Competitive Nash Equilibria and Two Period Fund Separation

We suggest a simple asset market model in which we analyze competitive and strategic behavior simultaneously. If for competitive behavior two-fund separation holds across periods then it also holds for strategic behavior. In this case the relative prices of the assets do not depend on whether agents behave strategically or competitively. Those agents acting strategically will however invest less in the common mutual fund. Constant relative risk aversion and absence of aggregate risk are shown to be two alternative sufficient conditions for two-period fund separation. With derivatives further strategic aspects arise and strategic behavior is distinct from competitive behavior even for those utility functions leading to two-fund separation.