Undiscounted bandit games - Godfrey Keller; Sven Rady (Sonderforschungsbereich/Transregio 15 - Governance and the Efficiency of Economic Systems (GESY), 2015)
We analyze continuous-time games of strategic experimentation with two-armedbandits when there is no discounting. We show that for all specifications of priorbeliefs and payoff-generating processes that satisfy some separability condition, the unique symmetric Markov perfect equilibrium can be computed in a simple closed form involving only the expected current payoff of the risky arm and the expected full-information payoff, given current information. The separability condition holds in a variety of models that have been explored in the literature, all of which assume that the risky arm's expected payoff per unit of time is time-invariant and actual payoffs are generated by a process with independent and stationary increments. The separability condition does not hold when the expected payoff per unit of time is subject to state-switching.
Keywords: C73; D83; 330; Strategic Experimentation; Two-Armed Bandit; Markov-Perfect Equilibrium