Strict pure strategy Nash equilibria in large finite‐player games

In the context of anonymous games (i.e., games where the payoff of a player is, apart from his/her own action, determined by the distribution of the actions made by the other players), we present a model in which, generically (in a precise sense), finite‐player games have strict pure strategy Nash equilibria if the number of agents is large. A key feature of our model is that payoff functions have differentiability properties. A consequence of our existence result is that, in our model, equilibrium distributions of non‐atomic games are asymptotically implementable by pure strategy Nash equilibria of large finite‐player games.

False beliefs can bootstrap cooperative communities through social norms

Building cooperative communities has always been a crucial problem for human societies. Much research suggests that cooperation is facilitated by knowing who exactly is a cooperator and defector, and being able to respond accordingly. As such, anonymous games is thought to hinder cooperation. Here, we show that this conclusion is altered dramatically in the presence of conditional cooperation norms and heterogeneous beliefs about others' behaviours. Specifically, we show that inaccurate beliefs about other players' behaviours can in fact help foster and stabilize cooperation via social norms. To show this, we combine the population dynamics of a social community with the game theory of interactions within the community. In our model, individuals can join a community based on beliefs generated by public signals regarding the level of cooperation within, and decide to cooperate or not depending on these beliefs. These signals may overstate how much cooperation there really is. We show that even if individuals eventually learn the true level of cooperation, the initially false beliefs can trigger a dynamic that sustains high level of cooperation within the community. We also characterize how the rates of joining, leaving, and learning in the community affect the cooperation level and community size simultaneously. Our results illustrate how false beliefs in the presence of conditional cooperation norms can help build up cooperative communities.

Observational learning in large anonymous games

I present a model of observational learning with payoff interdependence. Agents, ordered in a sequence, receive private signals about an uncertain state of the world and sample previous actions. Unlike in standard models of observational learning, an agent's payoff depends both on the state and on the actions of others. Agents want both to learn the state and to anticipate others' play. As the sample of previous actions provides information on both dimensions, standard informational externalities are confounded with payoff externalities. I show that in spite of these confounding factors, when signals are of unbounded strength, there is learning in a strong sense: agents' actions are ex post optimal given both the state of the world and others' actions. With bounded signals, actions approach ex post optimality as the signal structure becomes more informative.