Multiplayer Bandit Learning, from Competition to Cooperation
Simina Br\^anzei and
Papers from arXiv.org
The stochastic multi-armed bandit model captures the tradeoff between exploration and exploitation. We study the effects of competition and cooperation on this tradeoff. Suppose there are $k$ arms and two players, Alice and Bob. In every round, each player pulls an arm, receives the resulting reward, and observes the choice of the other player but not their reward. Alice's utility is $\Gamma_A + \lambda \Gamma_B$ (and similarly for Bob), where $\Gamma_A$ is Alice's total reward and $\lambda \in [-1, 1]$ is a cooperation parameter. At $\lambda = -1$ the players are competing in a zero-sum game, at $\lambda = 1$, they are fully cooperating, and at $\lambda = 0$, they are neutral: each player's utility is their own reward. The model is related to the economics literature on strategic experimentation, where usually players observe each other's rewards. With discount factor $\beta$, the Gittins index reduces the one-player problem to the comparison between a risky arm, with a prior $\mu$, and a predictable arm, with success probability $p$. The value of $p$ where the player is indifferent between the arms is the Gittins index $g = g(\mu,\beta) > m$, where $m$ is the mean of the risky arm. We show that competing players explore less than a single player: there is $p^* \in (m, g)$ so that for all $p > p^*$, the players stay at the predictable arm. However, the players are not myopic: they still explore for some $p > m$. On the other hand, cooperating players explore more than a single player. We also show that neutral players learn from each other, receiving strictly higher total rewards than they would playing alone, for all $ p\in (p^*, g)$, where $p^*$ is the threshold from the competing case. Finally, we show that competing and neutral players eventually settle on the same arm in every Nash equilibrium, while this can fail for cooperating players.
Date: 2019-08, Revised 2019-10
New Economics Papers: this item is included in nep-exp, nep-gth and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed
Downloads: (external link)
http://arxiv.org/pdf/1908.01135 Latest version (application/pdf)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1908.01135
Access Statistics for this paper
More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().