Game Theory Problem: Firm Competition Strategy Assume that two firms are competing for market share for a particular product. Each firm is considering what promotional strategy to employ for the coming period. Assume that the following payoff matrix describes the increase in market share of Firm A a
Game Theory Problem: Firm Competition Strategy
Assume that two firms are competing for market share for a particular product. Each firm is considering what promotional strategy to employ for the coming period. Assume that the following payoff matrix describes the increase in market share of Firm A and the decrease in market share for Firm B. Find the optimal strategy for each firm. Also determine value of the game.
$$\begin{array}{|c|c|c|c|}\hline \text{FirmA/FirmB} & \text{No promotion} & \text{Moderate promotion} & \text{Much promotion} \ \hline \text{No promotion} & 5 & 0 & -10 \ \text{Moderate promotion} & 10 & 6 & 2 \ \text{Much promotion} & 20 & 15 & 10 \ \hline \end{array}$$
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Payoff matrix (Firm A's gain = Firm B's loss), rows = Firm A strategies, columns = Firm B strategies: Firm A \ Firm B No promotion Moderate promotion Much promotion ------------ No promotion 5 0 -10 Moderate promotion 10 6 2 Much promotion 20 15 10 This is a two-person zero-sum game. Apply the ma...