 Marginal-equivalent equilibria in additive contests

If contest rewards and costs add, a fixed deviation's expected payoff depends on each rival's per-contest marginal distributions, rather than on dependence between that rival's efforts across contests. Replacing the conditional independent sampling of two active efforts by another copula with the same conditional marginals therefore preserves every deviation payoff. Consequently it preserves the Nash equilibrium, even when the new joint strategy distribution is different. This explains why unique participation probabilities and bid marginals need not imply a unique full mixed strategy.