Computational Extensive-Form Games

TL;DR

This paper introduces a framework for analyzing extensive-form games with computationally bounded players, defining computational game representations and equilibrium concepts that connect to classical game theory.

Contribution

It formalizes the notion of computational extensive-form games and extends equilibrium concepts to account for computational indistinguishability, linking cryptographic protocols with game-theoretic analysis.

Findings

Defines computational extensive-form games and their structure.

Establishes computational Nash and sequential equilibrium concepts.

Shows correspondence between classical and computational equilibria.

Abstract

We define solution concepts appropriate for computationally bounded players playing a fixed finite game. To do so, we need to define what it means for a \emph{computational game}, which is a sequence of games that get larger in some appropriate sense, to represent a single finite underlying extensive-form game. Roughly speaking, we require all the games in the sequence to have essentially the same structure as the underlying game, except that two histories that are indistinguishable (i.e., in the same information set) in the underlying game may correspond to histories that are only computationally indistinguishable in the computational game. We define a computational version of both Nash equilibrium and sequential equilibrium for computational games, and show that every Nash (resp., sequential) equilibrium in the underlying game corresponds to a computational Nash (resp., sequential) equilibrium in the computational game. One advantage of our approach is that if a cryptographic protocol represents an abstract game, then we can analyze its strategic behavior in the abstract game, and thus separate the cryptographic analysis of the protocol from the strategic analysis.