# Fabrizio Panebianco

## IBD Salle 21

AMU - AMSE

5-9 boulevard Maurice Bourdet

13001 Marseille

Ugo Bolletta: ugo.bolletta[at]univ-amu.fr

Mathieu Faure: mathieu.faure[at]univ-amu.fr

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 they payoff depends 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 his subjective expected payoff and update his beliefs according to what he observes. In particular, assume that each agent only observes his realized payoff. A steady state of such dynamic is a self-confirming equilibrium given the assumed feedback. We characterize the structure of the set of self-confirming equilibria in network games and we relate self-confirming and Nash equilibrium. 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 self-confirming equilibrium. We also study learning dynamics and show how agents can get stuck in non-Nash self-confirming equilibria. In such dynamics, the set of inactive agents can only increase in time, because once an agent finds it optimal to be inactive, he gets no feedback about the payoff state, hence does not change his beliefs and remains inactive.