Relative Minimax

To achieve robustness, a decision criterion that recently has been widely adopted is Wald's minimax, after Gilboa and Schmeidler (1989) showed that (one generalisation of) it can be given an axiomatic foundation with a behavioural interpretation. Yet minimax has known drawbacks. A better alternative is Savage's minimax regret, recently axiomatized by Stoye (2006). A related alternative is relative minimax, known as competitive ratio in the computer science literature, which is appealingly unit free. This paper provides an axiomatisation with behavioural content for relative minimax.