Oligopoly-Game Theory and Advertising Strategies

Scenario: Two airlines, Untied and Air "R" Us, operate a duopoly on the Collegeville-Bigtown route.
Strategies: Each airline can choose to charge either a high price or a low price for a ticket.
Payoff Matrix (Profits per seat in dollars):
Air "R" Us - Low Price Air "R" Us - High Price
Untied - Low Price $20, 20$ $50, 0$
Untied - High Price $0, 50$ $40, 40$

	Air "R" Us - Low Price	Air "R" Us - High Price
Untied - Low Price	$20, 20$	$50, 0$
Untied - High Price	$0, 50$	$40, 40$

Definition: The airlines interact only once.
Nash Equilibrium: The Nash Equilibrium in this one-shot game occurs when both airlines choose the low price. This yields a profit of $20 for each airline. This is because if one airline chooses a high price, the other airline has an incentive to undercut it by choosing a low price, thus earning a higher profit of$ 50.

Strategies: Airlines can choose between "always charge the low price" or "tit for tat".
Tit for Tat: Start by charging the high price in the first period, and in the second period, do whatever the other airline did in the previous period.
Payoffs to Untied, considering various strategies of Air "R" Us:
- i. Untied (Low Price) vs. Air "R" Us (Low Price):
  - Period 1: $20</li> <li>Period 2:$ 20
  - Total: $20 + 20 = 40$
- ii. Untied (Low Price) vs. Air "R" Us (Tit for Tat):
  - Period 1: $50 (Untied = Low, Air R Us = High initially)</li> <li>Period 2:$ 20 (Untied = Low, Air R Us = Low in response)
  - Total: $50 + 20 = 70$
- iii. Untied (Tit for Tat) vs. Air "R" Us (Low Price):
  - Period 1: $0 (Untied = High initially, Air R Us = Low)</li> <li>Period 2:$ 20 (Untied = Low in response, Air R Us = Low)
  - Total: $0 + 20 = 20$
- iv. Untied (Tit for Tat) vs. Air "R" Us (Tit for Tat):
  - Period 1: $40 (Both charge high price)</li> <li>Period 2:$ 40 (Both continue charging high price)
  - Total: $40 + 40 = 80$

Scenario: Philip Morris and R.J. Reynolds decide each year whether to spend money on advertising.
Payoffs:
- Neither firm advertises: Each earns $2 million.</li> <li>Both firms advertise: Each earns$ 1.5 million.
- One firm advertises, the other does not: The advertising firm earns $2.8 million, the other earns$ 1 million.

	R.J. Reynolds - Advertise	R.J. Reynolds - Don't Advertise
Philip Morris - Advertise	$1.5, 1.5$	$2.8, 1$
Philip Morris - Don't Advertise	$1, 2.8$	$2, 2$

If Philip Morris and R.J. Reynolds can write an enforceable contract, the cooperative solution is for neither firm to advertise. This results in each firm earning a profit of $2 million which is the highest combined payoff ($ 4 million total) and a pareto-efficient outcome.

The Nash Equilibrium without an enforceable contract is for both firms to advertise. This is because each firm has a dominant strategy to advertise, regardless of what the other firm does.
- Explanation:
  - If R.J. Reynolds advertises, Philip Morris's best response is to advertise ( 1.5 million > $1 million).
  - If R.J. Reynolds does not advertise, Philip Morris's best response is to advertise ( 2.8 million > $2 million).
  - The same logic applies to R.J. Reynolds. Thus, both firms advertising is the only stable outcome where neither firm has an incentive to unilaterally deviate.