Markov-perfect equilibria in intergenerational games with consistent preferences

This paper considers the subgame-perfect equilibria, in Markov strategies, of an abstract intergenerational game in which the generations’ preferences are consistent in the sense that they admit recursive aggregators. Given biconvergence, it is shown that such equilibria exist and are equivalent both to the solutions of Bellman’s recursive optimality equations and to the optima of the first generation’s utility function. These results are then applied to a simple model casting new light on the neutrality of government debt, and to another accommodating impure altrusim. Finally, two new examples crisply illustrate how the paper’s equivalences fail when biconvergence fails.