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### Course: AP®︎/College Microeconomics>Unit 4

Lesson 5: Oligopoly and game theory

# Game theory of cheating firms

We deepen our understanding of a Nash Equilibrium by exploring Pareto optimality and more on Nash Equilibrium. Created by Sal Khan.

## Want to join the conversation?

• In the table around in, isn't every item in the right hand column pareto optimal? Pareto efficiency is defined as you said, as a state of affairs where no party can be made better off without taking away from another party. Every data point in the right hand column effectively represents a PPF point, which are all by definition pareto efficient.
• no, only (250,250) is Pareto Efficient. To get to (280, 200) or (200, 280) one player was made better off but only by making the other one worse off. If there had been a point (280, 250) then you have made one player better off without making the other worse off.
• So does Nash disprove Pareto or are they not rival in nature?
• I wouldn't say Nash disproves Pareto but Nash approaches from a game theory individual's perspective while Pareto approaches it from the perspective of a Social Planner.

Ryan describes the process of moving to a Nash Equilibrium well but I disagree with Ryan's answer with regards to Pareto efficiency because the Pareto optimal state doesn't have anything to do with "the best returns" all it means is that the only way someone can be made better off is by making someone else worse off. Every single point in this table where one of the firms is earning more than 250 (in the right hand column and on the bottom row) is actually Pareto efficient.
• In this case, which place would be most Pareto efficient when factoring in the consumer surplus? Don't the consumers gains increase as the price goes down? Also, assuming we have all the necessary data, is Pareto efficiency always well defined, or could there be multiple points for Pareto efficiency?
• There are almost always multiple Pareto efficient equilibria. This happens because all you need for Pareto efficiency is that no one can be made better off without someone else being made worse off. Even situations that we would probably call unfair can be Pareto efficient, for example: if you have all the money in the world and everyone else has nothing that is still Pareto efficient because you can't give other people some money without giving some up and making yourself worse off.
• But, that's just a theory...a game theory!
• It actually can happen in real life. O_O
(1 vote)
• New guy here.. So this might sound stupid...
At about mins in, Sal says that 250 is the Pareto Optimum, but what about 70, or 150, or 30, or 110, or 230, or 190???
• Well as Sal says at , it means that there is no other equilibrium the balance could go to without making one of the two parties worse of.

So if you look at the table. Right above 250 - 250, is 280-200. You see that if you add those up, 480 < 500. Now why is that? It's because even though one increased it's outcome with 30, the other lost 50!
• Unfortunately this video paints a somewhat misleading and simplified picture. The problem arises that real life duopolies/cartels aren't usually based on single market transactions, but on iterated transactions. Iterating games essentially means that a participant doesn't have just one chance to make a strategic decision, as it would be in a single transaction situation, but instead there are multiple subsequent transactions and the participant can constantly re-evaluate their strategy during every single transaction. Essentially the participants replay the game constantly and remember all of their own previous strategies in individual iterations, as well those of the other parties'. This leads to some major differences from what is portrayed in the video above, which is what I'll attempt to explain below.

All of the following is assuming that MPC, market demand structure, average unit cost etc. do not vary with time and the participants have perfect information.

In a single, discrete case of the prisoner's dilemma, the Nash equilibrium is always non-cooperation. However, if you iterate the prisoner's dilemma indefinitely and the parties know that the game will be replayed, the Nash equilibrium moves from not cooperating to cooperation. This has to do with the fact that they know that the next iteration of the game will also give them a profit if they cooperate and they can assign a value for it, provided that there's enough reliable data without excess noise (I won't go into games with imperfect/asymmetric information, market variables and probability). The notion is generally called discounted cash flow, or DCF for short.

In this scenario, the participants will discount their anticipated profits from all future iterations and take them into account while making strategic decisions in every single iteration, which radically alters the payoff matrix. An important factor in the discounting process is that duopolies and cartels usually have a somewhat unforgiving trigger strategy in regards to cooperation, in which if the other one decides not to cooperate (undercut cartel prices or increase production), it will lead to the other party "losing trust" and not cooperating for the rest of the iterations of the game, thus returning to the classic Nash equilibrium of the Prisoner's dilemma. Simply put, an attempt by one party at hogging the cartel profits will lead to the collapse of the cartel and both participants returning to perfect competition, exactly in the manner as shown in this video. This leads to the following point: if the game is iterated indefinitely, the profits from cooperation are infinitely higher than not cooperating, the latter of which would result in the loss of all future cartel profits due to the grim trigger. If the discounted cash flow from cooperation now and in future iterations will always be higher than non-cooperation, neither party can improve its strategy by undercutting prices or increasing production. The Nash equilibrium hops over to the Pareto Efficient solution (in the reference frame of the participants of the game, not society as a whole).

All this complex jargon can be summed up by the old idiom of the stupidity of killing the goose that lays golden eggs in hopes for a quick slightly higher one-time profit. I appreciate the attempt at just explaining the basics, but unfortunately the basics lead to oversimplification and demonstrably false models. To truly understand cartel behavior in game theory, you a) have to differentiate between single games and iterated games, and b) understand basic trigger strategies and which of them applies in any given model.
• Since we know the behavior of firms in a duopolistic market where there is lack of coordination, ceteris paribus, could we use that understanding to find markets where coordination is present?
• Well, yes. but It's usually not a secret. OPEC doesn't hide the fact that it's an oil cartel. DeBeers doesn't hide the fact that it's a diamond cartel. There must be a large barrier to entry for a cartel to work - typically this involves land rights (mining), or intellectual property (IP).

An IP example would be licensed patents. A patent-holder for example might license his patent to multiple parties, but have them sign agreements to each only sell in certain markets or countries.

It would be hard to keep a commodity cartel secret though. As you imply, if there were only two producers of screws, and they both suddenly double their price (despite no increase in demand or dearth in factors of production like raw iron), people would immediately suspect foul play.
• How could we apply this theory in the business ? Will this be practical ? Or Is it just the way to analyze the situation and support in making decision
• The theory explains the existence of cartels in markets that in theory could be free markets. Recent EU decisions to crack down on cartels has shown cartels in markets for construction work, raw sugar and producing beer. These markets have enough suppliers to provide full competition and still they didn't. It also shows that due to the competitive nature of these markets there is a strong incentive for single suppliers to break the pact, which could lead to a dissolution of the cartel. In business it could be beneficial to collude, but you have to trust your partners. Knowing the economical impulse to cheat will be useful in business and that will support decision making in companies.
• I don't understand why 250|250 cannot be considered Nash Equilibrium if both parties have immediate knowledge of each other's decisions and the immediate ability to react. I'll be A and you be B. Right now we are both producing 25 for 250|250 profit:
``if (I decrease production) {    I immediately loose profit; //duh}else if (I increase production) {   while (my profit >= 0 && your profit >= 0) {        you will increase production; //to recover partial profit but make me lose more        I will increase production; //to recover partial profit but make me lose more   }   I have lost all my profit; //along with you}``

Therefore, no matter what action I take from 250|250, I will lose profit. Wouldn't that mean 250|250 is Nash Equilibrium?