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.

(A) Set up a payoff matrix for this game.

(B) 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