Analyzing Games with Ambiguous Player Types using the ${\rm MINthenMAX}$ Decision Model

TL;DR

This paper introduces the ${\rm MINthenMAX}$ decision model for analyzing games with extreme incomplete information, where players lack beliefs about others' preferences, and demonstrates its application to economic scenarios.

Contribution

The paper proposes the ${\rm MINthenMAX}$ model as a novel refinement of MiniMax for games with type ambiguity, providing a new equilibrium analysis framework.

Findings

Pure strategy equilibria always exist in the analyzed scenarios.

${\rm MINthenMAX}$ refines MiniMax for better modeling ambiguity.

Application to coordination and trade scenarios demonstrates model effectiveness.

Abstract

In many common interactive scenarios, participants lack information about other participants, and specifically about the preferences of other participants. In this work, we model an extreme case of incomplete information, which we term games with type ambiguity, where a participant lacks even information enabling him to form a belief on the preferences of others. Under type ambiguity, one cannot analyze the scenario using the commonly used Bayesian framework, and therefore he needs to model the participants using a different decision model. In this work, we present the ${\rm MINthenMAX}$ decision model under ambiguity. This model is a refinement of Wald's MiniMax principle, which we show to be too coarse for games with type ambiguity. We characterize ${\rm MINthenMAX}$ as the finest refinement of the MiniMax principle that satisfies three properties we claim are necessary for games with type ambiguity. This prior-less approach we present her also follows the common practice in computer science of worst-case analysis. Finally, we define and analyze the corresponding equilibrium concept assuming all players follow ${\rm MINthenMAX}$. We demonstrate this equilibrium by applying it to two common economic scenarios: coordination games and bilateral trade. We show that in both scenarios, an equilibrium in pure strategies always exists and we analyze the equilibria.