Question 1

For this question, assume the online retailing market is dominated by two firms. Let's name them Firms Alpha and Zeta. These firms sell a similar line of products and have very similar prices. However, one key strategic tool for each of them is advertising. Assume the two firms each have just two possible advertising strategies: spend a great deal of money on their advertising (High) or spend a modest amount on advertising (Low).

• If they both choose to have modest (Low) advertising budgets, they each have profits of $1,400.
• If they both have High advertising budgets, they incur greater costs. So the two companies earn just $850 each in profits.
• However, if Alpha has a Low advertising campaign and Zeta has a High advertising budget, Alpha has profits of $650 while Zeta has profits of $1,500.
• If Zeta has a Low advertising budget while Alpha has a High advertising budget, Zeta has profits of $900 while Alpha has profits of $1,500. This is a single-play, non-repeated game.

a) Construct a clear payoff matrix to describe this simple non-cooperative game. Fill the cells with the correct payoffs. Please put Alpha on top and Zeta on the left side of your payoff matrix.

b) Is there a dominant strategy equilibrium? Explain.

c) Is there/are there Nash equilibrium/equilibria? Explain.

d) If the two firms were owned by a single owner, and acted as a monopoly in this market, what advertising budget decisions would Alpha and Zeta make? What would be the monopoly profit (sum of the individual firms' profits) in this setting? Explain.

e) If Alpha could credibly threaten to run a High advertising budget, what is the maximum Alpha would be willing to pay Zeta in order to buy them out of the market and operate the two firms as a monopoly? What is the minimum that Zeta would be willing to accept to be bought out in this situation? Explain. Please recall that this is a single-play, non-repeated game, so no present valuation of future stream of profits is necessary.

Question 2

You and a good friend are supposed to meet in Paris, France. You know you have arranged to meet at either the Arc de Triomphe (AdT) or at the base of the Eiffel Tower (ET) but you cannot remember which and you cannot communicate with each other. You prefer the Arc de Triomphe. Your friend prefers the Eiffel Tower. But you both much prefer to be together rather than apart.

• If you and your friend each arrive at the Arc de Triomphe, your payoff is 10 and your friend's payoff is 7.
• If you and your friend each arrive at the Eiffel Tower, you friend's payoff is 10 but your payoff is 7.
• If you go to the Arc de Triomphe and your friend goes to the Eiffel Tower, your payoff is 4 and your friend's payoff is 4.
• If you go to the Eiffel Tower and your friend goes to the Arc de Triomphe, your payoff is 2 and your friend's payoff is 2.If it helps, you can think of these payoffs as units of enjoyment or utility you and your friendderive from the outcomes. (As you recall, while firms maximize profits, individuals maximizeutility). Assume that this is a single-play, non-repeated game.

a) Construct a payoff matrix with two choices for each player: ET (for Eiffel Tower strategy) and AdT (for Arc de Triomphe) strategy. Fill the cells with the correct payoffs. Please put yourself on top and your friend on the left side of your payoff matrix.

b) Do you have a dominant strategy? Explain.

c) Does your friend have a dominant strategy? Explain.

d) Of the 4 possible outcomes, identify which one(s), if any, satisfy the conditions of aNash Equilibrium. Explain your logic.

Question 2 You and a good friend are supposed to meet in Paris, France. You know you have arranged tomeet at either the Arc de Triomphe (AdT) or at the base of the Eiffel Tower (ET) but you cannotremember which and you cannot communicate with each other.You prefer the Arc de Triomphe. Your friend prefers the Eiffel Tower. But you both much preferto be together rather than apart. If you and your friend each arrive at the Arc de Triomphe, your payoff is 10 and yourfriend's payoff is 7. If you and your friend each arrive at the Eiffel Tower, you friend's payoff is 10 but yourpayoff is 7. If you go to the Arc de Triomphe and your friend goes to the Eiffel Tower, your payoff is4 and your friend's payoff is 4. If you go to the Eiffel Tower and your friend goes to the Arc de Triomphe, your payoff is 2 and your friend's payoff is 2.

If it helps, you can think of these payoffs as units of enjoyment or utility you and your friendderive from the outcomes. (As you recall, while firms maximize profits, individuals maximizeutility). Assume that this is a single-play, non-repeated game. a) Construct a payoff matrix with two choices for each player: ET (for Eiffel Tower strategy) and AdT (for Arc de Triomphe) strategy. Fill the cells with the correct payoffs. Please put yourself on top and your friend on the left side of your payoff matrix. b) Do you have a dominant strategy? Explain. c) Does your friend have a dominant strategy? Explain. d) Of the 4 possible outcomes, identify which one(s), if any, satisfy the conditions of a Nash Equilibrium. Explain your logic.