Suppose there are two criminals who are thinking about robbing either an insurance company or a liquor store. The take from the insurance company robbery would be Gh50,000 each, but the job requires two people (one to do the robbing and one to drive the getaway car). The take from robing a liquor store is only $1000 but can be done with one person acting alone or both. a. What are the strategies of these players (the two criminals)? b. Write this situation in a normal game form assuming they are acting simultaneously. c. What are the equilibria for this game? (Note: Both Pure strategy and Mixed strategy)

Suppose there are two criminals who are thinking about robbing either an insurance company or a liquor store. The take from the insurance company robbery would be Gh50,000 each, but the job requires two people (one to do the robbing and one to drive the getaway car). The take from robing a liquor store is only $1000 but can be done with one person acting alone or both. a. What are the strategies of these players (the two criminals)? b. Write this situation in a normal game form assuming they are acting simultaneously. c. What are the equilibria for this game? (Note: Both Pure strategy and Mixed strategy)

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.9P

See similar textbooks

Similar questions

We have a group of three friends: Kramer, Jerry and Elaine. Kramer has a $10 banknote that he will auction off, and Jerry and Elaine will be bidding for it. Jerry and Elaine have to submit their bids to Kramer privately, both at the same time. We assume that both Jerry and Elaine only have $2 that day, and the available strategies to each one of them are to bid either$0, $1 or $2. Whoever places the highest bid, wins the $10 banknote. In case of a tie (that is, if Jerry and Elaine submit the same bid), each one of them gets $5. Regardless of who wins the auction, each bidder has to pay to Kramer whatever he or she bid. Does this game have a Nash Equilibrium? (If not, why not? If yes, what is the Nash Equilibrium?)
We have a group of three friends: Kramer, Jerry and Elaine. Kramer has a $10 banknote that he will auction off, and Jerry and Elaine will be bidding for it. Jerry and Elaine have to submit their bids to Kramer privately, both at the same time. We assume that both Jerry and Elaine only have $2 that day, and the available strategies to each one of them are to bid either$0, $1 or $2. Whoever places the highest bid, wins the $10 banknote. In case of a tie (that is, if Jerry and Elaine submit the same bid), each one of them gets $5. Regardless of who wins the auction, each bidder has to pay to Kramer whatever he or she bid. Does Jerry have any strictly dominant strategy? Does Elaine?
If the players play pure strategies, the game has no Nash equilibrium. But what if they choose their moves randomly? Let each player instead opt for a mixed strategy instead of a pure strategy. The first will play action Z with probability p, and the second will play action L with probability q. At which pair (p, q) are the mixed strategies of the players in equilibrium? At which pair (p, q) does neither player want to change strategy? When are both strategies simultaneously the best response?
Boris and Angela are negotiating a new trade deal, which resembles a modified centipede game. When it is their turn, each of them decides whether to cooperate (C) or to decline (D). Unfortunately, Angela is not sure how much time Boris has for the negotiations before he needs to leave to talk to Emmanuel. With probability p = 4/5, Boris will stay and insist on making the final proposal (long game, L). With probability 1 − p = 1/5, Boris will have to rush off, so that the game ends after Angela’s move (short game, S). Boris has perfect knowledge of his schedule. The structure and payoffs are represented in the game tree below (Attached picture). (a) Specify the set of possible histories H of the game. Underline terminal histories.(b) Specify the set of possible strategies for Boris and Angela.(c) How many subgames does this game have? Indicate all subgames in this game
Assume the following game situation: If Player A plays UP and Player B plays LEFT then Player A gets $2 and Player B gets $4. If Player A plays UP and Player B plays RIGHT then Player A gets $3 and Player B gets $6. If Player A plays DOWN and Player B plays LEFT then Player A gets $5 and Player B gets $2. If Player A plays DOWN and Player B plays RIGHT then Player A gets $1 and Player B gets $1. What is the mixed strategy expected payout for Player B? 1 40/15 39/15 11/2
