This article develops a dynamic game-theoretic model of optimizing strategic behaviour by football teams. Teams choose continuously between defensive and attacking formations and between a non-violent and a violent playing style. Starting from the end of the match and working backwards, the teams' optimal strategies conditional on the current state of the match are determined by solving a series of two-person non-cooperative subgames. Numerical simulations are used to explore the sensitivity of strategic behaviour to variations in the structural parameters. The model is tested empirically, using English football league data. Teams that are trailing are willing to bear an increased risk of a player dismissal in order to increase the probability of scoring. Teams that are leading or level in scores play cautiously. The scoring rates of teams that are trailing are higher than those of teams that are ahead or level. Stochastic simulations are used to obtain probabilities for match results, conditional upon the state of the match at any stage. The article's main theoretical and empirical results constitute novel, non-experimental evidence that the strategic behaviour of football teams can be rationalized in accordance with game-theoretic principles of optimizing strategic behaviour by agents when payoffs are uncertain and interdependent.
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