Inference of Signs of Interaction Effects in Simultaneous Games With Incomplete Information

Authors

  • Áureo de Paula,

    1. Dept. of Economics, University College London, Gower Street, London, WC1E 6BT, United Kingdom, CeMMAP, Institute for Fiscal Studies, 7 Ridgmount Street, London WC1E 7AE, United Kingdom, and Dept. of Economics, University of Pennsylvania, 3718 Locust Walk, Philadelphia, PA 19104, U.S.A.; aureo@sas.upenn.edu
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  • Xun Tang

    1. Dept. of Economics, University College London, Gower Street, London, WC1E 6BT, United Kingdom, CeMMAP, Institute for Fiscal Studies, 7 Ridgmount Street, London WC1E 7AE, United Kingdom, and Dept. of Economics, University of Pennsylvania, 3718 Locust Walk, Philadelphia, PA 19104, U.S.A.; aureo@sas.upenn.edu
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    • We thank Andres Aradillas-Lopez, Federico Bugni, Ivan Canay, Andrew Chesher, Steve Durlauf, George Deltas, Yanqin Fan, Hanming Fang, Paul Grieco, Phil Haile, Jim Heckman, Bo Honoré, Jean-Francois Houde, Steffen Huck, John Kennan, Ivana Komunjer, Tong Li, Chuck Manski, Salvador Navarro, Aviv Nevo, Rob Porter, Seth Richards, Adam Rosen, Andres Santos, Frank Schorfheide, Azeem Shaikh, Matt Shum, Kevin Song, Yixiao Sun, Elie Tamer, Yuanyuan Wan, Haiqing Xu, and participants at various conferences and seminars for helpful comments. We also thank the editor, Jean-Marc Robin, and three anonymous referees for their recommendations. We owe special thanks to Andrew Sweeting for kindly providing us with the data and for helpful suggestions.


Abstract

This paper studies the inference of interaction effects in discrete simultaneous games with incomplete information. We propose a test for the signs of state-dependent interaction effects that does not require parametric specifications of players' payoffs, the distributions of their private signals, or the equilibrium selection mechanism. The test relies on the commonly invoked assumption that players' private signals are independent conditional on observed states. The procedure is valid in (but does not rely on) the presence of multiple equilibria in the data-generating process (DGP). As a by-product, we propose a formal test for multiple equilibria in the DGP. We also implement the test using data on radio programming of commercial breaks in the United States, and infer stations' incentives to synchronize their commercial breaks. Our results support the earlier finding by Sweeting (2009) that stations have stronger incentives to coordinate and air commercials at the same time during rush hours and in smaller markets.

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