Homework Answers
A game is a strategic interaction between two players. Each player has their own sets of actions called the strategies. Each strategy comes with a definite outcome, these outcomes are tied to some profit or loss called the payoff. One of the favorite examples of game theory is the Prisoners' dilemma.
In this game, two partners of crime are caught by police and held in different cells being interrogated separately. Both of them has two option either to confess or to be silent. The payoff they receive is in terms of years in jail. For example, if they both confess they get 12 years in jail and thus the payoff is -12 for each for strategy (confess, confess).
The game table is completed as below
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Consider a simple 2x 2 game theory matrix such as this one: Player 2 (P2) Action...
2. Consider the following sequential game. Player A can choose between two tasks, Tl and T2....
2. Consider the following sequential game. Player A can choose between two tasks, Tl and T2. After having observed the choice of A, Player B chooses between two projects Pl or P2. The payoffs are as follows: If A chooses TI and B chooses P1 the payoffs are (12, 8), where the first payoff is for A and the second for B; if A chooses T1 and B opts for P2 the payoffs are (20, 7); if A chooses T2...
2. Consider the following sequential game. Player A can choose between two tasks, TI and T2....
2. Consider the following sequential game. Player A can choose between two tasks, TI and T2. After having observed the choice of A, Player B chooses between two projects P1 or P2. The payoffs are as follows: If A chooses TI and B chooses Pl the payoffs are (12.8), where the first payoff is for A and the second for B; if A chooses TI and B opts for P2 the payoffs are (20,7); if A chooses T2 and B...
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....
GAME MATRIX Consider two players (Rose as player 1 and Kalum as player 2) in which each player has 2 possible actions (...
GAME MATRIX
Consider two players (Rose as player 1 and Kalum as player 2) in which each player has 2 possible actions (Up or Down for Rose; Left or Right for Kalum. This can be represented by a 2x2 game with 8 different numbers (the payoffs). Write out three different games such that: (a) There are zero pure-strategy Nash equilibria. (b) There is exactly one pure-strategy equilibrium. (c) There are two pure-strategy Nash equilibria.
Consider two players (Rose as player...
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...
(3) [Dutta, Ch 2 Exercise 2.5 and 2.10 Consider the following "divide the dollar" game. Two...
(3) [Dutta, Ch 2 Exercise 2.5 and 2.10 Consider the following "divide the dollar" game. Two player Pi and Pg decides how to split a dollar between themselves. Players move sequentially. First, Ps moves. P1 can make any offer to P2 in increments of 25 cents; that is P can offer $0.00, S0.25, $0.50, S0.75, or $1.00. Observing Pt's offer, F2 erving Pi's offer, P decides whether to accept the offer or to reject it. If P2 accepts the offer,...
Consider a game being played between player 1 and player 2. Player 1 can choose T...
Consider a game being played between player 1 and player 2. Player 1 can choose T or B. Player 2 can take actions Lor R. These choices are made simultaneously. The payoffs are as follows. If 1 plays T and 2 plays L, the payoffs are (0, 0) for Player 1 and 2, respectively. If 1 opts of B and 2 L, the payoffs are (5,7). If 1 plays T and 2 R, the payoffs are (6,2). Finally, both players...
Consider a game being played between player 1 and player 2. Player 1 can choose T...
Consider a game being played between player 1 and player 2. Player 1 can choose T or B. Player 2 can take actions Lor R. These choices are made simultaneously. The payoffs are as follows. If 1 plays T and 2 plays L, the payoffs are (0,0) for Player 1 and 2, respectively. If 1 opts of B and 2 L, the payoffs are (5,7). If 1 plays T and 2 R, the payoffs are (6,2). Finally, both players get...
The table below is the payoff marrix for a simple two-firm game Firms A and B...
The table below is the payoff marrix for a simple two-firm game Firms A and B are bidding on a government contract and each f's bid is not known by the other form. Each firm can bid other $14.000 or 55.000 The cost of completing the project for each firm is 53.000 The low bid firm will win the contractat its stated price the high dem wilgot nothing the two bids are equal, the two firms wil split the price...
Consider a game between a police officer (player 3) and two drivers (players 1 and 2)....
Consider a game between a police officer (player 3) and two drivers (players 1 and 2). Player 1 lives and drives in Wynwood, whereas player 2 lives and drives in Sweetwater. On a given day, players 1 and 2 each have to decide whether or not to use their cell phones while driving. They are not friends, so they will not be calling each other. Thus, whether player 1 uses a cell phone is independent of whether player 2 uses...
2. Consider the following sequential game. Player A can choose between two tasks, Tl and T2. After having observed the choice of A, Player B chooses between two projects Pl or P2. The payoffs are as follows: If A chooses TI and B chooses P1 the payoffs are (12, 8), where the first payoff is for A and the second for B; if A chooses T1 and B opts for P2 the payoffs are (20, 7); if A chooses T2...
2. Consider the following sequential game. Player A can choose between two tasks, TI and T2. After having observed the choice of A, Player B chooses between two projects P1 or P2. The payoffs are as follows: If A chooses TI and B chooses Pl the payoffs are (12.8), where the first payoff is for A and the second for B; if A chooses TI and B opts for P2 the payoffs are (20,7); if A chooses T2 and B...
GAME MATRIX
Consider two players (Rose as player 1 and Kalum as player 2) in which each player has 2 possible actions (Up or Down for Rose; Left or Right for Kalum. This can be represented by a 2x2 game with 8 different numbers (the payoffs). Write out three different games such that: (a) There are zero pure-strategy Nash equilibria. (b) There is exactly one pure-strategy equilibrium. (c) There are two pure-strategy Nash equilibria.
Consider two players (Rose as player...
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...
(3) [Dutta, Ch 2 Exercise 2.5 and 2.10 Consider the following "divide the dollar" game. Two player Pi and Pg decides how to split a dollar between themselves. Players move sequentially. First, Ps moves. P1 can make any offer to P2 in increments of 25 cents; that is P can offer $0.00, S0.25, $0.50, S0.75, or $1.00. Observing Pt's offer, F2 erving Pi's offer, P decides whether to accept the offer or to reject it. If P2 accepts the offer,...
Consider a game being played between player 1 and player 2. Player 1 can choose T or B. Player 2 can take actions Lor R. These choices are made simultaneously. The payoffs are as follows. If 1 plays T and 2 plays L, the payoffs are (0, 0) for Player 1 and 2, respectively. If 1 opts of B and 2 L, the payoffs are (5,7). If 1 plays T and 2 R, the payoffs are (6,2). Finally, both players...
Consider a game being played between player 1 and player 2. Player 1 can choose T or B. Player 2 can take actions Lor R. These choices are made simultaneously. The payoffs are as follows. If 1 plays T and 2 plays L, the payoffs are (0,0) for Player 1 and 2, respectively. If 1 opts of B and 2 L, the payoffs are (5,7). If 1 plays T and 2 R, the payoffs are (6,2). Finally, both players get...
The table below is the payoff marrix for a simple two-firm game Firms A and B are bidding on a government contract and each f's bid is not known by the other form. Each firm can bid other $14.000 or 55.000 The cost of completing the project for each firm is 53.000 The low bid firm will win the contractat its stated price the high dem wilgot nothing the two bids are equal, the two firms wil split the price...
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