[The existence of perfect equilibrium is demonstrated for a class of games with compact space of histories and continuous payoffs, and in which the set of actions feasible at any given period is a lower hemicontinuous correspondence of the previous history of the game. The proof is by construction. A set of histories is constructed, each of which is the equilibrium path of some perfect equilibrium point of the game. Also, any equilibrium path is a member of this set. The construction therefore provides a characterization of perfect equilibrium.]

Laboratory and field studies of time preference find that discount rates are much greater in the short-run than in the long-run. Hyperbolic discount functions capture this property. This paper solves the decision problem of a hyperbolic consumer who faces stochastic income and a borrowing constraint. The paper uses the bounded variation calculus to derive the Hyperbolic Euler Relation, a natural generalization of the standard Exponential Euler Relation. The Hyperbolic Euler Relation implies that consumers act as if they have endogenous rates of time preference that rise and fall with the future marginal propensity to consume (e.g., discount rates that endogenously range from 5% to 41% for the example discussed in the paper).

This paper extends the classic two-armed bandit problem to a many-agent setting in which N players each face the same experimentation problem. The main change from the single-agent problem is that an agent can now learn from the current experimentation of other agents. Information is therefore a public good, and a free-rider problem in experimentation naturally arises. More interestingly, the prospect of future experimentation by others encourages agents to increase current experimentation, in order to bring forward the time at which the extra information generated by such experimentation becomes available. The paper provides an analysis of the set of stationary Markov equilibria in terms of the free-rider effect and the encouragement effect.

Christopher Harris, Philip Reny, Arthur Robson, The Existence of Subgame-Perfect Equilibrium in Continuous Games with Almost Perfect Information: A Case for Public Randomization, Econometrica, Vol. 63, No. 3 (May, 1995), pp. 507-544