Learning and Selfconfirming Equilibria in Network Games

Consider a set of agents who play a network game repeatedly. Agents may not know the network. They may even be unaware that they are interacting with other agents in a network. Possibly, they just understand that their payoffs depend on an unknown state that in reality is an aggregate of the actions of their neighbors. Each time, every agent chooses an action that maximizes her subjective expected payoff and then updates her beliefs according to what she observes. In particular, we assume that each agent only observes her realized payoff. A steady state of such dynamic is a selfconfirming equilibrium given the assumed feedback. We characterize the structure of the set of selfconfirming equilibria in network games and we relate selfconfirming and Nash equilibria. Thus, we provide conditions on the network under which the Nash equilibrium concept has a learning foundation, despite the fact that agents may have incomplete information. In particular, we show that the choice of being active or inactive in a network is crucial to determine whether agents can make correct inferences about the payoff state and hence play the best reply to the truth in a selfconfirming equilibrium. We also study learning dynamics and show how agents can get stuck in non--Nash selfconfirming equilibria. In such dynamics, the set of inactive agents can only increase in time, because once an agent finds it optimal to be inactive, she gets no feedback about the payoff state, hence she does not change her beliefs and remains inactive

Dispersed Behavior and Perceptions in Assortative Societies

We take an equilibrium-based approach to study the interplay between behavior and misperceptions in coordination games with assortative interactions. Our focus is assortativity neglect, where agents fail to take into account the extent of assortativity in society. We show, first, that assortativity neglect amplifies action dispersion, both in fixed societies and by exacerbating the effect of social changes. Second, unlike other misperceptions, assortativity neglect is a misperception that agents can rationalize in any true environment. Finally, assortativity neglect provides a lens through which to understand how empirically documented misperceptions about distributions of population characteristics (e.g., income inequality) vary across societies

Dispersed Behavior and Perceptions in Assortative Societies

We formulate a model of social interactions and misinferences by agents who neglect assortativity in their society, mistakenly believing that they interact with a representative sample of the population. A key component of our approach is the interplay between this bias and agents’ strategic incentives. We highlight a mechanism through which assortativity neglect, combined with strategic complementarities in agents’ behavior, drives up action dispersion in society (e.g., socioeconomic disparities in education investment). We also suggest that the combination of assortativity neglect and strategic incentives may be relevant in understanding empirically documented misperceptions of income inequality and political attitude polarization