GAME THEORY UP or DOWN Made by Nastassia Sukavenka (33160)
Problem Player A can move UP or DOWN. If UP, then Player B can move YES and then it’s Player C move. If Player C moves RIGHT then the game is over and payoffs are respectively: 10; 3; 5. If Player C moves left, then the game is over with payoffs: 100; 0; 2. If, however, Player B moves NO, then the game is over with payoffs: 5; 4; 10. If Player A moves DOWN, then it is Player B turn. If B moves YES, then the game is over with payoffs: 0; 6; 0. If Player B moves NO, then the game is over with payoffs: 50; 4; 200. a) Draw the game tree and show the path of the game – find rollback equilibrium of this game. b) Assume that players A and B can bargain (negotiate) How much should Player A pay to Player B, so that Player B would be willing to change his choice? c) How does this bargaining change the rollback equilibrium of this game?
Solution (point A) RIGHT C YES UP B LEFT NO B 100; 0; 2 5; 4; 10 A DOWN 10; 3; 5 YES 0; 6; 0 NO 50; 4; 200
Rollback equilibrium RIGHT C YES UP B LEFT NO B 100; 0; 2 5; 4; 10 A DOWN 10; 3; 5 YES 0; 6; 0 NO 50; 4; 200 The rollback equilibrium is UP; NO. The payoffs are 5; 4; 10
Point B Assume that players A and B can bargain (negotiate). How much should Player A pay to Player B, so that Player B would be willing to change his choice? For player A the best option is DOWN; NO, because player C will always choose RIGHT. In the case of DOWN; NO the payoff are 50; 4; 200. So player C will be satisfied more than when he chooses RIGHT. In order to get this rollback equilibrium player A must negotiate with player B. Player A must pay more than 2 in order to change decision, therefore the both can benefit. A will obtain higher payoff as a result of negotiation and B will obtain same value or higher if player A negotiate.
Point C After bargaining the rollback equilibrium will be DOWN; NO. And the payoffs will be respectively 50, 4, 200. But player B will get higher payoff due to negotiations with player A, so all three players will be better off than without bargaining.
Thank you for attention
