Information sharing for a coordination game in fluctuating environments

Collective action dilemmas pervade the social and biological sciences - from human decision-making to bacterial quorum sensing. In these scenarios, individuals sense cues from the environment to adopt a suitable phenotype or change in behavior. However, when cues include signals from other individuals, then the appropriate behavior of each individual is linked. Here, we develop a framework to quantify the influence of information sharing on individual behavior in the context of two player coordination games. In this framework, the environment stochastically switches between two states, and the state determines which one of two actions players must coordinate on. Given a stochastically switching environment, we then consider two versions of the game that differ in the way players acquire information. In the first model, players independently sense private environmental cues, but do not communicate with each other. We find there are two types of strategies that emerge as Nash equilibria and fitness maximizers - players prefer to commit to one particular action when private information is poor, or prefer to employ phenotypic plasticity when it is good. The second model adds an additional layer of communication, where players share social cues as well. When the quality of social information is high, we find the socially optimal strategy is a novel \"majority logic\" strategy that bases decision-making on social cues. Our game-theoretic approach offers a principled way of investigating the role of communication in group decision-making under uncertain conditions.