33 Suppose two players are engaged in the partnership, where each partner puts costly effort in...

  

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33 Suppose two players are engaged in the partnership, where each partner puts costly effort in the firm to generate profits. How- ever, the firm generates some profits only in the case when both partners put at least one unit of effort. Specifically, each partner i = {1,2} chooses effort e; > 0. Partner i obtains the payoff: -ei, ui (ei, ej) = where j stands for the other player. ife; < 1, ((e; -1)+1) ee, if e; > 1, (a) Argue that (e1, e2)=(0,0) is a Nash equilibrium. (b) Find the best responses of each partner and plot them in the (e1, e2)-axes. (Hint: to find best responses, consider two cases: e; < 1 and e; > 1). (c) Find all the pure strategy Nash equilibria other than (0,0). Activate Windows Go to Settings to activate Windows. 33 Suppose two players are engaged in the partnership, where each partner puts costly effort in the firm to generate profits. How- ever, the firm generates some profits only in the case when both partners put at least one unit of effort. Specifically, each partner i = {1,2} chooses effort e; > 0. Partner i obtains the payoff: -ei, ui (ei, ej) = where j stands for the other player. ife; < 1, ((e; -1)+1) ee, if e; > 1, (a) Argue that (e1, e2)=(0,0) is a Nash equilibrium. (b) Find the best responses of each partner and plot them in the (e1, e2)-axes. (Hint: to find best responses, consider two cases: e; < 1 and e; > 1). (c) Find all the pure strategy Nash equilibria other than (0,0). Activate Windows Go to Settings to activate Windows.