Perceived Competition

We often compete for resources with an imperfect knowledge of the intensity of competition. We introduce a model in which such imperfect knowledge is made explicit through a perception network and with the notion of perception-consistent equilibrium (PCE) where agents’ actions are guided by the feedback structure provided by the perception network. We prove the existence of an equilibrium for a large class of competitive aggregative games. At each PCE, agents’ actions are proportional to an ordinal centrality measure (Sadler, 2020). For a subclass of games, actions are ordered according to eigenvector centrality, making explicit the endogenous reflection of the perception network on equilibrium actions. We characterize all PCEs based on an intuitive graph decomposition and an ordering of communities obtained from the perception network. The multiplicity of equilibria is the norm; in particular, inclusive equilibria co-exist with exclusionary equilibria that display local pockets of inactivity and market exclusion. By considering networks based on agents’ subjective perceptions of competition, we highlight a novel channel to uncover the unequal resource distribution and profits of seemingly identical agents, a feature otherwise unexplained by the fundamentals of the economy (e.g. differences in firms’ level of innovation).