The Role of Attitude Toward Risk in Strictly Competitive Decision-Making Situations

The impact of decision makers' attitudes toward risk has been studied extensively in the context of noncompetitive decision making but not in the context of competitive decision making. In this paper we study the effects of the utility functions of the players in a strictly competitive decision-making situation on (a) their strategies and (b) their expected monetary payoffs. The setting is that of a two-by-two, two-person, zero-sum (in money) game with exponential utility functions for the competitors. The monetary payoffs and utility functions are assumed to be public knowledge. Combinations of utility functions that preserve the zero-sum condition as well as combinations that do not preserve this condition are considered. As might be expected, results from noncompetitive decision making do not necessarily carry over into competitive situations. For example, an increase in the risk aversion of a player may actually increase that player's expected monetary payoff because of altered strategies on the part of the competitor. In general, the effects of nonlinear utility functions on a player's strategy and expected monetary payoff depend on the player's utility function, the opponent's utility function, and the relationship among the entries in the payoff table. Furthermore, it does not appear possible to express this dependence in the form of simple rules of thumb, although the results presented here indicate the direction of movement of strategies and expected payoffs as the inputs to the problem are varied in certain systematic ways.