Consider the following modified Cournot-game. Firm 2 is run by its owner whereas Firm 1 is run by a manager whose preferences are represented by the following payoff function u(91, 92) = II₁ (91, 92) + aq₁ and the marked demand function is P = 1 - Q. The game is played as follows. In the first stage the owner of the Firm 1 chooses 0 < a < 1. Then the manager of Firm 1 and the owner of Firm 2 observes a and choose q₁ and q2 to maximize u and II₂ respectively. What are the subgame-perfect equilibrium levels of a, q₁ and 92?

The “research and development” game is best analyzed as a simultaneous move game, because the parties lack information about each other’s investment decisions. Which game (in the attachment) describes the “research and development game” properly? Remember that investment costs $6, and that this should be reflected, whenever appropriate, in the correct game matrix. (Note: Firm A chooses the row and Firm B chooses the column.)

Three firms share a market. The demand function is P(q1, 92, 93) = 10 – q1 – 92 – 93, where q; is the output of firm i, Player i. The marginal cost per unit for each firm is zero. Suppose firm 1 is a market leader, and that firm 2, and firm 3 choose q2 and q3 simultaneously after observing q1 Find the SPE of this game. How much is produced by firm 2? Numerical answer How much is produced by firm 1, 2, and 3?

Consider a variation of the television station broadcast game of Exercise 4 in Chapter 7. Suppose the stations interact sequentially. First, MBC chooses between 6:00 and 7:00. Then, after observing MBC’s choice, RBC decides between 6:00 and 7:00. Finally, after observing the behavior of both MBC and RBC, CBC chooses either 6:00 or 7:00. Payoffs are as given before. Draw the extensive form of this sequential game and compute the subgame perfect equilibrium.

Superstore (S) and Megastore (M) are two competing discount supermarkets.  If neither store advertises, S makes $115 in profits and M makes $165.  If both stores advertise, S makes $80 and M makes $95.  If M advertises and S does not, they make $305 and $55 respectively.  If S advertises and M does not, they make $285 and $65 respectively.  Based on Game Theory, what will the two firms do?  Hint: illustrate the Nash equilibrium to support your answer.

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For various values of X(for player1 and player 2), find all Nash equilibria of the following game with von Neumann-Morgenstern preferences:

Consider the following situation: five individuals are participating in an auction for an old bicycle used by a famous cyclist. The table below provides the bidders' valuations of the cycle. The auctioneer starts the bid at an offer price far above the bidders' values and lowers the price in increments until one of the bidders accepts the offer.   Bidder Value ($) Roberto 750 Claudia 700 Mario 650 Bradley 600 Michelle 550   What is the optimal strategy of each player in this case? Who will win the auction if each bidder places his or her optimal bid? If Claudia wins the auction, how much surplus will she earn?

Two rival companies competing in the same market need to decide their plans for future expansion of their stores. The Table below shows the possible outcomes of their mutually interdependent actions (payoffs are profits in £m)     Giga Company Titanic Conglomerate   No Change Refurbishment of existing stores Large Expansion No Change     30, 40      25, 35    15, 24 Refurbishment of existing stores     35, 30      28, 32    18, 33 Large Expansion     12, 22     18, 20    20, 25   The Nash equilibrium:            (A)       does not exist. (B)       occurs when both firms choose Refurbishment of existing stores.              (C)       occurs when both firms choose Large Expansion. (D)       occurs when both firms choose No Change.

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.