Games, Incompetence, and Training

Abstract

In classical noncooperative matrix games the payoffs are determined directly by the players’ choice of strategies. In reality, however, a player may not be capable of executing his or her chosen strategy due to a lack of skill that we shall refer to as incompetence. A method for analysing incompetence in matrix games is introduced, examined and demonstrated. Along with the derivation of general characteristics, a number of interesting special behaviours are identified. These special behaviours are shown to be the result of particular forms of the game and/or of the incompetence matrices. The development of this simple model was motivated by applications where a decision to increase competence is to be evaluated. Investments that decrease incompetence (such as training) need to be related to the change in the value of the game. A game theory approach is used since possible changes in strategies used by other players must be considered. An analogy with the game of tennis is discussed, as is an analogy with capability investment decisions in the military.