Consider the following three-period game, which is due to harris (1990): In period 1, two gamblers…

Consider the following three-period game, which is due to harris (1990): In period 1, two gamblers A and B pick

Gambler A obtains a payoff of 1 – a if greyhound C is declared the winner by both referees, and – 1 – 1 otherwise. Similarly, gambler B obtains 1 – b if both referees declare D to be the winner, and – 1 – b otherwise. In other words, A wants C to win, B wants D to win, and both want a result. They would also like to keep their contributions to the injection as small as possible. The payoff to greyhound C is 2c if e = C and That is, the form of his payoff depends on whether he or the other greyhound is declared the winner by referee E, but either way he would prefer to run the race as slowly as possible. Also, he would prefer to be first rather than second provided that he does not have to run too fast. The payoff to greyhound D is 2d if e = D and 1 – (a + b) (1 d) if e = C; like greyhound C, he is interested only in the verdict of referee E. Lastly, referee E gets payoff d if he declares C to be the winner, and e if he declares d to be the winner. Referee F’s payoffs are identical. Show the there exists no MPE. (There actually exists no subgame-perfect equilibrium.)