Discussion Papers

Experimentation in Two-Sided Markets

Abstract:

We study optimal experimentation by a monopolistic platform in a two-sided market framework. The platform provider faces uncertainty about the strength of the externality each side is exerting on the other. It maximizes the expected present value of its profit stream in a continuous-time infinite-horizon framework by setting participation fees or quantities on both sides. We show that a price-setting platform provider sets a fee lower than the myopically optimal level on at least one side of the market, and on both sides if the two externalities are of approximately equal strenght. If the externality that one side exerts is sufficiently weaker than the externality it experiences, the optimal fee on this side exceeds the myopically optimal level. We obtain analogous results for expected prives when the platform provider chooses quantities. While the optimal policy does not admin closed-form representations in general, we identify special cases in which the undiscounted limit of the model can be solved in closed form.

 

Keywords: Two-Sided Market, Network Effects, Monopoly Experimentation, Bayesian Learning, Optimal Control

JEL-Classification: D42, D83, L12

Full text in pdf format:

365.pdf

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Dynamic Coordination via Organizational Routines

Abstract:

We investigate dynamic coordination among members of a problem solving team who receive private signals about which of their actions are required for a (static) coordinated solution and who have repeated opportunities to explore different action combinations. In this environment ordinal equilibria, in which agents condition only on how their signals rank their actions and not on signal strength, lead to simple patterns of behavior that have a natural interpretation as routines. These routine spartially solve the team’s coordination problem by synchronizing the team’s search efforts and prove to be resilient to changes in the environment by being expost equilibria, to agents having only a coarse understanding of other agents’ strategies by being fully cursed, and to natural forms of agents’ overconfidence. The price of this resilience is that optimal routines are frequently not optimal equilibria.

 

January 2011

 

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355.pdf

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Strategic Learning in Teams

Abstract:

This paper analyzes a two-player game of strategic experimentation with three-armed exponential bandits in continuous time. Players face replica bandits, with one arm that is safe in that it generates a known payoff, whereas the likelihood of the risky arms’ yielding a positive payoff is initially unknown. It is common knowledge that the types of the two risky arms are perfectly negatively correlated. I show that the efficient policy is incentive-compatible if, and only if, the stakes are high enough. Moreover, learning will be complete in any Markov perfect equilibrium with continuous value functions if, and only if, the stakes exceed a certain threshold.

 

Keywords: Strategic Experimentation, Three-Armed Bandit, Exponential Distribution, Poisson Process, Bayesian Learning, Markov Perfect Equilibrium
JEL Classification: C73, D83, O32

July 2010

 

Full text in pdf format:

333.pdf

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Technology Adoption, Social Learning, and Economic Policy

Abstract:

We study a two-player dynamic investment model with information externalities and provide necessary and sufficient conditions for a unique switching equilibrium. When the public information is sufficiently high and a social planer therefore expects an investment boom, investments should be taxed. Conversely, any positive investment tax is suboptimally high if the public information is sufficiently unfavorable.We also show that an investment tax may increase overall investment activity.

 

Keywords: Information Externality, Strategic Waiting, Delay, Information Cascade, Investment Boom, Optimal Taxation

JEL Classification: D62, D83

February 2010

 

Full text in pdf format:

306.pdf

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Screening and Merger Activity

Abstract:

In our paper targets, by setting a reserve price, screen acquirers on their (expected) ability to generate merger-specific synergies. Both empirical evidence and many common merger models suggest that the difference between high- and low-synergy mergers becomes smaller during booms. This implies that the target’s opportunity cost for sorting out relatively less fitting acquirers increases and, hence, targets screen less tightly during booms, which leads to a hike in merger activity. Our screening mechanism not only predicts that merger activity is intense during economic booms and subdued during recessions but is also consistent with other stylized facts about takeovers and generates novel testable predictions.

 

Keywords: Takeovers, Merger Waves, Defense Tactics, Screening

JEL Classification: D21, D80, L11.

August 2009

 

Full text in pdf format:

270.pdf

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Strategic Experimentation with Poisson Bandits

Abstract:

We study a game of strategic experimentation with two-armed bandits where the risky arm distributes lump-sum payoffs according to a Poisson process. Its intensity is either high or low, and unknown to the players. We consider Markov perfect equilibria with beliefs as the state variable. As the belief process is piecewise deterministic, payoff functions solve differential-difference equations.  here is no equilibrium where all players use cut-off strategies, and all equilibria exhibit an ‘encouragement effect’ relative to the single-agent optimum. We construct asymmetric equilibria in which players have symmetric continuation values at sufficiently optimistic beliefs yet take turns playing the risky arm before all experimentation stops. Owing to the encouragement effect, these equilibria Pareto dominate the unique symmetric one for sufficiently frequent turns. Rewarding the last experimenter with a higher continuation value increases the range of beliefs where players experiment, but may reduce average payoffs at more optimistic beliefs. Some equilibria exhibit an ‘anticipation effect’: as beliefs become more pessimistic, the continuation value of a single experimenter increases over some range because a lower belief means a shorter wait until another player takes over.

 

Keywords: Strategic Experimentation, Two-Armed Bandit, Poisson Process, Bayesian Learning, Piecewise Deterministic Process, Markov Perfect Equilibrium, Differential-Difference Equation

JEL Classification: C73, D83, O32

May 2009

 

Full text in pdf format:

260.pdf

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Negatively Correlated Bandits

Abstract:

We analyze a two-player game of strategic experimentation with two-armed bandits. Each player has to decide in continuous time whether to use a safe arm with a known payoff or a risky arm whose likelihood of delivering payoffs is initially unknown. The quality of the risky arms is perfectly negatively correlated between players. In marked contrast to the case where both risky arms are of the same type, we find that learn- ing will be complete in any Markov perfect equilibrium if the stakes exceed a certain threshold, and that all equilibria are in cutoff strategies. For low stakes, the equilib- rium is unique, symmetric, and coincides with the planner's solution. For high stakes, the equilibrium is unique, symmetric, and tantamount to myopic behavior. For inter- mediate stakes, there is a continuum of equilibria.

Keywords: Strategic Experimentation, Two-Armed Bandit, Exponential Distribution, Poisson Process, Bayesian Learning, Markov Perfect Equilibrium
JEL Classification: C73, D83, O32
August 2008

 

Full text in pdf format:

243.pdf

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