Computational Extensive-Form Games
Joseph Y. Halpern, Rafael Pass, Lior Seeman

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)…
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Taxonomy
TopicsGame Theory and Applications · Artificial Intelligence in Games · Computability, Logic, AI Algorithms
