Discussion Papers 2022

CIRJE-F-1203	"A New Folk Theorem in OLG Games"
Author Name	Morooka, Chihiro
Date	November 2022
Full Paper	PDF file
Remarks

Abstract
We study payoffs in the subgame perfect equilibria of general n-player discounted overlapping generations games. Without a public randomization device and the observability of mixed actions, we show that patient players can approximately obtain any payoffs in the smallest cube containing the feasible and individually rational one-shot payoffs in the sense of effective minimax values with pure actions. This result is obtained when we first choose the discount rate and then choose the players’ lifespan. When mixed actions are observable, the analogous result holds true for mixed minimaxing. We also show that players cannot obtain better payoffs outside this cube defined by mixed minimaxing.
Keywords: Overlapping Generations Games, Intertemporal Trade, Discounted Games, Folk Theorem, Cubic Hull, Payoff Approximation.

Abstract

We study payoffs in the subgame perfect equilibria of general n-player discounted overlapping generations games. Without a public randomization device and the observability of mixed actions, we show that patient players can approximately obtain any payoffs in the smallest cube containing the feasible and individually rational one-shot payoffs in the sense of effective minimax values with pure actions. This result is obtained when we first choose the discount rate and then choose the players’ lifespan. When mixed actions are observable, the analogous result holds true for mixed minimaxing. We also show that players cannot obtain better payoffs outside this cube defined by mixed minimaxing.

Keywords: Overlapping Generations Games, Intertemporal Trade, Discounted Games, Folk
Theorem, Cubic Hull, Payoff Approximation.