You play (an action) only once

Consider an N-player normal form game played repeatedly in which each player should choose each strategy exactly one time (payoffs are aggregated). Such “play only once” situations occur naturally in the context of scheduling. Assume that each player has the same number of strategies. Then, regardless of the playersʹ preferences, for each player to mix uniformly in each round over his remaining strategies constitutes a subgame perfect equilibrium.