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. A. 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.

Answer 1

A prisoner’s dilemma describes a situation where, according to game theory, two players acting strategically will ultimately result in a suboptimal choice for both. When it comes to the competition between two fast-food restaurants, understanding the structure of certain decisions as prisoner’s dilemmas can result in more favorable outcomes because it will allow balancing both competition and cooperation for mutual benefit.

Prisoner’s Dilemma Basics

The prisoner’s dilemma scenario works as follows: Two suspects have been apprehended for a crime and are now in separate rooms in a police station, with no means of communicating with each other. The prosecutor has separately told them the following:

• If you confess and agree to testify against the other suspect, who does not confess, the charges against you will be dropped and you will go scot-free.
• If you do not confess but the other suspect does, you will be convicted and the prosecution will seek the maximum sentence of three years.
• If both of you confess, you will both be sentenced to two years in prison.
• If neither of you confesses, you will both be charged with misdemeanors and will be sentenced to one year in prison.

Now, evaluating best course of action

Let’s begin by constructing a payoff matrix where two fast food restaurants located at one plaza compete with each other. Suppose one fast food restaurant is thinking of cutting the price then the other will have no choice but to follow suit for its fast-food to retain its market share. This may result in a significant drop in profits for both fast-food restaurants.

A price drop by either fast- food restaurant may thus be construed as defecting since it breaks an implicit agreement to keep prices high and maximize profits. Thus, if fast-food restaurant 1 drops its price but fast food restaurant 2 continues to keep prices high, the former is defecting, while the latter is cooperating (by sticking to the implicit agreement). In this scenario, fast food restaurant 1 win market share and earn incremental profits by selling more food.

Payoff Matrix

Let’s assume that the incremental profits that accrue to fast food restaurant 1 & 2 are as follows:

The payoff matrix looks like this: (the numbers represent incremental dollar profits in hundreds of millions):

	Fast food restaurant 1
Fast food restaurant 2		Cooperate	Defect
Cooperate	$100, $100	0,$75
Defect	$75, 0	$85, $85

Now,

i) If both the fast-food restaurants keep prices high, profits for each restaurants increase by $100 million ( because of normal growth in demand).

ii) If one drops prices (i.e. defects) but the other does not (cooperates), profits increase by $75 million for the former because of greater market share and are unchanged for the latter.

iii) If both the restaurants reduce prices, the increase in fast-food consumption offsets the lower price, and profits for each restaurants increase by $85 million.