What amount does each bidder bid in the Bayesian Nash equilibrium of a 2nd price auction? The expected value of the second highest bidder. One half of the expected value of the second highest bidder. Their own value. One half of their own value.
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- Consider the two Nash equilibria found above. Is any one of them a Perfect Bayesian Equilibrium (PBE)? Explain. In particular, consider each NE and argue why they are or are not part of a PBE. [Note: A complete description of PBE must specify beliefs as a part of description of the equilibrium.]Q:1 Jhon have server and many clients or bidders bidders who are bidding with their resources (datasize,bandwidth) and price they want to sell their resources. Jhon is using first price sealed bid auction here. Jhon need to select winners. Please apply Nash equilibrium strategy for clients to maximize the expected profit and expected utility theory to give guidance to the aggregator to obtain the expected resources from clients. Note: related material is attached in pictures.Question 1 Consider a first-price sealed bid auction of a single object with two biddersj = 1,2 and no reservation price. Bidder 1′s valuation is v1 = 2, and bidder 2′s valuation isv1 = 5. Both v1 and v2 are known to both bidders. Bids must be in whole dollar amounts.In the event of a tie, the object is awarded by a flip of a fair coin.(a) Find an equilibrium of this game.(b) Is the allocation of your answer to (a) efficient?
- 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 the following coordination game: Player 2P1 Comedy Show Concert Comedy Show 11,5 0,0 Concert 0,0 2,2 a. Find the Nash equilibrium(s) for this game.b. Now assume Player 1 and Player 2 have distributional preferences. Specifically, both people greatly care about the utility of the other person. In fact, they place equal weight on their outcome and the other person’soutcome, ρ = σ = ½. Find the Nash equilibrium(s) with these utilitarianpreferences.c. Now consider the case where Player1 and Player2 do not like each other. Specifically, any positive outcome for the other person is viewed as anegative outcome for the individual, ρ = σ = -1. Find the Nashequilibrium(s) with these envious preferences.See the extensive form game image attached. 1) Solve the game by backward induction 2) Find all the pure-strategy Nash equilibria (in complete contingent plans)of the extensive-form game (no need to write down thenormal-form representation)
- At a company, 20 employees are making contributions for a retirement gift.Each person is choosing how many dollars to contribute from the interval[0,10]. The payoff to person i is bi X xi - xi, where bi > 0 is the “warm glow”he receives from each dollar he contributes, and he incurs a personal cost of 1.a. Assume bi < 1 for all i. Find all Nash equilibria. How much is collected?b. Assume bi > 1 for all i. Find all Nash equilibria. How much is collected?c. Assume bi = 1 for all i. Find all Nash equilibria. How much is collected?Now suppose the manager of these 20 employees has announced that shewill contribute d > 0 dollars for each dollar that an employee contributes.The warm glow effect to employee i from contributing a dollar is now bi X(1 + d) because each dollar contributed actually results in a total contribution of 1 + d. Assume bi = 0.1 for i = 1, . . . , 5; bi = 0.2 for i = 6, . . . , 10; bi = 0.25 for i = 11, . . . , 15; and bi = 0.5 for i = 16, . . . , 20.d. What…Determine the Nash equilibriaDerive all of the rationalizable strategies for the game shown.
- H7. Find all pure strategy Nash equilibria and for each one, state whether or not it is subgame perfect.In 'the dictator' game, one player (the dictator) chooses how to divide a pot of $10 between herself and another player (the recipient). The recipient does not have an opportunity to reject the proposed distribution. As such, if the dictator only cares about how much money she makes, she should keep all $10 for herself and give the recipient nothing. However, when economists conduct experiments with the dictator game, they find that dictators often offer strictly positive amounts to the recipients. Are dictators behaving irrationally in these experiments? Whether you think they are or not, your response should try to provide an explanation for the behavior.on 8.1 Consider the following game: Player 1 A C D 7,6 5,8 0,0 Player 2 E 5,8 7,6 1, 1 F 0,0 1,1 4,4 a. Find the pure-strategy Nash equilibria (if any). b. Find the mixed-strategy Nash equilibrium in which each player randomizes over just the first two actions. c. Compute players' expected payoffs in the equilibria found in parts (a) and (b). d. Draw the extensive form for this game.