Two players bargain over $20. They proceed as follows. Player 1 first proposes a split(n; 20-n); where n is an integer in {0, 1,.... 20 }. Player 2 can either accept or reject this proposal. If player 1 accepts it, player 1 obtains $n and player 2 obtains $(20-n) If player 2 rejects it, the money is taken away from them and both players will get $0 Find one Nash equilibrium that is not a subgame perfect Nash equilibrium. Explain why it is a Nash equilibrium and why it is not subgame perfect.

Two players bargain over $20. They proceed as follows. Player 1 first proposes a split(n; 20-n); where n is an integer in {0, 1,.... 20 }. Player 2 can either accept or reject this proposal. If player 1 accepts it, player 1 obtains $n and player 2 obtains $(20-n) If player 2 rejects it, the money is taken away from them and both players will get $0 Find one Nash equilibrium that is not a subgame perfect Nash equilibrium. Explain why it is a Nash equilibrium and why it is not subgame perfect.

Managerial Economics: A Problem Solving Approach

5th Edition

ISBN:9781337106665

Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor

Chapter15: Strategic Games

Section: Chapter Questions

Problem 2MC

See similar textbooks

Similar questions

Player 1 and Player 2 are trying to agree on how to split a pie of size 1 in a two-stage bargaining game. If no agreement is reached after the two stages are complete, the pie is split for them according to a pre-arranged agreement that gives Player 1 and Player 2 one-quarter and three quarters of the pie, respectively. In the first stage, Player 1 makes an offer (x1, x2), where x1 + x2 = 1. Player 2 can either accept this offer (at which point the game ends and the pie is split according to Player 1’s offer), or can make a counter-offer. When Player 2 makes a counter offer, Player 1 can either accept (in which case the pie is split according to Player 2’s offer) or can reject, in which case the pie is split according to the pre-arranged agreement. Both players have a discount factor d – getting dx in the first stage (after Player 1’s proposal) is as good as getting x in the second stage (after Player 2’s proposal). a) In the last stage of the game, Player 1 will accept any offer…
two players, a and b are playing an asymmetrical game. there are n points on the game board. each turn player a targets a pair of points and player b says whether those two points are connected or unconnected. a can target each pair only once and the game ends when all pairs have been targeted. player b wins if a point is connected with all other points on the very last turn, while player a wins if any point is connected with all other points on any turn but the very last one or if no point is connected to all other points after the last turn. for what values of n does either player have a winning strategy?
Consider the following sequential strategic situation, called the centipede game. The game has 100 stages. Two players take turns making decisions, starting with player 1. At stage t = 1,...,99, player 1 (if the stage is odd) or player 2 (if the stage if even) chooses whether to "Terminate the game" or to "Continue the game." If the game is terminated instage t = 1,...,99, the player terminating the game receives a payoff of t, while the other player receives a payoff of zero. Finally, at stage t = 100, player 2 chooses between action A with a payoff of 99 for each player, or action B with a payoff of zero for player 1 and a payoff of 100 for player 2. Draw the game tree for this situation. What is the SPNE?
Consider the following game of ’divide the dollar.’ There is a dollar to be split between two players. Player 1 can make any offer to player 2 in increments of 25 cents; that is, player 1 can make offers of 0 cents, 25 cents, 50 cents, 75 cents, and $1. An offer is the amount of the original dollar that player 1 would like player 2 to have. After player 2 gets an offer, she has the option of either accepting or rejecting the offer. If she accepts, she gets the offered amount and player 1 keeps the remainder. If she rejects, neither player gets anything. Draw the game tree of the modified version of the ’divide the dollar’ game in which player 2 can make a counteroffer if she does not accept player 1’s offer. After player 2 makes her counteroffer - if she does - player 1 can accept or reject the counteroffer. As before, if there is no agreement after the two rounds of offers, neither player gets anything. If there is an agreement in either round then each player gets the amount agreed…
A payoff matrix is shown below. With the payoffs in each field indicated in the form (Player 1’s payoff, Player 2’s payoff). Player 2 Left Right Player 1 Up ($1, $1) ($2, $4) Down ($7, $8) ($3, $3) Which of the following is true? The only Nash Equilibrium is Player 1 playing ‘Up’ and Player 2 playing ‘Right’. The only Nash Equilibrium is Player 1 playing ‘Down’ and Player 2 playing ‘Left’. The only Nash Equilibrium is Player 1 playing ‘Down’ and Player 2 playing ‘Right’. None of the other answers provided are true.
Consider 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. Suppose that Player 1 chooses his strategy (10, 20 or 30), first, and subsequently, and after observing Player 1’s choice, Player 2 chooses his own strategy (of 10, 20 or 30). Which of the following statements is true regarding this modified game? I. It is a simultaneous move game, because the timing of moves is irrelevant in classifying games.II. It is a sequential move game, because Player 2 observes Player 1’s choice before he chooses his own strategy.III. This modification gives Player 1 a ‘first mover advantage’. A) I and IIB) II and IIIC) I and IIID) I onlyE) II only
Two players bargain over $20. Player 1 first proposes a split of(n, 20 - n), where n is an integer in {0, 1, ..., 20}. Player 2 can either accept or reject this proposal. If player accepts it, player 1 obtains $n and player 2 obtains $(20 - n). If player 2 rejects it, the money is taken away from them and both players will get $0. Question: Find two subgame perfect Nash equilibria of this game and state clearly each player's equilibrium strategies (recall that in a dynamic game, a player's strategy is a complete-contingent plan). Explain why the strategy profiles form a subgame perfect equilibrium.
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)
The 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 answer
Consider 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 (Player1) and the second payoff is for the column player (Player 2). Player 2 Player 1 E F G A 2, 7 7, 2 2, 6 B 5, 5 5, 4 8, 4 C 4, 6 8, 4 7, 5 D 1, 6 3, 5 6, 4 Highlight the correct answer: Player 1: Has a dominant strategy to choose A Has a dominant strategy to choose B Has a dominant strategy to choose C Has a dominant strategy to choose D Does not have a dominant strategy Player 2: Has a dominant strategy to choose E Has a dominant strategy to choose F Has a dominant strategy to choose G Does not have a dominant strategy The Nash equilibrium outcome to this game is: A/F B/E B/G C/F C/G There is no pure strategy Nash…
Consider the game the following game: - Two players, six rounds of decision-making alternating between player 1 and 2, starting with player 1. - Game starts with $0.50. The player making the decision is given the option to Grab (80% of the money), or Leave it to double in the next round. - If player 2 picks Leave in the last round, she receives $6.40, and player 1 receives $25.60. Solve game via Backwards Induction.
Two 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 > 0.7