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3 3 Player Games Suppose there are 3 players, PI, P2 and P3, with feasible strategies...
2. (5 marks total IEDS practice Use iterated elimination of dominated strategies to reduce the following...
2. (5 marks total IEDS practice Use iterated elimination of dominated strategies to reduce the following games. We will call the row player P1 and the column player P2; note that for each entry in the payoff matrices below, PI's payoff is listed first. Clearly indicate: the order in which you eliminate strategies; whether the eliminated strategy is strictly or weakly dominated; If you find a dominant strategy equilibrium, state what it is. Is it unique? 81 (1,5) 50, -11)...
6. Consider a sequential game with 3 players. Player 1 can choose A or B. Player...
6. Consider a sequential game with 3 players. Player 1 can choose A or B. Player 2 can choose C, D, E, or F (depending on what player 1 chooses). Player 3 can choose G, H, I, J, K, L, M, or N (depending on what player 1 and 2 choose). Player 1 (P1) goes first, player 2 (P2) goes second, and player 3 (P3) goes third. Payoffs are written as the payoffs for P1, P2, and the for P3....
(a) (5 points) Do the players have any strategies which are dominated? Any dominant strategies? (b)...
(a) (5 points) Do the players have any
strategies which are dominated? Any dominant strategies?
(b) (2 points) Suppose you could create a new strategy (D) which
consisted of A x = 75% of the time and C 1 − x = 25% of the time.
If your payoff from this new strategy is the average of your
payoffs from A and C (given the percentages), what is the payoff of
D? Add it to the matrix.
(c) (3 points)...
Player 1 can choose to either play against Player 2 or Player 3. If she chooses...
Player 1 can choose to either play against Player 2 or Player 3. If she chooses to play against Player 2, Player 2 gets to choose between moves X and and Y, and Player 1 picks between moves C and D. If Player 1 chooses to play against Player 3, Player 3 gets a choice between moves S and T, and Player 1 gets to choose between moves E and F. The payoffs for each combination of moves are as...
1 Consider the following normal-form game. P2 L CR P M (a) Does Pl (player 1)...
1 Consider the following normal-form game. P2 L CR P M (a) Does Pl (player 1) have any dominated strategies? (b) Does P2 (player 2) have any dominated strategies? (c) Suppose l2 beleves that Pl is rational, should P2 believe P1 will ever play B? (d) Suppose player P2 rales out the possibility that Pl plays B, is there a dominated ECON 306 Page 2 of 12 2018 strategy for player P2? (e) Can yoa find any more eliminated strategies...
(20 points) Exercise 3: (Midterm 2018) Consider the following normal-form game, where the pure strategies for...
(20 points) Exercise 3: (Midterm 2018) Consider the following normal-form game, where the pure strategies for Player 1 are U, M, and D, and the pure strategies for Player 2 are L, C, and R. The first payoff in each cell of the matrix belongs to Player 1, and the second one belongs to Player 2. Player 2 IL CR u 6,8 2,6 8,2 Player 1 M 8,2 4,4 9,5 8,10 4,6 6,7 (7) a) Find the strictly dominated (pure)...
Q2 Contribution Game Consider the following game. There are four players. Each player i (wherei 1,2,3,4)...
Q2 Contribution Game Consider the following game. There are four players. Each player i (wherei 1,2,3,4) si multaneously and independently selects her contribution s E [0, 10]. Each player gets a benefit related to all of the players choices of s,'s, but incurs a cost related to her own contribution s In particular, the payoff to each player i is given by: ul (s1 , s2, s3, s.) = si + s2 + s3 + 84-0.5s (a) Find best response...
4. (a) (10%) A player has three information sets in the game tree. He has four...
4. (a) (10%) A player has three information sets in the game tree. He has four choices in his first information set, four in his second and three in his third. How many strategies does he have in the strategic form? Circle one: (i) 11, (ii) 28 (iii) 48 (iv) 18. (b) (10%) Is it true that the following game is a Prisoners' Dilemma? Explain which features of a Prisoners' Dilemma hold and which do not. (Remember each player must...
