ABSTRACT
Elementary game theory is concerned with discrete optimization problems involving two players with conflicting interests. In a typical matrix game there are two players, u and υ, and a selection of strategies, u., i = 1, 2, …, m; and υj, j = 1, 2, …, n, for each player. For each pair of strategies there is a corresponding payoff,J = Lij . Player u attempts to minimize the payoff, while υ attempts to maximize it. This is a “perfect information game” in the sense that each player has all the information above and that each player knows the other player’s choice of strategies. Now, if υ (the maximizer) plays first, he should obviously pick the column with the largest minimum, since he knows u will subsequently pick the row with the minimum. Similarly, if u (the minimizer) plays first, he should pick the row with the smallest maximum, since he knows υ will subsequently pick the column with the maximum. An example of a 2 X 2 game is shown in Figure 9.1.1. A simple discrete game. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315137667/ebc3ad23-d2ed-4b59-a8e1-8861837bea7d/content/fig9_1_1.tif"/>
