Generalized Solution Concepts in Games with Possibly Unaware Players

TL;DR

This paper extends game theory to include players who may be unaware of certain game aspects, generalizing solution concepts like Nash equilibrium and analyzing their properties and relationships with rationalizability.

Contribution

It introduces a framework for analyzing games with unaware players and generalizes solution concepts such as Nash and sequential equilibrium within this context.

Findings

Generalized Nash equilibrium closely relates to rationalizability in unaware games.

The framework extends traditional solution concepts to account for unawareness.

Insights into the structure of games with unawareness are provided.

Abstract

Most work in game theory assumes that players are perfect reasoners and have common knowledge of all significant aspects of the game. In earlier work, we proposed a framework for representing and analyzing games with possibly unaware players, and suggested a generalization of Nash equilibrium appropriate for games with unaware players that we called generalized Nash equilibrium. Here, we use this framework to analyze other solution concepts that have been considered in the game-theory literature, with a focus on sequential equilibrium. We also provide some insight into the notion of generalized Nash equilibrium by proving that it is closely related to the notion of rationalizability when we restrict the analysis to games in normal form and no unawareness is involved.