Solve the following problem that illustrates how a mixed strategy N...

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Solve the following problem that illustrates how a mixed strategy Nash equi- librium can be viewed as the limit of a pure strategy Bayesian Nash equilibrium. Two firms i = 1,2 choose whether to invest in a project or not. As in the example we saw in class, each firm can observe its own benefit parameter from investing, but not that of the other firm. If firm type Oi invests, it gains 1 + Oi if it is the only firm to invest, loses 1 if both firms invest, and receives a zero payoff if it does not invest. The types 0i of firms i = 1,2 are uniformly and independently distributed on [-E, €], where € > 0. 1. Find a pure strategy Bayesian Nash equilibrium. [Hint: Solve directly for the cut-off levels 01 and 02]. 2. As € goes to zero, the game converges to a complete information game. Find all the pure and mixed strategy Nash equilibrium of this game. Discuss your finding.

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