Model of a Sudden-Death Field-Goal Football Game as a Sequential Duel

摘要

The idea of applying game theoretic analysis to football was proposed. In discussions with him and Frank Ryan it became evident that given the many details of football any first attempt to apply a formal mathematical model to the actual sport would require a high degree of abstraction. Yet an interesting extension of the military dueling literature appears to be feasible. Rather than claim immediate relevance to football as it is played, a highly simplified version of 'sudden-death' scoring is introduced. In a conventional duel the duelists approach each other with their revolvers, or the two tanks close range. A key element is that both sides have revolvers or other weapons for the offensive. The football game differs inasmuch as there is only one ball. One team or the other always has the initiative. There is only one pistol, a team can close on the target or fire. It may lose the pistol or fire and miss. In either case the other team may get the pistol. In tactical fights one side may capture resources of the other and use them. The possession of a key position may give the initiative to one side or the other. Thus although the context of the analysis here is primarily in terms of football or other sports the type of model appears to be related to duels with potential application to tactical combat. In particular the concept of initiative, often regarded as critical in tactics, emerges from the model.