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(a) There are two players in this game - A and B. A moves first and can go either left L or right...
3. (30 pts) Consider the following game. Players can choose either left () or 'right' (r) The tab...
3. (30 pts) Consider the following game. Players can choose either left () or 'right' (r) The table provided below gives the payoffs to player A and B given any set of choices, where player A's payoff is the firat number and player B's payoff is the second number Player B Player A 4,4 1,6 r 6,1 -3.-3 (a) Solve for the pure strategy Nash equilibria. (4 pta) (b) Suppose player A chooses l with probability p and player B...
6. The following stage game is played repeatedly for 2 periods. Note that both players observe...
6. The following stage game is played repeatedly for 2 periods. Note that both players observe the decisions made in period 1 before they play again in period 2. The final payoffs to each player are the sum of the payoffs obtained in each period. 112 L R T 1,1 5,0 B 0,3 7,7 (a) Represent this game in extensive form (tree diagram. How many subgames are there? (b) Using backward induction, find all subgame perfect Nash equilibria (SPE) in...
Consider a game in which Player 1 first selects between L and R. If Player 1...
Consider a game in which Player 1 first selects between L and R. If Player 1 selects L, then players 1 and 2 play a prisoner’s dilemma game represented in the strategic form above. If Player 1 selects R then, Player 1 and 2 play the battle-of-the-sexes game in which they simultaneously and independently choose between A and B. If they both choose A, then the payoff vector is (4,4). If they both choose B, then the payoff vector is...
Q1. Suppose two players, First and Second, take part in a sequential-move game. First moves first,...
Q1. Suppose two players, First and Second, take part in a sequential-move game. First moves first, Second moves second, and each player moves only once. (a). Draw a game tree for a game in which First has two possible actions (Up or Down), and Second has three possible actions (Top, Middle, or Bottom) at each node. Show which nodes are terminal/decision and write down all the (pure) strategies of each player. (b). Draw a game tree for a game in...
Consider a sequential move game with two players. If the player who moves first has two...
Consider a sequential move game with two players. If the player who moves first has two or more strategies that offer him the same payoff, which one will he choose?
Problem 1. (20 points) Consider a game with two players, Alice and Bob. Alice can choose...
Problem 1. (20 points) Consider a game with two players, Alice and Bob. Alice can choose A or B. The game ends if she chooses A while it continues to Bob if she chooses B. Bob then can choose C or D. If he chooses C the game ends, and if he chooses D the game continues to Alice. Finally, Alice can choose E or F and the game ends after each of these choices. a. Present this game as...
First part: Consider the following two-player game. The players simultaneously and independently announce an integer number...
First part: Consider the following two-player game. The players simultaneously and independently announce an integer number between 1 and 100, and each player's payoff is the product of the two numbers announced. (a) Describe the best responses of this game. How many Nash equilibria does the game have? Explain. (b) Now, consider the following variation of the game: first, Player 1 can choose either to "Stop" or "Con- tinue". If she chooses "Stop", then the game ends with the pair...
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....
Consider the following game: there are two players, an incumbent (denoted I) and a potential entrant...
Consider the following game: there are two players, an incumbent (denoted I) and a potential entrant (denoted E) to the market. The entrant has two actions: it can either enter the market in which the incumbent operates, or not enter. The incumbent has two actions: it can either fight the entrant, or accommodate. The payoffs are as follows: if E enters and I fights, E gets -1 and I gets 2. If E does not enter, I gets 10 for...
2. consider the following simultaneous move game. Player B LEFT RIGHT Player A UP 4,1 1,4...
2. consider the following simultaneous move game. Player B LEFT RIGHT Player A UP 4,1 1,4 DOWN 2,3 3,2 a. If there is a Nash equilibrium in pure strategies, what is it and what are the payoffs? b. If there is a Nash equilibrium in mixed strategies, what is it and what are the expected payoffs? 3. Continue with the previous game but suppose this was a sequential game where Player A got to go first. a. Diagram the game...
3. (30 pts) Consider the following game. Players can choose either left () or 'right' (r) The table provided below gives the payoffs to player A and B given any set of choices, where player A's payoff is the firat number and player B's payoff is the second number Player B Player A 4,4 1,6 r 6,1 -3.-3 (a) Solve for the pure strategy Nash equilibria. (4 pta) (b) Suppose player A chooses l with probability p and player B...
6. The following stage game is played repeatedly for 2 periods. Note that both players observe the decisions made in period 1 before they play again in period 2. The final payoffs to each player are the sum of the payoffs obtained in each period. 112 L R T 1,1 5,0 B 0,3 7,7 (a) Represent this game in extensive form (tree diagram. How many subgames are there? (b) Using backward induction, find all subgame perfect Nash equilibria (SPE) in...
Q1. Suppose two players, First and Second, take part in a sequential-move game. First moves first, Second moves second, and each player moves only once. (a). Draw a game tree for a game in which First has two possible actions (Up or Down), and Second has three possible actions (Top, Middle, or Bottom) at each node. Show which nodes are terminal/decision and write down all the (pure) strategies of each player. (b). Draw a game tree for a game in...
Problem 1. (20 points) Consider a game with two players, Alice and Bob. Alice can choose A or B. The game ends if she chooses A while it continues to Bob if she chooses B. Bob then can choose C or D. If he chooses C the game ends, and if he chooses D the game continues to Alice. Finally, Alice can choose E or F and the game ends after each of these choices. a. Present this game as...
First part: Consider the following two-player game. The players simultaneously and independently announce an integer number between 1 and 100, and each player's payoff is the product of the two numbers announced. (a) Describe the best responses of this game. How many Nash equilibria does the game have? Explain. (b) Now, consider the following variation of the game: first, Player 1 can choose either to "Stop" or "Con- tinue". If she chooses "Stop", then the game ends with the pair...
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