Question: An old lady is looking for help crossing the street. Only oneperson is needed to help her; more are ok but no better than one.Amy

An old lady is looking for help crossing the street. Only oneperson is needed to help her; more are ok but no better than one.Amy and Zita are the two people in the vicinity who can help. Theyhave to choose simultaneously whether to do so. Each of the them(Amy and Zita) will get pleasure worth 3 from the lady’s success incrossing the street (no matter who helps her). But each one whogoes to help will bear a cost of 1, this being the value of timetaken up in helping. Each will get a payoff 0 if the lady is nothelped.

(a) Set this up as a game between Amy and Zita. Write thepayoff table and find all pure-strategy Nash equilibria. [3 points]

(b) Suppose Amy chooses Help with probabiliry p and Zita choosesHelp with probabiliry q. Find the mixed-strategy Nash equilibrimfor this game. [6 points]

(c) Illustrate all the Nash equiliria ofthis game using a graph of best-response curves (with Amy’s p onthe horizontal axis and Zita’s q on the verticle axis). [5points]

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