Game-theoretic Modeling of Players' Ambiguities on External Factors

TL;DR

This paper introduces a comprehensive game-theoretic model that captures players' ambiguity attitudes towards external factors, extending traditional frameworks to include preferences, multiple equilibrium concepts, and applications like auctions.

Contribution

It develops a unified framework for modeling ambiguity attitudes in games, establishing equilibrium existence, continuity properties, and relations between different equilibrium concepts.

Findings

Equilibrium existence is proven under various ambiguity structures.

Equilibrium sets are upper hemi-continuous with respect to ambiguity attitudes.

Pure equilibria exist in ambiguity-seeking games with strategic complementarities.

Abstract

We propose a game-theoretic framework that incorporates both incomplete information and general ambiguity attitudes on factors external to all players. Our starting point is players' preferences on payoff-distribution vectors, essentially mappings from states of the world to distributions of payoffs to be received by players. There are two ways in which equilibria for this preference game can be defined. When the preferences possess ever more features, we can gradually add ever more structures to the game. These include real-valued utility-like functions over payoff-distribution vectors, sets of probabilistic priors over states of the world, and eventually the traditional expected-utility framework involving one single prior. We establish equilibrium existence results, show the upper hemi-continuity of equilibrium sets over changing ambiguity attitudes, and uncover relations between the two versions of equilibria. Some attention is paid to the enterprising game, in which players exhibit ambiguity seeking attitudes while betting optimistically on the favorable resolution of ambiguities. The two solution concepts are unified at this game's pure equilibria, whose existence is guaranteed when strategic complementarities are present. The current framework can be applied to settings like auctions involving ambiguity on competitors' assessments of item worths.