Repeated games with stochastic discounting
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This paper provides folk theorems for infinitely repeated games where the discount factor is stochastic. When discount factors are independently distributed and the current discount factor is unobservable prior to current actions, standard trigger strategies support a 'full' folk theorem when the infimum of the mean of the sequence of discount factors is sufficiently close to one. When players choose actions in each period after having observed the current discount factor, this result breaks down; payoffs on the boundary of the set of individually rational payoffs are unobtainable as Nash equilibrium average payoffs to the supergame. In order to highlight the impact of stochastic discounting on the analysis of supergames, we provide the stochastic discounting analogue to Friedman's perfect folk theorem.
