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- This is question 13.7Which of the following gambles is “unfair”? a. A game that promises to pay you $1 if a coin comes up head and cost you $1 if a coin comes up tail, with no entry fee. b. A game that promises to pay you $10 if a coin comes up head and cost you $1 if a coin comes up tail, with no entry fee. c. A game that promises to pay you $10 if a coin comes up head and cost you $1 if a coin comes up tail, with an entry fee of $4.50 for the right to play. d. All of the above.Game theory: Consider a collective action game with thirty individuals (N = 30). When the number of participants in the joint project is n, each individual, including shirkers, receives a benefit of B(n) = 18n and each participant incurs a cost of C(n) = 32 − 2n. 1. Find all of the Nash equilibria, both stable and unstable ones. 2. Find the socially optimal outcome. 3. Check if any of the Nash equilibria is socially optimal. Explain your answer.
- a) Write out the extensive form of a game between a farmer (playing in the first round) and nature (playing a mixed strategy in the second round). Assume that the farmer can either pay a cash rent of $1500 for land (English system) or 1/2 of crop production to the landlord (sharecropping). Assume the farmer is planting corn and will produce 2 tons of corn. Assume that nature has a 50% chance of playing a strategy in which the price of corn is $3500/ton and a 50% chance of playing a strategy in which the price of corn is $500/ton. The farmer keeps any money left after paying cash rent and sells any corn left after paying the landlord in sharecropping. b)What is the most that a risk neutral farmer would be willing to pay for an accurate prediction of the price of corn in problem 1 before choosing whether to pay cash rent or sharecrop?2. Reviewing on social media can take many forms such as reposting your followers feedback on IG stories or asking them to answer a Poll. a. True b. False64. (This problem assumes knowledge of the basic rulesof baseball.) George Lindsey (1959) looked at boxscores of more than 1000 baseball games and foundthe expected number of runs scored in an inning foreach on-base and out situation to be as listed in the fileP09_64.xlsx. For example, if a team has a man on firstbase with one out, it scores 0.5 run on average untilthe end of the inning. You can assume throughout thisproblem that the team batting wants to maximize theexpected number of runs scored in the inning.a. Use this data to explain why, in most cases,bunting with a man on first base and no outs isa bad decision. In what situation might buntingwith a man on first base and no outs be a gooddecision?b. Assume there is a man on first base with one out.What probability of stealing second makes an attempted steal a good idea?