c. Ben is considering entering the ice cream market. His hated high school nemes

Question

c. Ben is considering entering the ice cream market. His hated high school nemesis, Jerry, has the only ice cream parlour in town. His business makes him $120,000 a year. Having heard of Ben's intentions, Jerry has started bullying Ben again. Jerry claims he will lower prices to drive Ben out of business. If Ben decides to enter the market and his rival lowers prices then Ben will suffer $10,000 in losses. Jerry will only make $40,000. However, if Jerry adopts a less agressive strategy (by maintaining current prices) he will enjoy $90,000 in profits and Ben $50,000. Write down this game in extensive form. Find the Nash Equilibrium. Should Ben risk losing $10,000? What will the outcome of this fierce rivalry be if a (potential) merger could give them a combined $150,000?

d. Players 1 and 2 have to agree on how to split some money. Originally there are $64. Players take turns suggesting how to split the money. After each suggestion, the opposing player decides whether to accept or reject the o§er. If he accepts the game ends there and if he rejects, then he gets to make an offer. The problem is that anytime a player rejects an offer the total amount of money gets cut by half. The game ends when they reach an agreement or when there is less than a dollar to be split In that case both players must pay a fine of $1 for not having reached an agreement.

Explanation / Answer

c)

The extensive form of the game is darwn below. See that Jerry makes a choice in the subgame below where he decides to adopt a less agressive strategy (by maintaining current prices).In this way, he will enjoy $90,000 in profits and Ben $50,000. Given this Ben decides to enter. So we have a Nash equilibrium where Ben enters and erry accomodates

If the joint profit is $150,000, both should agree since the current profit when added up is less than 150,000.

d) We have $64 in the pool. Two player need to divide it in such a way that both agrees. Important thing to note here is anytime a player rejects the offer total money cuts by half.
So, Player 1 make a strategy like this : He should keep $31 and player B should get $33.
Player B cannot reject this strategy as if he rejects, total money will be $32 which is max he could get in worst case, giving player B $33 in the first turn, will make him accept the offer and end the game there.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.