Self-accessibility and repeated games with asymmetric discounting

We propose a simple geometric construct called ‘self-accessibility’ to study discounted infinitely repeated games with perfect monitoring. Self-accessibility delivers payoffs by computing action paths that keep all continuation payoff vectors close to the target payoff. It unifies the analysis of games with symmetric and asymmetric discounting, dispenses with public randomization, and generates pure on-path strategies. We first use it to simplify Fudenberg and Maskin (1986, 1991) and generalize their results to asymmetric discounting. Next, we use self-accessibility to find all payoff profiles that are realizable via some path at some (possibly asymmetric) discount vector. Finally, we offer an easily-verifiable sufficient and almost necessary condition for a payoff profile to arise in a subgame-perfect equilibrium, and use self-accessibility to explicitly construct the corresponding equilibrium strategies. We show that achieving cooperation via intertemporal trade among unequally patient players may require very different arrangements from those proposed earlier by Lehrer and Pauzner (1999) for two players using public randomization.