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On the Predictive Power of Theories of One-Shot Play

We propose a novel challenge for assessing the predictive power of a theory of one shotplay in games (subjects playing a game exactly once): we test the predictive power of theories in situations for which we do not (yet) have any data. To do so, we consider a variety of such theories and fix their parameter estimates from the recent large scale meta-analysis of Wright and Leyton-Brown (2017). We then compare the predictive power of these theories, measured in terms of log-likelihood, for a series of symmetric hawk-dove games played in the lab. We find that even for such a narrow class of games, no theory is uniformly better than all others across all treatments. Furthermore, the theory that provides the highest overall log-likelihood for our data is Nash equilibrium with risk aversion, with an estimated risk aversion parameter taken from Hey and Orme (1994) and its replication in Harrison and Rutstrom (2009). In particular, it significantly beats the two theories (based on quantal level k and cognitive hierarchy models) which performed best in Wright and Leyton-Brown’s (2017) standard out-of-sample prediction task.