Competing Conventions with Costly Information Acquisition

Abstract

We consider an evolutionary model of social coordination in a 2 × 2 game where two groups of players prefer to coordinate on different actions. Players can pay a cost to learn their opponent’s group: if they pay it, they can condition their actions concerning the groups. We assess the stability of outcomes in the long run using stochastic stability analysis. We find that three elements matter for the equilibrium selection: the group size, the strength of preferences, and the information’s cost. If the cost is too high, players never learn the group of their opponents in the long run. If one group is stronger in preferences for its favorite action than the other, or its size is sufficiently large compared to the other group, every player plays that group’s favorite action. If both groups are strong enough in preferences, or if none of the groups’ sizes is large enough, players play their favorite actions and miscoordinate in inter-group interactions. Lower levels of the cost favor coordination. Indeed, when the cost is low, in inside-group interactions, players always coordinate on their favorite action, while in inter-group interactions, they coordinate on the favorite action of the group that is stronger in preferences or large enough.

Ethnicity and Cultural Dynamics

“…The Cross-cultural Competence Model demonstrates the potentially important role that cross-cultural competence can play in cultural dynamics in ethnically-structured populations (see also Rozzi (2021) for a similar model and compatible conclusions). Note, however, that the model is limited to a single generation and homogeneous interactions among in-and out-group members (i.e., a simplistic interaction network structure).…”

Statistical inference in evolutionary dynamics

“…The game of this type is studied in Salant and Cherry (2020). It captures the nature of anti-coordination -agents have an incentive to differ from others.…”

“…The equilibrium selection problem in coordination games lies at the heart of evolutionary game theory starting from Foster and Young (1990), Young (1993) and Kandori et al (1993). See more recent contributions by Maruta (2002), Blume (2003), Peski (2010), Sandholm (2010), Neary (2012), Staudigl (2012), Staudigl and Weidenholzer (2014), Kreindler andYoung (2013) Sandholm andStaudigl (2016), Hwang and Newton (2017), Sawa and Wu (2018a,b), Nax and Newton (2019), Bilancini and Boncinelli (2020), Hwang and Rey-Bellet (2021), Newton (2021), andRozzi (2021), among many others. We investigate if our Bayesian dynamic has any equilibrium selection property.…”

“…Since agents' preferences are diverse, we propose a solution concept called the Bayesian SESI, in which each agent bestresponds to the estimate derived from the drawn sample using statistical inference. Though it is conceptually equivalent to the original SESI in Salant and Cherry (2020), it provides a formal mathematical expression for the action distribution for each preference. Then we propose a Bayesian k-sampling statistical inference best response dynamic (Bayesian dynamic, for short) based on the evolutionary model with heterogeneous preferences (Ely and Sandholm 2005).…”

“…Then we propose a Bayesian k-sampling statistical inference best response dynamic (Bayesian dynamic, for short) based on the evolutionary model with heterogeneous preferences (Ely and Sandholm 2005). 1 The Bayesian dynamic gives rise to a simple aggregate dynamic with one variable, the proportion of agents playing one of the actions, which coincides with the dynamic in Salant and Cherry (2020). Our first main result shows that the Bayesian dynamic converges to a Bayesian SESI if and only if the aggregate dynamic converges to the corresponding SESI proportion.…”