Microeconomics
11th Edition
ISBN: 9781260507140
Author: David C. Colander
Publisher: McGraw Hill Education
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Question
Chapter 20, Problem 10QE
To determine
Roll back strategy of a player in a simultaneous move game.
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How do we solve a Sequential-move game?
If a game does not have an equilibrium in pure strategies, then it will not have an equilibrium in mixed strategies either.
True or False?
Provide an example of a 2-player normal form game where each player has 3 (pure) strategies such that:
(i) There is no pure strategy Nash equilibrium.
Chapter 20 Solutions
Microeconomics
Ch. 20.1 - Prob. 1QCh. 20.1 - Prob. 2QCh. 20.1 - Prob. 3QCh. 20.1 - Prob. 4QCh. 20.1 - Prob. 5QCh. 20.1 - Prob. 6QCh. 20.1 - Prob. 7QCh. 20.1 - Prob. 8QCh. 20.1 - Prob. 9QCh. 20.1 - Prob. 10Q
Ch. 20.A - Netflix and Hulu each expects profit to rise by...Ch. 20.A - Prob. 2QECh. 20 - Prob. 1QECh. 20 - Prob. 2QECh. 20 - Prob. 3QECh. 20 - Prob. 4QECh. 20 - Prob. 5QECh. 20 - Prob. 6QECh. 20 - Prob. 7QECh. 20 - Prob. 8QECh. 20 - Prob. 9QECh. 20 - Prob. 10QECh. 20 - Prob. 11QECh. 20 - Prob. 12QECh. 20 - Prob. 13QECh. 20 - Prob. 14QECh. 20 - Prob. 15QECh. 20 - Prob. 16QECh. 20 - Prob. 1QAPCh. 20 - Prob. 2QAPCh. 20 - Prob. 3QAPCh. 20 - Prob. 4QAPCh. 20 - Prob. 5QAPCh. 20 - Prob. 6QAPCh. 20 - Prob. 1IPCh. 20 - Prob. 2IPCh. 20 - Prob. 3IPCh. 20 - Prob. 4IPCh. 20 - Prob. 5IPCh. 20 - Prob. 6IPCh. 20 - Prob. 7IP
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Similar questions
- Can a strategy be dominant for one player in a Nash equilibriumarrow_forwardConsider a game where player A moves first, choosing between Left and Right. Then, after observing player A’s choice, player B moves next choosing between Up and Down. Which of the following is true? This is a game where players A and B have the same number of strategies. Player A will get a higher payoff than player B as A moves first. This is game will only have one Nash equilibrium. This is a game of perfect information.arrow_forwardProve that in a 2 × 2 zero-sum game, if equilibrium strategies exist then one of the players has a dominated strategy.arrow_forward
- Consider the following game. There are two companies that sell Haitian coffee. Each company currently makes$5 million in revenue. They need to determine whether they should engage in a social media advertising campaign. Advertising costs$2 million for each company. If one company advertises, and the other does not, then the one that advertises captures$3 million from the company that does not. If both companies advertise, they gain nothing. Draw the payoff matrix. What is this game’s Nash equilibrium (or equilibria)arrow_forwardConsider the game shown below. In this game, players 1 and 2 must move at the same time without knowledge of the other player’s move. Player 1’s choices are shown in the row headings (A, B, C), Player 2’s choices are shown in the column headings (D, E, F). The first payoff is for the row player (Player 1) and the second payoff is for the column player (Player 2). Player 2 Player 1 D E F A 6, 8 4, 7 2, 9 B 2, 3 2, 6 4, 7 C 5, 4 7, 5 3, 6arrow_forwardConsider the payoff matrix of a two player game below what are the strategies in the Nash equilibriumarrow_forward
- In the game above, what is/are the EFFICIENT sub-game perfect Nash equilibrium?arrow_forwardConsider the following game. There are two payers, Player 1 and Player 2. Player 1 chooses a row (10, 20, or 30), and Player 2 chooses a column (10/20/30). Payoffs are in the cells of the table, with those on the left going to Player 1 and those on the right going to player 2. For example, a payoff 100/200 would mean Player 1 receives 100 and Player 2 receives 200.What is [are] the Nash Equilibrium [Equilibria] of this game?A) (10/10) and (20/20)B) (30/30)C) (10/20) and (20/10)D) (20/20)E) (30/30)arrow_forwardAssume a Hawk -Dove game with the following payoff matrix, where the first entry is Animal A’s payoff, and the second entry is Animal B’s payoff: Animal A (rows)/Animal B (columns) Hawk Dove Hawk (-5,-5) (10,0) Dove (0,10) (4,4) An animal that plays Hawk will always fight until it wins or is badly hurt. An animal that plays Dove makes a bold display but retreats if his opponent starts to fight. If two Dove animals meet they share. Explain why there cannot be an equilibrium where all animals act as Doves. Explore whether there are any Nash equilibria in pure strategies and explain which these are and why. Derive a mixed strategy Nash equilibrium (MSNE). What is the proportion of Hawks and Doves? If the proportion of Hawks in the population of animals is greater than the mixed strategy equilibrium proportion you calculated, which strategy does better, Hawks of Doves?arrow_forward
- Suppose there are two farmers, each of whom has the right to graze cows on the village common. Denote by sA and sB the number of cows farmers A and B graze, respectively. The payoff per cow is given by 120-sA-sB and farmers decide on the number of cows they will graze on the common simultaneously (a) Formulate this situation as a strategic game and find the Nash equilibrium (b) Compare the equilibrium farmer profits to those that would have been realized if each farmer grazed 30 cows on the village common. Explainarrow_forwardConsider a simultaneous game where player A has a dominant strategy and player B has two strategies (none of which is a dominant strategy). How many pure strategy Nash equilibria will this game have? A) Exactly 1 B) Exactly 2 C) Either 1 or 2 D) Nonearrow_forwardConsider the game shown below. In this game, players 1 and 2 must move at the same time without knowledge of the other player’s move. Player 1’s choices are shown in the row headings (A, B, C, D), Player 2’s choices are shown in the column headings (E, F, G). The first payoff is for the row player (Player 1) and the second payoff is for the column player (Player 2). Player 2 Player 1 E F G A 2, 4 7, 7 2, 6 B 10, 6 1, 7 12, 4 C 4, 6 8, 8 7, 7 D 1, 6 3, 9 6, 7arrow_forward
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