Obtaining a fair arbitration outcome

The ‘minimax theorem’ is the most recognized theorem for determining strategies in a two-person zero-sum game. Other common strategies exist such as the ‘maximax principle’ and ‘minimize the maximum regret principle’. All these strategies follow the Von Neumann and Morgenstern linearity axiom which states that numbers in the game matrix must be cardinal utilities and can be transformed by any positive linear function f(x)=ax+b, a > 0, without changing the information they convey. This paper describes risk-aversestrategies for a two-person zero-sum game where the linearity axiom may not hold. With connections to gambling theory, there is evidence to show why it can be optimal for the favourable player to adopt risk-averse strategies. Based on this approach, an arbitration value is obtained in a litigation game, where the amount awarded to the victim is less than expectation and shown to be ‘fairer’ when compared with the amount obtained using the Von Neumann and Morgenstern game theory framework.