Is the pricing decision facing Alpha and Beta a Prisoner’s Dilemma? Why or why not?

1. Find the solution to the following advertising decision game between Coke and Pepsi by using the method of successive elimination of dominated strategies. Pepsi’s Budget Coke’s Budget

2. Alpha and Beta, two oligopoly rivals in a duopoly market, choose prices of their products on the first day of the month. The following payoff table shows their monthly payoffs resulting from the pricing decisions they make. Alpha’s Price Beta’s Price

· Is the pricing decision facing Alpha and Beta a Prisoner’s Dilemma? Why or why not?

· What is the cooperative outcome? What is the non-cooperative outcome?

· Which cells represent cheating in the pricing decision? Explain.

· If Alpha and Beta make their pricing decision just one time, will they choose the cooperative outcome? Why or why not?

· Can Alpha make a credible threat to punish Beta with a retaliatory price cut? Can Beta also adopt a similar retaliatory price cut?

3. The secretary general of OPEC, Ali Rodriquez, stated that it would be easier for OPEC nations to make future supply adjustments to fix oil prices that are too high, than it would be to rescue prices that are too low. Evaluate this statement.

4. Two firms A and B produce goods A and B, respectively. The linear demands for the two goods are, respectively, QA = 100 – 4PA + 1.5PB

QB = 120 – 2PB + 0.5PA

Production costs are constant but not equal:

LACA = LMCA = $2

LMCB = LMCB = $3

· Using calculus, derive the equations for best response curves.

· Sketch a graph of the two best-response curves. Label both axes and response curves.

· If firm A expects firm B to set its prices at $20, what is firm A’s best response? If firm B predicts firm A will price good A at $36, what is firm B’s best response?

· What is the Nash equilibrium price and quantity for each firm?

· How much profit does each firm earn in Nash equilibrium?

· If firm A and firm B set prices of $22 and $35 respectively, how much profit does each firm earn? Why don’t they choose these prices then?

5. Thomas Selling, an expert on nuclear strategy and arms control, observed in his book The Strategy of Conflict (Cambridge, MA: Harvard University Press, 1960), “The power to constrain an adversary depends upon the power to bind oneself.” Explain this statement using the concept of strategic commitment.

ANSWER

The solution to the advertising decision game between Coke and Pepsi can be found using the method of successive elimination of dominated strategies. This method involves identifying and eliminating any strategies that are dominated by another strategy, meaning that they are always worse off than another strategy no matter the actions of the other player.

In this game, Pepsi’s budget and Coke’s budget are the two possible strategies for each player. If Pepsi chooses a high budget and Coke chooses a low budget, Pepsi will have a higher advertising reach and therefore a higher payoff. Similarly, if Pepsi chooses a low budget and Coke chooses a high budget, Coke will have a higher advertising reach and therefore a higher payoff.

Therefore, the strategy of choosing a low budget is dominated by the strategy of choosing a high budget for both Pepsi and Coke. By eliminating these dominated strategies, the only remaining strategies are for both Pepsi and Coke to choose a high budget. This results in a Nash equilibrium, where neither player has an incentive to deviate from their ch

osen strategy.

It is not possible to determine whether the pricing decision facing Alpha and Beta is a Prisoner’s Dilemma without more information about the payoffs in their payoff table. In a Prisoner’s Dilemma, both players have an incentive to choose the non-cooperative outcome, despite the fact that the cooperative outcome would be better for both players.
The cooperative outcome in a Prisoner’s Dilemma is when both players choose the strategy that leads to the highest combined payoff for both players. The non-cooperative outcome is when both players choose the strategy that leads to the highest individual payoff, even if it is lower than the cooperative outcome.
The cells that represent cheating in a pricing decision are those in which one player chooses a lower price and the other player chooses a higher price, resulting in a higher individual payoff for the player who chose the lower price.
It is not possible to determine whether Alpha and Beta will choose the cooperative outcome without more information about their payoffs and preferences. In general, players in a Prisoner’s Dilemma may not choose the cooperative outcome because they have an incentive to choose the non-cooperative outcome that leads to the highest individual payoff.
It is not possible to determine whether Alpha and Beta can make credible threats to punish each other with retaliatory price cuts without more information about their payoffs, preferences, and the strategic environment they are operating in. In general, players can make credible threats if they have the ability and willingness to follow through on their threats and if their threats are credible to the other player.

Ali Rodriguez’s statement can be evaluated based on the ability of OPEC nations to effectively coordinate their supply adjustments in order to control oil prices. If OPEC nations are able to successfully coordinate their actions and make supply adjustments in response to prices that are too high or too low, then it may be easier for them to fix prices that are too high compared to rescuing prices that are too low. This is because making supply adjustments to reduce excess supply and raise prices may be a more straightforward and effective approach than trying to increase supply and lower prices, which could be more difficult to achieve and may require more coordination among OPEC nations.
To derive the equations for best response curves, we can start by setting the marginal cost (MC) equal to the price (P) for each good, and solving for the quantity (Q) produced by each firm. For firm A, the equation is MC = P = 2 = 100 – 4PA + 1.5PB, which can be solved for PA to get PA = (100 – 2PB)/4. For firm B, the equation is MC = P = 3 = 120 – 2PB + 0.5PA, which can be solved for PB to get PB = (120 – 1.5PA)/2. These equations represent the best response curves for firms A and B, respectively.
To sketch the graph of the best response curves, we can plot the equations derived above on the same graph with P on the y-axis and Q on the x-axis. The best response curve for firm A would be a downward-sloping line, while the best response curve for firm B would be an upward-sloping line. The x-axis would represent the quantity of each good produced, while the y-axis would represent the price of each good. The labels on the axes and the response curves would indicate which firm and good each line represents.
If firm A expects firm B to set its price at $20, then firm A’s best response would be to set its price at the intersection of its best response curve and firm B’s best response curve. This would be the Nash equilibrium price and quantity for each firm. In this case, firm A’s profit would be the difference between its revenue and cost at the Nash equilibrium, which can be calculated by substituting the equilibrium prices and

Is the pricing decision facing Alpha and Beta a Prisoner’s Dilemma? Why or why not?

ANSWER

Stop Stressing. Your Academic Success is Guaranteed.