equilibria lie in the first layer, Z₁. The ...