Payment schemes for sustaining cooperation in dynamic games

Abstract

It is a challenge to sustain cooperation in a finite-horizon dynamic game. Since players generally have an incentive to deviate to their noncooperative strategies in the last stage, a backward induction argument leads them to defect from cooperation in all stages. In this paper, we propose two payment schemes having some desirable properties, namely, individual rationality and stability, which ensure that the players cooperate throughout the entire planning horizon. The setup and the results are general, that is, they do not rest on particular specifications of the payoff functionals or the state dynamics. We illustrate our results with a linear-quadratic dynamic game of pollution control.