Elementary team strategies in a monotone game

We face a complex game between Alice and Bob where the victory probabilityof each contender grows monotonically by unknown amounts with the resources s/heemploys. For a fixed effort on Alice’s part Bob increases his resources on the basis ofthe results of the individual contests (victory, tie or defeat) with the aim of reducing thedefeat probability under a given threshold. We read this goal in terms of computing aconfidence interval for the losing probability and in a previous paper we identified thisinterval on the basis of two joint statistics regarding the game history. In this paper wemove to a contest between teams where each member plays a monotone game with amember of the adversary team, with the additional benefit of a coordinating action onthe parts of Alice and Bob in the role of team leaders. With analogous constraints onAlice’s teammates and the same joint statistics collected by each contender, we showhow the statistics combine to reach the goal of binding the overall losing probability ofBob’s team. The analysis of the course of the bounds with the statistics suggests a pairof strategies for reducing the resources that are necessary to achieve the goal.