Biased-Belief Equilibrium

Abstract

We investigate how distorted, yet structured, beliefs can persist in strategic situations. Specifically, we study two-player games in which each player is endowed with a biased-belief function that represents the discrepancy between a player's beliefs about the opponent's strategy and the actual strategy. Our equilibrium condition requires that: (1) each player choose a best-response strategy to his distorted belief about the opponent's strategy, and (2) the distortion functions form best responses to one another. We obtain sharp predictions and novel insights into the set of stable outcomes and their supporting stable biases in various classes of games.JEL classification: C73, D83.

The Benefits of Coarse Preferences

“…Remark 1. Theorem 1 shows that CUE yields results that are qualitatively different from most existing related solution concepts (e.g., clustered preferences (Heifetz et al, 2007a), delegation (Fershtman and Judd, 1987), biased beliefs (Heller and Winter, 2020), and naive analytics (Berman and Heller, 2021)). All these existing solution concepts predict that players treat their opponents worse than they would using their unclustered best replies in games with strategic substitutes.…”

Naive analytics equilibrium

“…Our research is also related to solution concepts that represent agents with misconceptions (e.g., conjectural equilibrium (Battigalli and Guaitoli, 1997;Esponda, 2013), self-confirming equilibrium (Fudenberg and Levine, 1993), analogy-based expectation equilibrium (Jehiel, 2005), cursed equilibrium (Eyster and Rabin, 2005;Antler and Bachi, 2019), coarse reasoning and categorization (Azrieli, 2009(Azrieli, , 2010Steiner and Stewart, 2015;Heller and Winter, 2016), Berk-Nash equilibrium (Esponda and Pouzo, 2016), rational inattention (Steiner, Stewart, and Matějka, 2017), causal misconceptions (Spiegler, 2017(Spiegler, , 2019, and noisy belief equilibrium (Friedman, 2018). These equilibrium notions have been helpful in understanding strategic behavior in various setups, and yet they pose a conceptual challenge: why do players not eventually learn to correct their misconceptions?…”

“…See also the related literature on the "indirect evolutionary approach" (e.g.,Güth and Yaari, 1992;Heifetz and Segev, 2004;Dekel, Ely, and Yilankaya, 2007;Heifetz, Shannon, and Spiegel, 2007;Herold and Kuzmics, 2009;Heller and Winter, 2020).…”

Anchored strategic reasoning

“…Note the difference between this concept and the concept of biased-based equilibrium Heller and Winter (2020). consider a game by which beliefs about the opponent's strategy is the function of the opponent's strategy, hence, they are not influenced by an exogenous factor.6 Note that the cumulative distribution function in the case of complete information is particularly simple as qi is deterministic.…”