Ugo Bolletta: ugo.bolletta[at]univ-amu.fr
Mathieu Faure: mathieu.faure[at]univ-amu.fr
In this paper, we define strategic advantage for general games with strategic complementarities. The strategic advantage of a player is its relative performance against similar and sufficiently smart players. The definition, inspired by the beauty contest proposed by Nagel (AER, 1996), also allows us to compare games in terms of their strategic fairness. We first characterize the equilibrium in a networked guessing game, a natural extension of Nagel's guessing game, that allows for strategic heterogeneity. Thereby we find that equilibrium uniqueness directly relates to the network of dependencies ($i.e.,$ disregarding specific weights). Second, we define and characterize strategic advantage in smooth supermodular games: when agents are sufficiently rational, strategic advantage is fully captured by the dominant eigenvector of the Jacobian matrix of best replies at the equilibrium point. In a guessing game, strategic advantage translates simply into the probability of getting trapped in an anchor during a random walk in the network. Finally, we analyze in the laboratory how network structure and position may determine outcomes in our guessing game. Our results support the hypothesis that individuals with lower strategic advantage (which translates into a higher "distance" to the game's anchor points) are those who perform worse. We show how strategic advantage can also be used in a simple way to retrieve individuals' levels of reasoning based on a set of choices.