On the sequential price of anarchy of isolation games.

We study the performance of subgame perfect equilibria, a solution concept which better captures the players’ rationality in sequential games with respect to the classical myopic dynamics based on the notions of improving deviations and Nash equilibria, in the context of sequential isolation games. In particular, for two important classes of sequential isolation games, we show upper and lower bounds on the sequential price of anarchy, that is the worst-case ratio between the social performance of an optimal solution and that of a subgame perfect equilibrium, under the two classical social functions mostly investigated in the scientific literature, namely, the minimum utility per player and the sum of the players’ utilities.