Does it matter to play Nash: the case of adaptive sellers ?

Usual models of search markets describe the equilibrium pricing strategies of sellers confronted to a population of buyers searching for the best deal: in equilibrium, a seller perfectly anticipates both the pricing strategy of his rivals and the search behaviour of buyers, and optimally responds to it. We show in this paper that “less rational” sellers are not able to learn this Nash-equilibrium pricing rule through adaptation and repeated interactions. The strategy of sellers can be summed by the distribution of posted prices. Using an analytical model characterized by consumers using a fixed-sample size searching rule, we first define the variance and mean of this price distribution. We then compare the characteristics of this Nash-theoretical distribution with the one obtained through a reinforcement learning process. Interestingly, we show that the qualitative properties of the Nash search equilibrium (NSE) of changes in the market structure are still valid for the RL distribution. That is, mean price and variance exhibit similar variations to a change in the degree of information of consumers.