The ultimatum game is a game in economic experiments. The first player (the proposer) receives a sum of money and proposes a fair proposal (F-5;5) or unfair proposal (U - 8;2). The second player (the responder) chooses to either accept (A) or reject (R) this proposal. If the second player accepts, the money is split according to the proposal. If the second player rejects, neither player receives any money. 1 A 5:5 2 F R 0; 0 U A 8:2 2 1. Find the subgame perfect Nash Equilibrium using backward induction. R 0:0
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- In this version of the ultimatum game experiment, one participant is given £100, and is told to offer to split that amount with another participant. The second player can either refuse to accept the division, in which case the participant receiving the £100 has to give it back, or can accept the division, in which case, the player receiving the money splits the £100 as proposed. For the participant who has to accept or reject the offer A) The best strategy is to accept any offer which meets the social norm for fairness. B) The best strategy is to threaten to turn down any transfer of less than £100 to ensure that the person receiving the money makes a fair offer. C) There is a dominant strategy to accept any offer because gaining some money is better than gaining no money D) There is a dominant strategy to turn down any offer other than £50 because an unequal split would be unfair.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 existWhen a famous painting becomes available for sale, it is often known which museum or collector will be the likely winner. Yet, the auctioneer actively woos representatives of other museums that have no chance of winning to attend anyway. Suppose a piece of art has recently become available for sale and will be auctioned off to the highest bidder, with the winner paying an amount equal to the second highest bid. Assume that most collectors know that Valerie places a value of $15,000 on the art piece and that she values this art piece more than any other collector. Suppose that if no one else shows up, Valerie simply bids $15,000/2=$7,500 and wins the piece of art. The expected price paid by Valerie, with no other bidders present, is $________.. Suppose the owner of the artwork manages to recruit another bidder, Antonio, to the auction. Antonio is known to value the art piece at $12,000. The expected price paid by Valerie, given the presence of the second bidder Antonio, is $_______. .
- onsider the game described by the ff table. what is thE best response for the column player if he/she knows that the row player will make the Y move?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 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…
- 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…A Bank has foreclosed on a home mortgage and is selling the house at auction. There are two bidders for the house, Zeke and Heidi. The bank does not know the willingness to pay of these three bidders for the house, but on the basis of its previous experience, the bank believes that each of these bidders has a probability of 1/3 of valuing it at $800,000, a probability of 1/3 of valuing at $600,000, and a probability of 1/3 of valuing it at $300,000. The bank believes that these probabilities are independent among buyers. If the bank sells the house by means of a second- bidder, sealed-bid auction, what will be the bank’s expected revenue from the sale? The answer is 455, 556. Please show the steps in details thank you!(The All-Pay Auction). The seller has an item for sale. The valuations of the bidders are independently and identically distributed on R+ with a c.d.f. F. Find the symmetric equilibrium of an auction with two bidders in which both bidders pay their own bids but only the highest bidder wins the object. Show that each bidder’s expected payment is the same in this auction and in the first-price auction.
- Suppose two bidders compete for a single indivisible item (e.g., a used car, a piece of art, etc.). We assume that bidder 1 values the item at $v1, and bidder 2 values the item at $v2. We assume that v1 > v2. In this problem we study a second price auction, which proceeds as follows. Each player i = 1, 2 simultaneously chooses a bid bi ≥ 0. The higher of the two bidders wins, and pays the second highest bid (in this case, the other player’s bid). In case of a tie, suppose the item goes to bidder 1. If a bidder does not win, their payoff is zero; if the bidder wins, their payoff is their value minus the second highest bid. a) Now suppose that player 1 bids b1 = v2 and player 2 bids b2 = v1, i.e., they both bid the value of the other player. (Note that in this case, player 2 is bidding above their value!) Show that this is a pure NE of the second price auction. (Note that in this pure NE the player with the lower value wins, while in the weak dominant strategy equilibrium where both…Consider two bidders – Alice and Bob who are bidding for a second-hand car. Each of them knows the private value she/he assigns to the car, but does not know the exact value of others. It is common knowledge that the value of other bidders is randomly drawn from a uniform distribution between 0 and $10000. Assume that Alice values the car at $8500 and Bob values the car at $4500. a) If Alice and Bob participated in the second-price sealed bid auction, what would they bid and what would be the result of the auction? Explain your answer. b) If they participate instead in a first-price sealed bid auction, what would they bid and what would be the result of the auction? Explain your answer. c) Calculate and compare the revenue of the seller in the above situations. Which type of auction should the seller use? Explain your answerThe count is three balls and two strikes, and the bases are empty. The batter wants to maximize the probability of getting a hit or a walk, while the pitcher wants to minimize this probability. The pitcher has to decide whether to throw a fast ball or a curve ball, while the batter has to decide whether to prepare for a fast ball or a curve ball. The strategic form of this game is shown here. Find all Nash equilibria in mixed strategies.