Recombinant Estimation for Normal-Form Games, with Applications to Auctions and Bargaining

In empirical studies of simultaneous-move games, such as sealed-bid auctions, researchers frequently wish to estimate quantities which depend on interactions between the strategies of different players. Examples include the expected revenues of an auction, or the mean allocative efficiency in a market experiment. For such applications, we present an improved statistical estimator based on "recombinant estimation": recombining the strategies of individual players to compute what the outcomes would have been if players had been matched in different groups. We calculate the improvement in efficiency of the recombinant estimator relative to the standard estimator, and show how to estimate standard errors for the recombinant estimator. We present an application to a two-player sealed-bid auction and a two-player ultimatum bargaining game. In these applications, the improved efficiency of our estimator is equivalent to an increase of between 40% and 200% in the sample size, and we expect even larger improvements for games with three or more players. We discuss how to design experiments in order to be able to take full advantage of recombinant estimation. Finally, we discuss practical computational issues, showing how one can avoid combinatorial explosions of computing time while still yielding significantly improved efficiency of estimation.