Super- and submodularity of stopping games with random observations
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Super- and submodularity of stopping games with random observations Svetlana Boyarchenko1 Received: 22 November 2018 / Accepted: 8 May 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract Models of learning and experimentation based on two-armed Poisson bandits addressed several important aspects related to strategic and motivational learning, but they are not suitable to study effects that accumulate over time. We propose a new class of models of strategic experimentation which are almost as tractable as exponential models, but incorporate such realistic features as dependence of the expected rate of news arrival on the time elapsed since the start of an experiment. In these models, the experiment is stopped before news is realized whenever the rate of arrival of news reaches a critical level. This leads to longer experimentation times for experiments with possible breakthroughs than for equivalent experiments with failures. We also show that the game with conclusive failures is supermodular, and the game with conclusive breakthroughs is submodular. Keywords Stopping games · Supermodular games · Time-inhomogeneous Poisson process
I am grateful to the Editor and two anonymous referees for their valuable comments. I am thankful for discussions of earlier versions of the paper to participants of research seminars at Institut Henri Poincaré, Bielefeld University, Toulouse School of Economics, Carlos III University of Madrid, Tilburg University, The Center for Rationality in the Hebrew University of Jerusalem, the University of Tel Aviv, Haifa University, Rice University, the Research University Higher School of Economics, Moscow and St. Petersburg, and Texas A&M University. I am thankful for discussions to Rabah Amir, Adrien Blanchet, Jean-Paul Decamps, Hülya Eraslan, William Fuchs, Ángel Hernando-Veciano, Kuno Huisman, Ilan Kremer, Peter Kort, Rida Laraki, Ehud Lehrer, Amnon Maltz, Abraham Neyman, Mallesh Pai, Sven Rady, Frank Riedel, Anna Rubinchik, Maher Said, Larry Samuelson, Elon Solan, Jan-Henrik Steg, Max Stinchcombe, Jusso Välimäki, Nicolas Vieille, and Eyal Winter. I benefited from the feedback of participants of the following conferences: The 71st European Meeting of the Econometric Society, August 27–31, Cologne, Germany; International Conference on Game Theory, Stony Brook University, July 16–20, 2018, Stony Brook, NY; XXVII European Workshop on General Equilibrium Theory (EWGET 2018), June 27–29, 2018, University Paris 1 Panthéon-Sorbonne, Centre d’Economie de la Sorbonne & Paris School of Economics, Paris, France; The 2018 North American Summer Meeting of the Econometric Society, June 21–24, University of California, Davis, CA. The usual disclaimer applies.
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Svetlana Boyarchenko [email protected] The University of Texas at Austin, 2225 Speedway Stop C3100, Austin, TX 78712, USA
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JEL Classification C73 · C61 · D81
1 Introduction This paper brings together two strands of literature: stopping games in continuous time with random observations and super(su
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