EBK MICROECONOMICS
2nd Edition
ISBN: 9780134524931
Author: List
Publisher: YUZU
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Question
Chapter 18, Problem 6Q
To determine
Scenario where the friend-foe game ends with both the players splitting the money.
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Does either of the player have a dominant strategy
The dominant strategy for player 2 in the accompanying game is?
In the collusion game, collusion was only sustainable in the infinite horizon repeated game. One Nash Equilibrium of that game can be found when all players play a “grim trigger” strategy, where they collude until an opponent chooses to compete, and then compete for all future rounds as a punishment. In such a game, if the one period bonus that comes from competing is low enough, firms always collude and the punishment is never triggered. Is the punishment (vowing to compete forever after one deviates) realistic, especially if firms can communicate freely? Why or why not? (Hint: Is a grim trigger Nash Equilibrium a Subgame Perfect Nash Equilibrium? What kinds of Nash Equilibria does Subgame erfection rule out in sequential games?)
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- Refer to the normal-form game of price competition in the payoff matrix below Firm B Low Price High Price Firm A Low Price 0, 0 50, −10 High Price −10, 50 20, 20 Suppose the game is infinitely repeated, and the interest rate is 20 percent. Both firms agree to charge a high price, provided no player has charged a low price in the past. This collusive outcome will be implemented with a trigger strategy that states that if any firm cheats, then the agreement is no longer valid, and each firm may make independent decisions. Will the trigger strategy be effective in implementing the collusive agreement? Please explain and show all necessary calculations.arrow_forwardThe following payoff table lists the profits of a buyer and a seller. The seller acts first by choosing a sale price ($9, $8, or $6). The buyer then decides the quantity of the good to purchase (two units, four units, six units, or eight units). a. Suppose the buyer and seller transact only once. Does the buyer have a dominant strategy? Depending on the price quoted, what is his best response? What price should the seller set? Explain carefully. Buyer Quantities 2 Units 4 Units 6 Units 8 Units P $9 10, 6 20, 5 30, 0 40, 8 Seller P $8 8, 8 16, 9 24, 6 32, 0 Prices P $6 4, 12 8, 17 12, 18 16, 16 b. Suppose the seller and buyer are in a multiyear relationship. Each month, the buyer quotes a price and the seller selects her quantity. How might this change each player’s behavior? c. Now suppose the buyer and seller are in a position to negotiate an agreement specifying price and quantity. Can they improve on the result in part (a)? Which quantity should they set? What price would be…arrow_forwardConsider a simultaneous move game with two players. Player 1 has three possible actions (A, B, or C) and Player 2 has two possible actions (D or E.) In the payoff matrix below, each cell contains the payoff for Player 1 followed by the payoff for Player 2. Identify any dominated strategies in this game. If there are none, state this clearly.arrow_forward
- Consider the following representation of a hockey shootout. The shooter can shoot on their forehand, or deke to their backhand, and the goalie can anticipate either move. The number in each cell in the table below represents the percentage chance that the shooter scores for each pair of pure strategies. Anticipate Forehand Anticipate Backhand Shoot Forehand 20 40 Deke Backhand 40 10 In the mixed strategy Nash equilibrium of this game, what is the percentage chance that the player scores? (ie. An 80% chance should be recorded as 80)arrow_forwardThe London Metro Bus is crowded for travel during peak hours. During such travel hours two daily passengers ‘James’ and ‘Robert’ enter the Metro. Luckily, two adjacent seats are free in the bus. Each of them must decide whether to sit or stand. For both, sitting alone is more comfortable than sitting next to the other person, which in turn is more comfortable than standing. consider James as ‘row player’ and Robert as ‘column player). a) Model the situation as a strategic game, assuming both ‘James’ and ‘Robert’ care only about their own comfort. Find the Nash equilibrium (equilibria) if it exists. Also, does a dominant strategy exist for either ‘James’ or ‘Robert’? show ALL steps and working in support to the answerarrow_forwardIn a sequential game, the first mover into a new market Multiple Choice always earns a greater payoff than the second mover. may discourage the second mover from entering that market. only enters when there is a dominant strategy. guarantees that a Nash equilibrium will result.arrow_forward
- Consider the above extensive-form game. If player 1 chooses U, player 2 will choose____. If player 1 chooses D, player 2 will choose _____. Based on this, player 1 should choose to play ____.arrow_forwardTwo players, Player 1 and Player 2, are playing a repeated prisoner’s dilemma. Payoffs are described in the following matrix. Answer which statement is correct: Select one: a. A trigger strategy will never support (A,A) as an equilibrium b. A tit-for-tat strategy will never support (A,A) as an equilibrium c. A tit-for-tat strategy will support (A,A) as an equilibrium if δ > 0.7 d. A trigger strategy will support (A,A) as an equilibrium if δ > 0.7arrow_forward
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