Modified Max-Min Algorithm for Game Theory

Abstract

The recent advancements in the game theory have led to it being applied in various applications such as communication, networks, business, biology, political system etc. Precisely, Max-Min Algorithm is a decision based rule used in the game theory for deciding the next step of a player out of a set of possible steps. It can be thought of maximizing the minimum profit of the player. The assumption made in the current literature of zero-sum game theory is that both players are rational and logical to decide the best possible step out of the available options. On the Prima Facie, we expect a player to choose the best possible step for himself/herself. But in doing so, he/she might give away his/her move to his/her rival, who, being a rational thinker, can manipulate the game to take his/her advantage or alternatively rival's loss. Our proposed approach seeks to overcome this loophole presented in the current Max-Min approach by construction of a function which solves the trade-off between predictability and maximum profit. The key idea here is to select a step with a potential to earn high profit and being unpredictable in picking up that step at the same moment, thus making it nearly impossible for the adversary to predict the next step. In the nut shell, our work is an attempt to reduce the worst case complexity of original Max-Min approach.