Consider the finite 2 player game, representing price competition in a market where al costumers buy...
Consider the finite 2 player game, representing price competition in a market where al costumers buy from the seller with the lowest price. Both sellers simultaneously choose price, p1 and p2, where pi is in P = {0,1,2,3,4}. The profits to each seller are given in the payoff bi-matrix below, where seller 1 chooses row and seller 2 column. Firm 2 p=0 p=1 p=2 p=3 p=4 p=0 -5,-5 -10,0 -10,0 -10,0 -10,0 p=1 0,-10 0,0 0,0 0,0 0,0 p=2 0,-10...
1. Consider a gam e in which 2 friends have decided to meet outside of there...
1. Consider a gam e in which 2 friends have decided to meet outside of there game theory class to go for a bike ride, but they did not coordinate on bringing road bikes or mountain bikes and they cannot communicate with each other before class. Assume that both friends have mountain and road bikes. Assume that if they both bring road bikes each gets a payoff of 2, if they both bring mountain bikes each gets a payoff of...
2. (5 marks total IEDS practice Use iterated elimination of dominated strategies to reduce the following games. We will call the row player P1 and the column player P2; note that for each entry in the payoff matrices below, PI's payoff is listed first. Clearly indicate: the order in which you eliminate strategies; whether the eliminated strategy is strictly or weakly dominated; If you find a dominant strategy equilibrium, state what it is. Is it unique? 81 (1,5) 50, -11)...
(a) (5 points) Do the players have any
strategies which are dominated? Any dominant strategies?
(b) (2 points) Suppose you could create a new strategy (D) which
consisted of A x = 75% of the time and C 1 − x = 25% of the time.
If your payoff from this new strategy is the average of your
payoffs from A and C (given the percentages), what is the payoff of
D? Add it to the matrix.
(c) (3 points)...
1 Consider the following normal-form game. P2 L CR P M (a) Does Pl (player 1) have any dominated strategies? (b) Does P2 (player 2) have any dominated strategies? (c) Suppose l2 beleves that Pl is rational, should P2 believe P1 will ever play B? (d) Suppose player P2 rales out the possibility that Pl plays B, is there a dominated ECON 306 Page 2 of 12 2018 strategy for player P2? (e) Can yoa find any more eliminated strategies...
(20 points) Exercise 3: (Midterm 2018) Consider the following normal-form game, where the pure strategies for Player 1 are U, M, and D, and the pure strategies for Player 2 are L, C, and R. The first payoff in each cell of the matrix belongs to Player 1, and the second one belongs to Player 2. Player 2 IL CR u 6,8 2,6 8,2 Player 1 M 8,2 4,4 9,5 8,10 4,6 6,7 (7) a) Find the strictly dominated (pure)...
Q2 Contribution Game Consider the following game. There are four players. Each player i (wherei 1,2,3,4) si multaneously and independently selects her contribution s E [0, 10]. Each player gets a benefit related to all of the players choices of s,'s, but incurs a cost related to her own contribution s In particular, the payoff to each player i is given by: ul (s1 , s2, s3, s.) = si + s2 + s3 + 84-0.5s (a) Find best response...
4. (a) (10%) A player has three information sets in the game tree. He has four choices in his first information set, four in his second and three in his third. How many strategies does he have in the strategic form? Circle one: (i) 11, (ii) 28 (iii) 48 (iv) 18. (b) (10%) Is it true that the following game is a Prisoners' Dilemma? Explain which features of a Prisoners' Dilemma hold and which do not. (Remember each player must...
1. Consider a gam e in which 2 friends have decided to meet outside of there game theory class to go for a bike ride, but they did not coordinate on bringing road bikes or mountain bikes and they cannot communicate with each other before class. Assume that both friends have mountain and road bikes. Assume that if they both bring road bikes each gets a payoff of 2, if they both bring mountain bikes each gets a payoff of...
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