Business, 23.05.2020 23:02, punkinrichard1oxon2i

Each of two firms has one job opening. Suppose that (for reasons not discussed here but relating to the value of offering each opening) the firms offer different wages: firm i the wage wi , where 1/2w1 < w2 < 2w1. (That is, neither of the wages is more than double the other.) Imagine that there are two workers, each of whom can apply to only one firm. The workers simultaneously decide whether to apply to firm 1 or firm 2. If only one worker applies to a given firm, that worker gets the job; if both workers apply to one firm, the firm hires one worker at random and the other worker is unemployed (which has a payoff of zero).

(1) Suppose the two workers' payoff functions satisfy the Expected utility hypothesis, write out the strategic form (payoff matrix) of this game.
(2) Find the Nash equilibrium in pure strategies.
(3) Find the Nash equilibrium in mixed strategies.

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Each of two firms has one job opening. Suppose that (for reasons not discussed here but relating to...