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Strategic experimentation with asymmetric players.
Kaustav Das1, Nicolas Klein2, Katharina Schmid3
1University of Exeter Business School, Exeter, UK.
Economic Theory
|July 21, 2020
Summary
This study on a two-player bandit game shows that asymmetric players can reach a welfare-dominant equilibrium using cut-off strategies, unlike symmetric players. The amount of experimentation is constant across equilibria.
Area of Science:
- Game Theory
- Econometrics
- Decision Theory
Background:
- Examines a two-player game with two-armed exponential bandits.
- Players utilize distinct technologies for exploring a risky option, as per Keller et al. (2005).
Purpose of the Study:
- Characterize the set of Markov perfect equilibria in this asymmetric bandit game.
- Investigate the existence and properties of cut-off strategies for players with differing technologies.
Main Methods:
- Analysis of Markov perfect equilibria in a two-player exponential bandit setting.
- Comparative statics on player asymmetry and its impact on equilibrium strategies.
Main Results:
- An equilibrium always exists where the player with inferior technology uses a cut-off strategy.
- All Markov perfect equilibria yield the same total experimentation but vary in uncertainty resolution speed.
- A welfare-dominant Markov perfect equilibrium with mutual cut-off strategies exists only when player asymmetry is sufficiently high.
Conclusions:
- High asymmetry enables a superior welfare equilibrium with mutual cut-off strategies, contrasting with symmetric cases.
- The speed of uncertainty resolution, not the total amount of experimentation, differentiates equilibria.
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