Optimism and Pessimism in Strategic Interactions under Ignorance

TL;DR

This paper explores how players with limited beliefs in strategic interactions decide optimistically or pessimistically, formalizing these attitudes and revealing their implications for rationalizability and game theory concepts.

Contribution

It introduces formal models of optimism and pessimism in ignorance, including Wald Rationalizability for pessimism, and connects these attitudes to existing rationalizability concepts and game theory insights.

Findings

Optimism relates to Point Rationalizability and wishful thinking.

Pessimism is captured by a new algorithm called Wald Rationalizability.

Dropping the belief-implies-truth assumption reverses certain existence results.

Abstract

We study players interacting under the veil of ignorance, who have -- coarse -- beliefs represented as subsets of opponents' actions. We analyze when these players follow $\max \min$ or $\max\max$ decision criteria, which we identify with pessimistic or optimistic attitudes, respectively. Explicitly formalizing these attitudes and how players reason interactively under ignorance, we characterize the behavioral implications related to common belief in these events: while optimism is related to Point Rationalizability, a new algorithm -- Wald Rationalizability -- captures pessimism. Our characterizations allow us to uncover novel results: ($i$) regarding optimism, we relate it to wishful thinking \'a la Yildiz (2007) and we prove that dropping the (implicit) "belief-implies-truth" assumption reverses an existence failure described therein; ($ii$) we shed light on the notion of rationality in ordinal games; ($iii$) we clarify the conceptual underpinnings behind a discontinuity in Rationalizability hinted in the analysis of Weinstein (2016).