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Chapter 14: Problem 8
Philip Morris and R.J. Reynolds spend huge sums of money each year toadvertise their tobacco products in an attempt to steal customers from eachother. Suppose each year Philip Morris and R.J. Reynolds have to decidewhether or not they want to spend money on advertising. If neither firmadvertises, each will earn a profit of \(\$ 2 million. If they both advertise,each will earn a profit of \)\$ 1.5 million. If one firm advertises and theother does not, the firm that advertises will earn a profit of \(\$ 2.8 millionand the other firm will earn \)\$ 1$ million. a. Use a payoff matrix to depict this problem. b. Suppose Philip Morris and R.J. Reynolds can write an enforceable contractabout what they will do. What is the cooperative solution to this game? c. What is the Nash equilibrium without an enforceable contract? Explain whythis is the likely outcome.
Short Answer
Expert verified
The payoff matrix shows all possible profits considering advertising decisions. The cooperative solution is both firms agreeing not to advertise, leading to a profit of \(2 million each. The Nash equilibrium without an enforceable contract is both firms advertising and earning \)1.5 million each because neither can unilaterally improve their payoff by changing their strategy.
Step by step solution
01
Define the Payoff Matrix
Create a matrix with two players, Philip Morris (PM) and R.J. Reynolds (RJR), and their two strategies: to advertise or not to advertise. Each cell of the matrix will contain an ordered pair representing the profits for PM and RJR respectively, given their chosen strategies.
02
Fill in the Payoff Matrix
Using the information given, fill in the payoff matrix with the profits for each possible outcome: both firms advertise (\text{(PM profit, RJR profit) = (\text{\(1.5 million, \)1.5 million))}), only one firm advertises (\text{(PM profit, RJR profit) = (\text{\(2.8 million, \)1 million))} or vice versa), or neither firm advertises (\text{(PM profit, RJR profit) = (\text{\(2 million, \)2 million))}).
03
Determine the Cooperative Solution
Identify the outcome where both firms can agree to choose the strategy that maximizes their combined profits. This involves collaboration and an enforceable contract which ensures that neither firm will deviate from the agreed strategy.
04
Identify the Nash Equilibrium
A Nash equilibrium is reached when no player can benefit by changing strategies while the other player(s) keep theirs unchanged. Find the strategy combination where neither PM nor RJR has an incentive to deviate, given the strategy of the other.
05
Explain the Likely Outcome Without an Enforceable Contract
Analyze the incentives for both firms and explain why, without a binding agreement, they would likely choose the Nash equilibrium strategy, despite it potentially offering a lower payoff than the cooperative solution.
Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Nash Equilibrium
The concept of a Nash Equilibrium is crucial in game theory and is a situation where, in a strategic game like the one Philip Morris and R.J. Reynolds are involved in, no player can benefit from changing their strategy if the other player keeps theirs unchanged. It's an indication of predictable behavior in competitive situations.
In the tobacco advertising game, the Nash Equilibrium occurs when both firms choose to advertise, each earning a profit of \(1.5 million\). Even though advertising results in lower profit than if neither advertised (\(2 million\)), neither firm can unilaterally improve its payoff by changing its strategy, because the other would then have a higher payoff, which would not be equitable. The firms are essentially 'stuck' in this equilibrium if they act in their self-interest without an enforceable contract to cooperate.
Cooperative Game
A cooperative game is a scenario in which players can form binding commitments or contracts to adopt coordinated strategies. In economics, this principle is often applied to scenarios where cooperation can lead to a more favourable outcome for all parties involved, compared to what they would achieve by acting alone.
The cooperative solution to the advertising problem facing Philip Morris and R.J. Reynolds would be for both firms to agree not to advertise, thus saving on advertising costs and each earning the higher profit of \(2 million\). This outcome can only be assured if there is an enforceable contract to prevent either firm from breaking the agreement and unilaterally choosing to advertise to gain an advantage.
Microeconomics Principles
Microeconomics principles help explain the decisions made by individuals and firms and the allocation of resources. In this tobacco advertising predicament, key principles such as opportunity cost, incentives, and profit maximization come into play.
The opportunity cost of not advertising for either firm is the lost potential profit if the rival firm decides to advertise. These companies also respond to incentives: for instance, the potential to gain higher profits influences their decision to advertise, despite the cost. Lastly, both firms aim to maximize profits, whether through advertising or by cooperating to eliminate advertising costs altogether.
Oligopoly Strategies
Oligopoly strategies are employed by firms in a market where a few large sellers dominate. The actions of any one firm can significantly impact the others. In oligopolies, firms might engage in strategic behavior such as setting prices, controlling supply, or—in our example—advertising.
Philip Morris and R.J. Reynolds face a classic oligopoly scenario. They can either choose to compete aggressively through advertising (non-cooperative strategy) or collude implicitly or explicitly to refrain from advertising (cooperative strategy). In reality, without legally binding agreements, firms tend to default to non-cooperative strategies, as predicted by the Nash Equilibrium, to ensure they are not at a disadvantage relative to their competitors.
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