Consider the following Bayesian game. There are two players 1 and 2. Both players choose whether to play A or B. Two states are possible, L and R. In the former, players play a stag-hunt game, and in the latter, players play a matching pennies game. Suppose that Player 2 knows the state, while Player 1 thinks that the state is L with probability q and R with probability 1 ! q. Payo§s in each state respectively satisfy: Player 1 is the row player, and their payo§ is the first to appear in each entry. Player 2 is thecolumn player and their payo§ is the second to appear in each entry. (a) What is the set of possible strategies for the two players in this game? (b) Find all the pure strategy Bayes Nash equilibria for any value of q 2 (0, 1).
Consider the game of Chicken in which each player has the option to “get out of the way” and “hang tough” with payoffs: Get out of the way Hang tough Get out of the way 2,2 1,3 Hang tough 3,1 00 a. Find all pure strategy Nash equilibria, if they exist b. Let k be the probability that player 1 chooses “hang tough” and u be the probability that player two chooses “hang tough.” Find the mixed stragety Nash equilibria, if they exist
Two street racers are playing a simultaneous game of chicken. They have to race towards each other and whoever swerves first is chicken and faces shame, a loss of 8. while the winner enjoys a gain of 3. If neither stop, they would crash into each other, a loss of 10. If both of them swerve at the same time, they are both chicken and face a loss of 5 each If player B destroys his own brakes before the race, and player A sees that, what would the new Nash equilibrium be in this case? a. Player A stops, Player B does not b. Player B stops, Player A does not c. Both players stop d. Neither players stop
Two players bargain over 1 unit of a divisible object. Bargaining starts with an offer of player 1, which player 2 either accepts or rejects. If player 2 rejects, then player 1 makes another offer; if player 2 rejects once more, then player 2 makes an offer. If player 1 rejects the offer of player 2, then once more it is the turn of player 1 where he makes two consecutive offers. As long as an agreement has not been reached this procedure continues. For example, suppose that agreement is reached at period 5, it follows that player 1 makes offers in period 1,2 then player 2 makes an o er in period 3, then player 1 makes offers in 4,5. Negotiations can continue indefinitely, agreement in period 't' with a division (x, 1- x) leads to payoffs ( , (1-x)).(The difference from Rubinstein's alternating offer bargaining is that player one makes two consecutive offers, whereas player 2 makes a single offer in her turn.) a. Show that there is a subgame perfect equilibrium in which player 2's…
Suppose that player 1 (row) and player 2 (column) play a simultaneous game. Player 1 can choose to go out (Go) or stay at home (Stay). Player 2 can then choose whether to buy tickets to the movies (Movie), to the basketball game (Game) or not buy tickets (None). This game is shown below. Player 1(row) Player 2 (column) Movie Game None Go (6, 4) (4, 6) (0, 0) Stay (2, - 2) (2, - 4) (3, 3) What is the Maxi-Min strategy for player 1 and for player 2? Explain why. What are the Nash equilibrium or equilibria for this game? Explain why. What kind of game is this? Argue what is the most likely outcome.
Each actor has two possible actions: reduce greenhouse-gas emissions or increase emissions. Each player's payoffs for various combinations of actions are shown in the cells: by convention, the row player (EU)'s payoffs are shown first, and the column player (China)'s payoffs are shown second. Based on this matrix, which of the following statements are true? A.The EU is better off reducing its emissions, but only if China also reduces its emissions B. China is better off increasing its emissions, but only if the EU also increases its emissions C.Both China and the EU are better off increasing their emissions, whatever the other player does D.All of the above E.None of the above
Suppose that 5 risk neutral competitors participate in a rent seeking game with a fixed prize of $100. Each player may invest as much as he wishes in the political contest, although those investments have an opportunity cost equal 1. The probability of winning is directly proportional to the candidate’s share of the total rent-seeking investment. What is the profit-maximizing investment by player 1 as a function of the investment by all the others? What is a Nash equilibrium investment by each player in a symmetric game?