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 any asymmetric one in terms of aggregate pay-offs.
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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number
3814.
Find related papers by JEL classification: C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information H41 - Public Economics - - Publicly Provided Goods - - - Public Goods O32 - Economic Development, Technological Change, and Growth - - Technological Change - - - Management of Technological Innovation and R&D
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Godfrey Keller & Sven Rady, 2009.
"Strategic Experimentation with Poisson Bandits,"
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Nicolas Klein & Sven Rady, 2008.
"Negatively Correlated Bandits,"
Discussion Papers
243, SFB/TR 15 Governance and the Efficiency of Economic Systems, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
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Francisco J. Buera & Alexander Monge-Naranjo & Giorgio E. Primiceri, 2008.
"Learning the Wealth of Nations,"
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Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2004.
"Social Learning in One-Arm Bandit Problems,"
Discussion Papers
1396, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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Daniel Krähmer, 2005.
"Equilibrium Learning in Simple Contests,"
Discussion Papers
73, SFB/TR 15 Governance and the Efficiency of Economic Systems, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
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