A Note on Purifying Mixed Strategy Equilibria in the Search Model of Money

The simple search-theoretic model of fiat money has three symmetric Nash equilibria: all agents accept money with probability 1; all agents accept money with probability 0; and all agents accept money with probability y ε (0,1). Here we construct a nonsymmetric pure strategy equilibrium, payoff-equivalent to the symmetric mixed strategy equilibrium, where a fraction N ε (0,1) of agents always accept money and 1-N never accept money. Count to what has been conjectured previously, we find N>y. We also study evolutionary dynamics, and show that the economy converges to monetary exchange if the initial proportion of agents accepting money exceeds N.