We model a soccer match between two heterogeneous teams as a two-stage contest where each team chooses its attacking and defending effort for each half of the match. We characterize the optimal teams’ efforts as well as the optimal effort allocation between offense and defense. In contrast to the theoretical literature on soccer we show, for example, that the leading team may preempt its competitor in the first half. Our analysis also sheds new light on empirical studies that investigate the change in winning points on the number of ties by showing that this effect depends crucially on teams’ heterogeneity.

中文翻译：

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“球是圆的，比赛持续了90分钟，其他一切都是纯理论”

我们将两支异类球队之间的足球比赛分为两个阶段进行建模，其中每支球队在比赛的每一半中选择进攻和防守的努力。我们描述了最佳团队的努力以及攻防之间的最佳努力分配。与关于足球的理论文献相反，例如，我们表明，领先的球队可能在上半年抢先竞争对手。我们的分析还为实证研究提供了新的亮点，该实证研究通过研究这种影响主要取决于团队的异质性来调查平局数量上获胜点的变化。