Risk-bearing in a winner-take-all contest

A parsimonious model is used to explore the risk-bearing decision under a payoff structure that emphasizes relative performance. Equilibrium betting amounts are derived for players who start with unequal endowments and face a lottery that offers either a positive or negative expected return. If the lottery offers negative expected return, disadvantaged players are willing to risk a portion of their endowment, and this induces advantaged players to also gamble, defensively. Although there are equilibria in which the advantaged preemptively gamble more than the disadvantaged, in the robust equilibrium it is the disadvantaged who make the larger bets. If the lottery offers positive expected return, there are equilibria in which the advantaged invest less than the disadvantaged, but full investment by all players is a more robust equilibrium.