Refer to Problem 29. Use linear programming and a geometric approach to find the expected value of the game for Ron. What is the expected value for Cathy?

Data from problem 29

Consider the following finger game between Ron (rows) and Cathy (columns): Each points either 1 or 2 fingers at the other. If they match, Ron pays Cathy $2. If Ron points 1 finger and Cathy points 2, Cathy pays Ron $3. If Ron points 2 fingers and Cathy points 1, Cathy pays Ron $1.

Set up a payoff matrix for this game.

Use formulas from Section 11.2 to find the optimal strategies for Ron and for Cathy.

Formula from section 11.2

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DEFINITION Strategies for R and C Given the game matrix a b M 1 = [1 2] C R's strategy is a probability row matrix: P = [P₁ P₂] P₁ ≥ 0 P2 = 0 P₁ P₂ = 1 C's strategy is a probability column matrix: Q = 91 91 92 91 +92 = 1