Perceived competition in networks

Abstract

We consider an aggregative game in which agents have an imperfect knowledge about the set of agents they are in competition with. We model this lack of knowledge through a directed graph that we call the perception network. In this framework, a natural equilibrium concept emerges, the Perception-Consistent Equilibrium (PCE). At a PCE, each agent chooses an action level that maximizes her subjective perceived utility while the action levels of all individuals must be consistent. We prove the existence of PCEs in a large class of aggregative games. We also show that, at any PCE, the efforts are always ordered accordingly to some centrality measure in the perception network. For a specific subclass of aggregative games, we decompose the network into communities and completely characterize the PCEs by identifying which sets of agents are active, as well as their effort level. We prove that, at the unique stable PCE, the agents’ action levels are proportional to their eigenvector centrality in the perception network. We illustrate our results with two well-known models: Tullock contest and Cournot competition.