Evolutionary Forces in a Banking System with Speculation and System Risk

For an N players coordination games, Tanaka (2000) proved that the notion of N/2 stability defined by Schaffer (1988) is a necessary and sufficient condition for such a long run equilibrium in an evolutionary process with mutations (in the sense of Kandori, et. al. (1993)). We argue that the critical number in Schaffer’s stability is not unique in every application, but can vary with variables determined before the coordination games. In our specific model, these variables are the portfolio choices of the banks. We derived a Z* stability condition for the long run equilibrium for the banking system, in which there is no speculative bank run. This critical number of players is a function of the size for risky investment, and varies with total risky investments when there are more than two banks. We use this framework to analyze the effect of speculative behavior on banks’ risk taking and the phenomenon of system risk, calculating the probability when more than one banks fail together (system risk).