Suppose two firms, Allstom from France, and Bombardier from Canada, are bidding on a contract to replace train cars for the subway system in Mexico City. If they bid the same amount, they share the contract, otherwise, the low bid wins. The figure below shows the payoff matrix for this contest. Bombardier (B) B bids $60 million B bids $40 million A bids $60 million Profit to A: $12 m Profit to B: $12 m Profit to A: $0 m Profit to B: $6 m Allstom (A) ... A bids $40 million Profit to A: $6 m Profit to B: $0 m Profit to A: $3 m Profit to B: $3 m O A. each firm bids $40 million, and earns profit of $3 million. O B. each firm bids $60 million, and earns profit of $12 million. O C. Bombardier bids $40 million, and earns profit of $6 million, while Allstom bids $60 million and earns profit of $0. O D. Bombardier bids $60 million, and earns profit of $0, while Allstom bids $40 million and earns profit of $6 million.

Suppose that Jason and Chad each are thinking of opening up a diet coke stand on the fourth floor of this building. Suppose that potential customers are evenly spaced on a distance that is normalized to 1. Customers will buy a diet coke from whichever stand requires the least walking. If they are the same distance the customer will flip a coin. This is depicted below. 1/4 1/2 3/4 Suppose that Jason and Chad are simultaneously choosing the location of their stands, what is the Nash Equilibrium location? a. One of them puts a stand at 3/4 and the other puts a stand at 1/4 b. Chad and Jason put their stands right next to each other at 1/2 c. One of them puts a stand at 0 and the other puts a stand at 1 d. There is no Nash Equilibrium

Firm B Q=5 Q=6 Q=5 (24, 24) (30, 10) Q=6 (10, 30) (19, 19) Firm A This table shows a game played between two firms, Firm A and Firm B. In this game each firm must decide how much output (Q) to produce: 5 units or 6 units. The profit for each firm is given in the table as (Profit for Firm A, Profit for Firm B). Refer to Table. The dominant strategy For Firm A is to produce 5 units and the dominant strategy for Firm B is to produce 6 units. 5 units and the dominant strategy for Firm B is to produce 5 units. 6 units and the dominant strategy for Firm B is to produce 5 units. 6 units and the dominant strategy for Firm B is to produce 6 units.

t 0886951] Two firms are competing in a market by simultaneously deciding the quality of their manufactured product. The payoff matrix for this competition is depicted in the image. Firm 1 This game can be solved by deleting dominated strategies. Use this tactic to identify all pure-strategy Nash equilibria in this game. Low Medium High 53 54 66 Low A. Firm 1 chooses high and Firm 2 chooses high. 25 34 43 B. Firm 1 chooses low and Firm 2 chooses high. 43 68 77 C. Firm 1 chooses medium and Firm 2 chooses medium. Firm 2 Medium D. Firm 1 chooses medium and Firm 2 chooses low. 12 45 E. Firm 1 chooses low and Firm 2 chooses low. 74 96 89 F. Firm 1 chooses high and Firm 2 chooses low. High G. Firm 1 chooses medium and Firm 2 chooses high. 39 48 H. Firm 1 chooses low and Firm 2 chooses medium. I. Firm 1 chooses high and Firm 2 chooses medium. 50 21

5. The following problem was first considered by John von Neumann and is a fundamentalresult game theory.A and B play the following game:ˆA writes down either number 1 or number 2, and B must guess which one.ˆIf the number that A has written down is i and B has guessed correctly, B receives i units from A.ˆIf B makes a wrong guess, B pays 4/5 of a unit to A.First we consider the expected gain of player B.ˆSuppose B guesses 1 with probability p and 2 with probability 1 −p.ˆLet X1 denote B’s gain (or loss) in a game where A has written down 1.ˆLet X2 denote B’s gain (or loss) in a game where A has written down 2.(a)  Find the pmf of X1 and X2(b)  Find B’s expected gain for these two cases, E[X1] and E[X2].(c)  What value of p maximizes the minimum possible value of B’s expected gain?Now consider the expected loss of player AˆSuppose that A writes down 1 with probability q and 2 with probability 1 −q.ˆLet Y1 be A’s loss (or gain) if B chooses number 1.ˆLet Y2 be A’s loss (or gain) if B…

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2. Consider two players playing a simultaneous moves game. These players can be one of the two states of the world, state 1 or state 2, while playing the game. The payoffs-matrix for the two state games are as follows: State 1 P1 U D P2 L R 1,4 1,0 1,6 2,16 0,0 0,24 M State 2 P1 U D P2 L M R 1,0 1,4 1,6 2,16 0,24 0,0 Each players believes that the two states are equally likely, Derive the BNE of the game.

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Dynamic Game: US Tax No Tax Fiji Fiji Tax No Tax Tax No Tax 10,000,10 9900,-9989 10,100,-89.990 Sub-game_1 10,000,-99,989 Sub-game_2 Sub-game_3 1. Is there a Nash Equilibrium of this game in which Fiji improves its payoffs relative to the Sub-game Perfect Nash equilibrium? If there is, explain carefully why this strategy profile is not a Sub-game Perfect Nash equilibrium.

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