a) Consider the following scenario. Carole is an animal-rights activist who owns a sanctuary called Large Cat Rescue, while Joe owns a zoo called Tiger Kingdom. There is an ongoing feud between them with Carole alleging abuse of animals in Tiger Kingdom while Joe counteracts with similar accusations about Large Cat Rescue. In a recent escalation of this feud, Carole sues Joe for making defamatory comments about her personal life on a social media forum called Rumorville. Five weeks from now a judge will decide whether or not Joe is guilty. If found guilty Joe will be ordered to pay $1 million in damages to Carole; if not, there will be no payment.

However, Carole and Joe can settle out of court in the four weeks prior to the hearing, in which case they do not go to court in Week 5. The negotiation for settlement proceeds as follows. In each week {1, 2,3, 4} Carole or Joe can make a settlement offer St and the other party has to decide whether to accept it. Carole and Joe take turns making offers; Carole makes offers in weeks 1 and 3, while Joe gets his turn in weeks 2 and 4. If the offer is accepted in any particular week, the game ends and Joe pays St (the amount decided in week t) to Carole.

Carole is risk-averse and her utility from receiving payment x is (x)1/2. She does not discount future payoffs and does not incur any costs of negotiation for going to court. Joe, however, is riskneutral and needs to pay a small fee c > 0 to lawyers for every week the negotiations take place. Use backward induction to analyse the above scenario. For the purpose of your analysis you may assume a probability p=0.6 of Carole winning the court case if the negotiations are not settled. {Hint: Start with the scenario in week 5 and calculate payoffs using the expected utility model. It will be convenient to express payoffs in million-dollar units. Then work backwards to figure out the offer Joe will make in period 4, Carole in Week 3, Joe in Week 2 and Carole in Week 1.}

(b) Explain and discuss the following statement: "When more issues are on the table or more parties are participating, agreements may be easier to reach, but bargaining may be riskier or the agreements more difficult to enforce."