Imagine a lottery with a jackpot consisting of sixteen $1 coins. There are just 2 people...

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Imagine a lottery with a jackpot consisting of sixteen $1 coins. There are just 2 people who can buy tickets in this lottery, Adam and Bea. The price of a lottery ticket is $1, and both Adam and Bea have five $1 coins. Let TA and TB denote the number of the lottery tickets that Adam and Bea buy, respectively. Since each person has five $1 coins, both strategy sets are {0, 1, 2, 3, 4, 5}. If either TA > 0 or TB > 0, the probability that Adam wins the jackpot, PA, is TA/(TA + TB), and the probability that Bea wins the jackpot, PB, is TB/(TA + TB). If TA = TB = 0 then PA = PB = 0. The payoff functions are TA %3D 16PA – TA for Adam and TB = 16PB - TB for Bea. (a) If you were either Adam or Bea, how many tickets would you buy? (b) What is the Nash equilibrium of this game? (c) What are the Pareto-optimal strategy combinations? (d) Now suppose that Adam has only three $1 coins to spend on lottery tickets, and that Bea still has five. What is the Nash equilibrium of this revised game? What are the Pareto-optimal strategy combinations? Imagine a lottery with a jackpot consisting of sixteen $1 coins. There are just 2 people who can buy tickets in this lottery, Adam and Bea. The price of a lottery ticket is $1, and both Adam and Bea have five $1 coins. Let TA and TB denote the number of the lottery tickets that Adam and Bea buy, respectively. Since each person has five $1 coins, both strategy sets are {0, 1, 2, 3, 4, 5}. If either TA > 0 or TB > 0, the probability that Adam wins the jackpot, PA, is TA/(TA + TB), and the probability that Bea wins the jackpot, PB, is TB/(TA + TB). If TA = TB = 0 then PA = PB = 0. The payoff functions are TA %3D 16PA – TA for Adam and TB = 16PB - TB for Bea. (a) If you were either Adam or Bea, how many tickets would you buy? (b) What is the Nash equilibrium of this game? (c) What are the Pareto-optimal strategy combinations? (d) Now suppose that Adam has only three $1 coins to spend on lottery tickets, and that Bea still has five. What is the Nash equilibrium of this revised game? What are the Pareto-optimal strategy combinations?

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Quiz a I would buy 4 tickets in this lottery game As a rational person I would buy as many tickets as possible so that my payoff is as high as possibl... View the full answer