Working Paper: CEPR ID: DP3814
Authors: Martin Cripps; Godfrey Keller; Sven Rady
Abstract: This Paper studies a game of strategic experimentation with two-armed bandits whose risky arm might yield a pay-off only after some exponentially distributed random time. Because of free-riding, there is an inefficiently low level of experimentation in any equilibrium where the players use stationary Markovian strategies with posterior beliefs as the state variable. After characterizing the unique symmetric Markovian equilibrium of the game, which is in mixed strategies, we construct a variety of pure-strategy equilibria. There is no equilibrium where all players use simple cut-off strategies. Equilibria where players switch finitely often between the roles of experimenter and free-rider all lead to the same pattern of information acquisition; the efficiency of these equilibria depends on the way players share the burden of experimentation among them. In equilibria where players switch roles infinitely often, they can acquire an approximately efficient amount of information, but the rate at which it is acquired still remains inefficient; moreover, the expected pay-off of an experimenter exhibits the novel feature that it rises as players become more pessimistic. Finally, over the range of beliefs where players use both arms a positive fraction of the time, the symmetric equilibrium is dominated by anyasymmetric one in terms of aggregate pay-offs.
Keywords: Bayesian learning; Exponential distribution; Markov perfect equilibrium; Public goods; Strategic experimentation; Two-armed bandits
JEL Codes: C73; D83; H41; O32
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| freeriding (H40) | inefficiently low level of experimentation (C93) |
| players' beliefs (Z22) | strategic choices (L21) |
| type of equilibrium (D50) | efficiency of outcomes (D61) |
| players' sharing of experimentation burden (C90) | efficiency of information acquisition (D83) |
| equilibria where players switch roles (C73) | constant amount of information acquisition (D83) |
| expected payoff of an experimenter (C99) | players become more pessimistic (C73) |