Two firms in a local market compete in the manufacture of cyberwidgets. Each firm must decide if they will engage in product research to innovate their version of the cyberwidget. The payoffs of each firm's strategy are a function of the strategy of their competitor as well. The payoff matrix is presented below. Firm #2 chooses to innovate with probability 20/21. If Firm #1 does the same, what is the expected payoff? Is this a Mixed Strategy Nash Equilibrium? Suppose, instead, that firm #2 innovates with probability 2/3. Should player #1 always innovate?

Question

Two firms in a local market compete in the manufacture of cyberwidgets. Each firm must decide if they will engage in product research to innovate their version of the cyberwidget. The payoffs of each firm's strategy are a function of the strategy of their competitor as well. The payoff matrix is presented below.  Firm #2 chooses to innovate with probability 20/21. If Firm #1 does the same, what is the expected payoff? Is this a Mixed Strategy Nash Equilibrium? Suppose, instead, that firm #2 innovates with probability 2/3. Should player #1 always innovate?

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The Answer of Two firms in a local market compete in the manufacture of cyberwidgets. Each firm must decide if they will engage in product research to innovate their version of the cyberwidget. The payoffs of each firm's strategy are a function of the strategy of their competitor as well. The payoff matrix is presented below.  Firm #2 chooses to innovate with probability 20/21. If Firm #1 does the same, what is the expected payoff? Is this a Mixed Strategy Nash Equilibrium? Suppose, instead, that firm #2 innovates with probability 2/3. Should player #1 always innovate?

Two Firms in a Local Market Compete in the Manufacture