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

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.