Sequential Equilibrium in Computational Games

TL;DR

This paper explores sequential equilibrium concepts in computational games where agents pay for computation, showing that two different notions of equilibrium align under natural assumptions in this setting.

Contribution

It demonstrates that conceptual issues with the interim equilibrium notion in imperfect recall games diminish in computational games, leading to their equivalence.

Findings

The two equilibrium notions coincide in computational games under natural assumptions.

Conceptual problems with interim equilibrium are largely resolved in the computational setting.

Agents' rational forgetting and computational costs influence equilibrium analysis.

Abstract

We examine sequential equilibrium in the context of computational games, where agents are charged for computation. In such games, an agent can rationally choose to forget, so issues of imperfect recall arise. In this setting, we consider two notions of sequential equilibrium. One is an ex ante notion, where a player chooses his strategy before the game starts and is committed to it, but chooses it in such a way that it remains optimal even off the equilibrium path. The second is an interim notion, where a player can reconsider at each information set whether he is doing the "right" thing, and if not, can change his strategy. The two notions agree in games of perfect recall, but not in games of imperfect recall. Although the interim notion seems more appealing, \fullv{Halpern and Pass [2011] argue that there are some deep conceptual problems with it in standard games of imperfect recall. We show that the conceptual problems largely disappear in the computational setting. Moreover, in this setting, under natural assumptions, the two notions coincide.