6. 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

 

6. 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 16PA TA for Adam and B = 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?