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