maximize their return. Linear algebra can be used to describe this situation exactly how linear algebra enters into formulating strategies. Key Words: Two person zero-sum game, Payoff matrix, Strategy, Expected payoff, Optimal strategy. valde game, Saddle point, Fundamental theorem of a 2-person zero-sum game. References: Basic books on Operations Research (a branch of applied mathematics which studies these types of problems) are a good place to look for information. http://www.zweigmedia.com/pdfs/GameTheory.pdf Problem 1: Suppose that a game pays off according to the following table: ii ii iv -464 1 A il ili -8 0 -7 3. -2 (a) Suppose that player A uses strategy i half of the time, strategy ii half of the time, and strategy ii none of the time. Suppose also that player B uses each of the four strategies one fourth of the time. Find the expected payoff of the game. (b) If player B keeps his strategy the same as in part (a), what strategy should player A choose to maximize her expected payoff? (c) If player A keeps her strategy the same as in part (a), what strategy should player B choose to maximize his expected payoff? ahlem 2: Determine the optimal pure strategies under the minimax criterion for both players. Indicate datermined, and give its value if this is the case. B