Optimism in Games with Non-Probabilistic Uncertainty

TL;DR

This paper introduces a new framework for analyzing one-shot two-player games with non-probabilistic uncertainty, incorporating players' attitudes from optimism to pessimism, and explores how these attitudes influence strategic beliefs and equilibria.

Contribution

It develops the concept of uncertainty equilibrium and a two-phase game model where players select attitudes before playing, offering new insights into strategic behavior under non-probabilistic uncertainty.

Findings

Uncertainty equilibrium extends traditional game solutions.

Players' attitudes significantly affect strategic choices.

The approach provides novel insights into plausible strategies.

Abstract

The paper studies one-shot two-player games with non-Bayesian uncertainty. The players have an attitude that ranges from optimism to pessimism in the face of uncertainty. Given the attitudes, each player forms a belief about the set of possible strategies of the other player. If these beliefs are consistent, one says that they form an uncertainty equilibrium. One then considers a two-phase game where the players first choose their attitude and then play the resulting game. The paper illustrates these notions with a number of games where the approach provides a new insight into the plausible strategies of the players.