Rational Inattention in the Infield

This paper provides evidence of rational inattention by experienced professionals in strategic interactions. We add rational inattention to a game of matching pennies with state-dependent payoffs. Unlike the full-information mixed-strategy Nash equilibrium, payoffs of different actions need not be equated state-by-state. Moreover, players respond partially to payoff differences, this responsiveness is stronger when attention costs are lower, strategies converge to full-information Nash as stakes increase, and average payoffs across all states are approximately equal across actions. We test these predictions using data on millions of pitches from Major League Baseball, where we observe strategies, payoffs, and proxies for attention costs.