We consider a two player dynamic game played over T \leq \infty periods. In each period each player chooses any probability distribution with support on [0,1] with a given mean, where the mean is the realized value of the draw from the previous period. The player with the highest realization in the period achieves a payoff of 1, and the other player, 0; and each player seeks to maximize the discounted sum of his per-period payoffs over the whole time horizon. We solve for the unique subgame perfect equilibrium of this game, and establish properties of the equilibrium strategies and payoffs in the limit. 
We consider a two player dynamic game played over T \leq \infty periods. In each period each player chooses any probability distribution with support on [0,1] with a given mean, where the mean is the realized value of the draw from the previous period. The player with the highest realization in the period achieves a payoff of 1, and the other player, 0; and each player seeks to maximize the discounted sum of his per-period payoffs over the whole time horizon. We solve for the unique subgame perfect equilibrium of this game, and establish properties of the equilibrium strategies and payoffs in the limit. The solution and comparative statics thereof provide insight about intertemporal choice with status concerns. In particular we find that patient players take fewer risks.
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The solution and comparative statics thereof provide insight about intertemporal choice with status concerns. In particular we find that patient players take fewer risks.