4. An auctioneer holds a second-price auction for two bidders, Ann (A) and Bonnie (B), who have independent private values of the good 0 and 0. If a bidder wins, her payoff is her value 0 minus the price she pays, and if she loses, her payoff is 0. The values are independently and identically distributed, but otherwise you don't need to know the specific distributions to solve the problem. Ann and Bonnie's respective strategies are to bid some value be). that is, bid given their privately-known value (type). a. Explain what a second price auction is, who wins given some pair of bids b, and bg and what the winner pays. b. Why is a strategy where Ann bids above her own value e, weakly dominated by a strategy where she bids her value? c. Why is a strategy where Ann bids below her own value e, weakly dominated by a strategy where she bids her value?

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Consider a market entry game with imperfect information as depicted in the following picture. 2. Market entry P, A, A, A, 1-p B, B, B, В. B, B, B, \B, 7 7 7 5 5 4 4 4 3 13 3 10 16 (a) Write down all strategies of the players. Transform the game into a normal-form. Find all pure strategy Nash equilibria. (b) Find all weak-perfect Bayesian Nash equilibria in pure strategies. Do not forget the systems of beliefs. Argue well if there is none.

Suppose that the following prisoner's dilemma game (stage game) is played repeatedly and players discount future payoffs with the common discount factor δ <1.  a)    Carefully specify the strategy spaces for both players, draw the extensive form game and find a subgame perfect Nash equilibrium when the stage game is played twice, and both players observe the outcome of the first play.

Suppose there are two bidders for a single object. Each bidder has a value for the object, v1 and v2, which is randomly drawn uniformly from 0 to 80. (Note that this means the probability that a value is 25 or lower is 25/80, and more generally, the probability that a value is k or lower is k/80). Bidders see their own values but not the values of their rival bidders. Consider a first price sealed bid auction where the winner of the object is the bidder who submits the highest bid and pays the price that he bid. Suppose that you are bidder 1 and you believe that your rival always bids a constant fraction α of his value. (For example, if bidder 2’ value is 15, he will bid 15α.). 1. What is your expected winning probability of the auction from any given bid b1? (Hint, you win the auction when your bid amount b1 is greater than your opponent’s bid). 2. What is your expected payoff from any given bid, b1? (You need to write your answer as a function of v1, b1, and α). 3. Compute your best…

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Jane is interested in buying a car from a used car dealer. Her maximum willingness to pay for thecar is 12 ($12,000). Bo, the dealer, is willing to sell the car as long as he receives at least 9($9,000). What is the Nash bargaining solution to this game?

Microsoft and a smaller rival often have to select from one of two competing technologies, A and B. The rival always prefers to select the same technology as Microsoft (because compatibility is important), while Microsoft always wants to select a different technology from its rival. If the two companies select different technologies, Microsoft's payoff is 6 units of utility, while the small rival suffers a loss of utility of 2. If the two companies select the same technology, Microsoft suffers a loss of utility of 2 while the rival gains 2 units of utility. Using the given information, fill in the payoffs for each cell in the matrix, assuming that each company chooses its technology simultaneously.   Microsoft Technology A Technology B Rival Technology A Rival:   , Microsoft   Rival:   , Microsoft   Technology B Rival:   , Microsoft   Rival:   , Microsoft   True or False: There is no equilibrium in pure strategies. True False Note:- Do not provide handwritten…

1) Define Cartel and give an example. 2) Thelma and Louise are being charged for a murder/robbery. They are separated by police and interrogated. They are given the choice to confess or not to confess. The payoff matrix below identifies the years that they will each spend in jail, for the various outcomes. Louise Confess Don't Confess Confess (2 10,10 15.2 Thelma Don't Confess 2,15 3,3 a. Identify the Dominant Strategy for either player, or state that there isn't one. Remember, a "Strategy" is the players move. In this example, state "Confess" or "Don't Confess" for each player, not the payoff. b. Identify the Nash Equilibrium.

What is Revenue Equivalence Theorem for the standard auction types?