ИСТИНА

We consider repeated games with sliding planning horizons. The inicial game includes two stages: the first is a game that generalizes the known model “The Tragedy of the Commons”. At the second one the players redistribute the payoffs by means of side payments. Our purpose is to find conditions for existance in the repeated game of a subgame perfect equilibrium (SPE) realizing some Pareto-optimal outcome. The problem is of interest in context of the study of international ageements on limitation of environmental pollution. Existance of the SPE means the possibility for a stable and efficient agreement of such sort. This concept takes into account a possibility of unexpected breaking the agreement by some country and assumes that only endogeneous economic mechanisms in frame of the agreement prevent such breaking. Note that in the one-short game there is a “bad” Nash equilibrium in dominant strategies corresponding to a high pollution level. We examine two types of SPE realizing some Pareto-optimal outcome: 1) after any deviation, all players start playing dominant strategies; 2) if one player deviates, the rest continue cooperation maximizing their total payoff under the dominant strategy of the disturber; after the second deviation everybody plays his dominant strategy. For each type, we determine the set of Pareto-optimal SPE outcomes and examine how maximal and minimal SPE payoffs of a player depend on planning horizons.