| Abstract: |
Mixed-strategy Nash equilibrium (MSNE) is a commonly-used solution concept in
game-theoretic models in various fields in economics, management, and other
disciplines, but the experimental results whether the MSNE predicts well
actual play in games is mixed. Consequently, evidence for naturally-occurring
games in which the MSNE predicts the outcome well is of great importance, as
it can justify the vast use of MSNE in models. The game between the kicker and
goalkeeper in soccer penalty kicks is a real-world game that can be used to
examine the application of the MSNE concept or its accuracy because payoffs
are a common knowledge, the players have huge incentives to play correctly,
the game is simple enough to analyze, its Nash equilibrium is in mixed
strategies, and players' actions can be observed. We collected and analyzed
data on the direction of kicks and jumps in penalty kicks in various top
leagues and tournaments. Our analysis suggests that the MSNE predictions are
the closest to the actual sample data, even though some other prediction
methods use information on the marginal distribution of kicks or jumps whereas
the MSNE does not. |