A Necessary and Sufficient Condition for Convergence of Statistical to Strategic Equilibria of Market Games

In our model, we treat a market game where traders are heterogeneous not only with respect to their rationality level but also with the formation of their subjective beliefs for the strategy of their opponents. Under these conditions, the market mechanism results a statistical equilibrium, where traders randomise among their available actions due to their limited rationality. Here, we provide a necessary and sufficient condition for convergence of statistical to strategic equilibria of market games, when traders become more informed and increasingly rational.