Reproducing a Nash-Equilibrium macrostate in a price-setting game under local interactions

We develop an interaction-based model grounded in the concept of Nash equilibrium to examine how changes in the amount of money in circulation - representing nominal aggregate demand - affect the average price level and aggregate output. The economy consists of a large number of producers, each of whom must predict the average price level in order to set a payoff-maximizing price. Producers periodically choose between two prediction strategies: an extrapolative strategy, anchored to the one-period-lagged price level and therefore costless, and a probing strategy, based on a costly random search over other producers. Numerical simulations are used to investigate the coevolution of the microstate - represented by the frequency distribution of prediction strategies across producers - and the macrostate - represented by the average price level and aggregate output. The simulations show that the system converges to a steady microstate in which producers use heterogeneous prediction strategies. This heterogeneity arises because producers set their payoff-maximizing prices under incomplete and local information. Nevertheless, the resulting steady macrostate is characterized by an average price level and aggregate output that are approximately equivalent to those of the symmetric Nash equilibrium that would emerge if all producers had complete information and correctly anticipated that the other producers would behave likewise.