= Lottery over joint action profiles
{title2=$\rho_{ij}\geq0,\quad\sum_{ij}\rho_{ij}=1$}
= Correlated payoff lottery
{synonym}
A probability distribution over joint action profiles implements a <convex combination> of their two-player payoff vectors. The attainable expected payoffs form the <convex hull> of the pure joint payoffs. The distribution need not factor into independent <mixed strategies>, and a freely enforceable lottery need not satisfy the incentive constraints of a <Nash equilibrium>.
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