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 pay-offs of each firm's strategy is a function of the strategy of their competitor as well. The pay-off matrix is presented below.
Firm #2 chooses to innovate with probability 20/21. If Firm #1 does the same, what is the expected pay-off? 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 pay-offs of each firm's strategy is a function of the strategy of their competitor as well. The pay-off matrix is presented below.  
Firm #2 chooses to innovate with probability 20/21. If Firm #1 does the same, what is the expected pay-off? 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 pay-offs of each firm's strategy is a function of the strategy of their competitor as well. The pay-off matrix is presented below.  
Firm #2 chooses to innovate with probability 20/21. If Firm #1 does the same, what is the expected pay-off? 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