Two people are dividing a pot of p dollars. Person 1 offers person2 an amount c up to p. If person 2 accepts this offer, then person 1 receives the remaining p−c. If person 2 rejects the offer then neither receives any payoff. Suppose further that before dividing the pot person 2 can decide the size p of the pot. If she puts in effort, the pot will be large p=ph. If she does not put any effort the pot will be small p=pL where pL, pH are constants and pH> Pl. Since effort is costly, if person 2 puts in effort, her payoff will be x−e where x is what she gets from the division and e is some non-negative number representing her cost of exerting effort.

a). How many strategies does each player have? What are the strategies for player 2 in this game? Be very careful when describing strategies.

b). Assuming person 2 takes the action preferred by person 1 when indifferent. What is the unique rollback solution outcome of this game? What are the players strategies under the rollback solution.