P1 \ P2 A B C D A (17,5) (7, 13) (12,2) (1,20) B (11, 16) (2, 10) (6,9) (10, 20) C (15,4) (13,9) (20,8) (2, 12) D (3, 16) (20,5) (3,7) (1, 17)

Consider that there is one auctioneer who would like to sell one commodity and there are 2 individuals, 1 and 2. The auctioneer will apply the following tie-breaking rule: If there are multiple bidders who announce the highest bid, then select the bidder with the smallest index will be picked up as the winner. (For instance, let b(i) = b(j) . Then, i is the winner if and only if i < j.) Let each individual i's private value of the commodity, v(i), is given as: v(1) = $1600; v(2) = $2100. Considering a first-price auction, specify the set of Nash equilibria in this game.

A total of 10 players are each choosing a number from {0,1,2,3,4,5,6,7,8}. If a player's number equals exactly half of the average of the numbers submitted by the other nine players, then she is paid $100; otherwise, she is paid 0. Solve for the strategies that survive the IDSDS.

In the normal form game below, the payoff matrix depends on the parameter a. 1 1 2 ABC a 0,2 6,4 -2,4 b 0, -24 -2a, 2a 8, 2 C 4,0 0,4 0, 14 Find the values of a, for which at least one pure strategy Nash equilibrium exists. Compute the value of a for which the expected payoff is the same for both players when the mixed strategy profile (01,02) = ((1/3,2/3,0), (0,1/4,3/4)) is played. Find the best response of player 1 (as a function of the parameter a) to player's 2 mixed strategy o2 = (1/2,1/2,0). Assuming a = 0 eliminate iteratively all dominated strategies and find a mixed strategy Nash equilibrium in this game.

The Government of Malaca has decided to sell pollution permits that will allow people to discharge pollutants into its largest freshwater lake. Each permit represents the right to discharge one tonne of pollutants. Malaca has determined that the lake will tolerate a maximum of 10 tonnes of pollutants per year and has decided to sell the permits using a Dutch auction. This means that the auction starts at a very high price, which is reduced in steps until the price reaches a level that will result in all 10 tonnes of pollution permits being sold at the same price. The results of the bidding are shown in table below. Price per Pollution Bidder Bidder Bidder Bidder Bidder Permit A. B D $5, 500 1 5,000 4,500 4,000 1. 1. 1 2 2. 3 2 1 2 3,500 3,000 2,500 2,000 4 3 2 4 4 4 3 4 4 1,500 7 a. What will be the price of pollution permits as a result of this auction? Price: $ b. Suppose that Bidder E happened to be an environmental protection group. If this group had not participated in the…

Extend the Cournot model discussed in class to two firms with setup costs. Firm 2 chooses to produce q; at cost cq; where c> 0. The set up costs are denoted by K₁ < K2 respectively for firm 1 and 2. The selling price is P(Q) = (a - bQ) where Q = 91 + 92. What are the optimal production quantities for each firm? (Hint: A firm has the option of not producing at all with a cost of zero).

Problem 4: Consider an infinitely repeated game, where the base game is the following 2-person 2x2 game: A A 0,0 10, 10 S1: choose A always S2: choose B always B 10, 10 0,0 Assume both players discount the future at the same rate of r, 0 < r < 1. Limiting each player's strategies to the following six possibilities, S3: Choose A then mimic the other player's previous choice S4: Choose B, then mimic the other player's previous choice S5: Choose A, then choose the opposite of the other player's previous choice S6: Choose B, then choose the opposite of the other player's previous choice a. present the strategic form of this game, b. identify all pure-strategy Nash equilibria c. does repetition with these strategies "solve" the coordination dilemma that confronts the players in the single play of the above game.