Estimation of Equilibria in an Advertising Game with Unknown Distribution of the Response to Advertising Efforts

We study a class of discrete-time advertising game with random responses to the advertising efforts made by a duopoly. The firms are assumed to observe the values of the random responses but they do not know their distributions. With the recorded values, firms estimate distributions and play estimated equilibrium strategies. Under suitable assumptions, we prove that the estimated equilibrium strategies converge to equilibria of the advertising game with the true distributions. Our results are numerically illustrated for specific cases.