Question

It is illegal for any two firms that sell similar products to engage in price fixing agreements. Violating the anti-trust laws can bring both civil and criminal prosecutions. Nevertheless, price fixing does take place. Examples would be found at the service plazas along the NY State Thruway and the NJ Turnpike. Each location has a small number of fast food restaurants. Each fast food restaurant belongs to a different firm, which should create competition, yet at service plazas all have uncommonly high prices. 1) Draw a prisoner’s dilemma type of game (2x2) to show the pricing choices and strategies of two competing fast food restaurants, located at one service plaza. Payoffs are daily profits. Create sensible numbers. Write a brief explanation for the different numbers that you have created. 2.) Identify John Nash’s equilibrium, as well as the optimal outcome for the two fast food outlets. Also find and label any strictly dominant strategies. 3:) Actual long run pricing results at the service plaza may be contrary to the results predicted by the 2x2 diagram from part A. Explain why actual results may differ in the long run. Why is competition between different firms unable to bring lower prices to the consumer at the service plaza?

Answer 1

1) Let there be two Restaurents RES1 and RES2, and both have two strategies i.e. High price and Low price. The 2×2 game can be shown as-

The game shown above is a prisoner's dilemma as when both the Restaurents keep low price they get a profit of $10 each and when they both keep high price they get a profit of $20 each but when one keeps high and the other keeps low, the Res keeping low price gains a very high profit of $40.

2) Here the Nash equilibrium is at both firms charging Low price and earning $10 each, which is shown above where both numbers are circled.

But the optimal outcome must be to keep a High price for botb firms because it gives both of them a higher profit.

Here we can see that to keep a Low price is the dominant stretegy for both the Restaurents as can be seen from the payoffs circled which gives them higher profit whatever stretegy the other firm adopts.

3) The actual results may be different in the long run from the Nash equilibrium shown above this is because in the long run both the firms will decide mutually to keep a high price and hence earn a higher profit.