Under what condition can we infer that D is a dominant strategy for Player 1? Player 1 x>y.z<1. x< 1, 2>0. x>0, y< 1. Ⓒy< 1. z>0. U D L X, 0 1, z Player 2 R 0, y z, 1
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- 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…There are 3 workers W1,W2,W3. Neither of these workers can be employed alone so that their value for remaining single is 0. The pair W1 and W2 if employed jointly can earn 100. Likewise the pair W1 and W3. Say the pair W2 and W3 if employed jointly can earn z. The three workers cannot be employed together. What is the maximum value for z such that there is a stable matching in this game ?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 bidders compete in a second price auction (i.e., the winning bidder pays the losing bidder’s bid, and the losing bidder does not pay anything). They submit sealed bids, and the one with the highest bid wins the contract and pays the other bidder’s bid. Each bidder i’s private valuation is vi and is distributed independently and uniformly between 0 and 50. 1. For any given bidder, prove that he has a dominant strategy bid and show what it is. 2. Assuming each bidder bids his dominant strategy noted above, if a bidder with vi = 40 wins, what price does he expect to pay?Consider the charity auction. In many charity auctions, altruistic celebrities auction objects with special value for their fans to raise funds for charity. Madonna, for example, held an auction to sell clothing worn during her career and raised about 3.2 million dollars. In the charity auction the winner of the lot is the highest bidder. The difference with the standard auction is that all bidders are required to pay an amount equal to what they bid. Suppose there are two bidders and assume bidders have valuations randomly drawn from the interval [2, 4] according to the uniform distribution. 1. Derive the equilibrium bidding function. Hint: After getting the differential equation given by the FOC, propose a non-linear bidding function b(v) = α + βv2 as solution. Your task is to find α and β. 2. Derive the revenue of the seller in the charity auction. 3. Would the seller obtain higher profits if she organized a first-price sealed bid auction instead? A. Yes, higher revenue B. No, lower…The Nash equilibrium of the accompanying game is Player 1 Multiple Choice O O O (Y. B). (X, B). X Y Z (Z. C). Player 2 A 9, 8 5, 6 10, 9 none of the provided answers because there is no Nash equilibrium in this game. B 10, 12 12, 20 13, 4 C 3, 15 4, 10 8, 12
- 5.Each of Player 1 and Player 2 chooses an integer from the set {1, 2, ..., K}. If they choose the same integer, P1 gets +1 and P2 gets -1; if they choose different integers, P1 gets -1 and P2 gets +1. (a) Show that it is a NE for each player to choose every integer in {1, 2, ..., K} with equal probability, K1 . (b) Show that there are no NE besides the one you found in (a).One way of which has been proposed for sustaining high levels of contribution in voluntary contribution games is to allow participants to pay to punish free-riders. We believe that this is effective when A) Participants are not altruistic and so are willing to punish free riding. B) All of the other three statements are partial explanations, with participants being willing to punish free riding, potential free riders realising that adherence to the social norm is now the payoff maximising strategy, and the Nash equilibrium becoming adherence to the social norm. C) Participants who are tempted to reduce contributions anticipate future punishment and so conclude that they are better off maintaining contributions. D) Giving participants the ability to punish violation of a social norm means that adherence to the social norm becomes the Nash equilibrium of the game.The mixed stratergy nash equalibrium consists of : the probability of firm A selecting October is 0.692 and probability of firm A selecting December is 0.309. The probability of firm B selecting October is 0.5 and probability of firm selecting December is 0.5. In the equilibrium you calculated above, what is the probability that both consoles are released in October? In December? What are the expected payoffs of firm A and of firm B in equilibrium?
- Consider a simultaneous move game between a union and a company. If both the parties bargain hard, each would gain nothing. If only one party bargains hard the accommodating party gets a profit of $1 million while the bargaining party gets a $5 million, while if they both accommodate, they each get $3 million. If the union leader has already sent strikers to the picket line before entering negotiations, the union has a. Eliminated half of the strategies of the game b. Forced the firm to choose the best response in the union’s best interest c. Made it in the firm’s best interest to accommodate their requests d. All of the aboveConsider a simultaneous move game between a union and a company. If both the parties bargain hard, each would gain nothing. If only one party bargains hard the accommodating party gets a profit of $1 million while the bargaining party gets a $5 million, while if they both accommodate, they each get $3 million. If the union leader has already sent strikers to the picket line before entering negotiations, the union has a. Eliminated half of the strategies of the game b. Forced the firm to choose the best response in the union’s best interest c. Made it in the firm’s best interest to accommodate their requestsWhat is the secure strategy for player B in the game presented in Table
