ABSTRACT
A topic which we have not covered is utility theory. When we introduced the payoff matrix in two-person games the numbers we assigned were only intended to represent players' orderings over the possible outcomes. However, subsequently it was necessary to interpret the payoffs as representing preference intensities. Thus, when considering the mixed extension of a game we dealt with expected payoffs, which are sums of payoffs weighted by probabilities, and when we analyzed cooperative games we assumed there existed numbers representing the "worth" of each coalition. We can justify such procedures by assuming that payoffs are in money units and that each player has a utility function which is linear in terms of money. For a detailed treatment of the problem see Luce and Raiffa [1957].
