The asset market game

This paper models asset markets as a game where assets pay according to an arbitrary returns matrix, investors decide on fractions of wealth to allocate to each asset, and prices result from market clearing. The only pure-strategy Nash equilibrium is to split wealth proportionally to the assets' expected returns, which can be interpreted as investing according to the fundamentals. Further, the equilibrium strategy is evolutionarily stable in the sense of Schaffer [Journal of Theoretical Biology 132 (1988) 469-478]. We also study the stability properties of the equilibrium in an evolutionary dynamics where wealth flows with higher probability into those strategies that obtain higher realized payoffs.