Enriching Interactions: Incorporating Outcome Data into Static Discrete Games

When modeling the behavior of firms, marketers and micro-economists routinely confront complex problems of strategic interaction. In competitive environments, firms make strategic decisions that not only depend on the features of the market, but also on their beliefs regarding the reactions of their rivals. Structurally modeling these interactions requires formulating and estimating a discrete game, a task which, until recently, was considered intractable. Fortunately, two-step estimation methods (imported from the auction literature) have cracked the problem, fueling a growing literature in both marketing and economics that tackles a host of issues from the optimal design of ATM networks to the choice of pricing strategy. However, most existing methods have focused on only the discrete choice of actions, ignoring a wealth of information contained in post-choice outcome data and severely limiting the scope for performing informative counterfactuals or identifying the deep structural parameters that drive strategic decisions. The goal of this paper is to provide a method for incorporating post-choice outcome data into static discrete games of incomplete information. In particular, our estimation approach adds a selection correction to the two-step games approach, allowing the researcher to use revenue data, for example, to recover the costs associated with alternative actions. Alternatively, a researcher might use R&D expenses to back out the returns to innovation. The authors would like to thank participants at the 2007 Choice Symposium at the University of Pennsylvania and the 2007 QME conference at the University of Chicago. The authors have benefitted from conversations with Pat Bajari, Jeremy Fox, Han Hong, and Harikesh Nair. All remaining errors are our own. Department of Economics, Duke University, Durham NC 27708. Email: [email protected]. Corresponding author. William E. Simon School of Business Administration, University of Rochester, Rochester, NY 14627. Email: [email protected].