When to copy or avoid an opponent's strategy

Models of two-player games are analyzed in which contestants strive to maximize relative success (market share). Each contestant divides its resources among a set of investment strategies. For a particular investment strategy the contestants may receive different expected rates of return. Each strategy also returns to both contestants an additional payoff that is unpredictable. Depending on particular assumptions, a contestant may maximize relative success by copying or avoiding its opponent's allocation pattern. In other cases a contestant may be favored to diversify its investments equally among strategies and minimize its total variance in returns, or to invest only in one strategy and maximize its total variance in returns.