By Bhagwad Jal Park, on July 30th, 2008
In the previous article, I explained how in any game, it is reasonable to assume that a stable outcome will be a Nash Equilibrium. Today, I will show how it is impossible for rational people like us to save the planet by cooperating to stop using carbon fuels.
Currently, as things stand, carbon fuels definitely have an edge over traditional fuels. As of now, they are cheaper, and they can deliver more power than automobiles that run on eco-friendly sources like electricity. (Let us ignore for the moment the truth that electricity is largely produced using carbon fuels!)
If it weren’t for the fact that the large scale use of carbon fuels in our automobiles is destroying the environment, life would be great. Sure, they’ll run out someday but not in our time. In the world of game theory, each person is uniquely selfish. We’re not caring about future generations here. By the time our great-grandchildren realize that the earth has no more fuels, we won’t be around to face the consequences.
Also, we need to keep in mind the fact that one person using eco-friendly fuels is not going to save the environment. Concordantly, if everyone else is using eco-friendly fuels, then one person using carbon fuels isn’t going to destroy the environment either.
It’s also true that if you’re the only one using carbon fuels, you gain a massive advantage over everyone else. You reach your workplace faster, and you can perhaps even rob a bank and get away, as the police will not be using carbon fuels, and hence can’t keep up with you.
Conversely, if you’re the only one to use eco-friendly fuels, you will get creamed personally (babes stay away from you) as well as professionally (more time to reach a client, you have to stay closer to work, etc).
So let’s split the population into two segments. You, and everyone else. There are two choices for each segment. Using eco-friendly fuels, and using carbon based fuels. The diagram above shows the possible outcomes for each situation where each both parties have made their choices.
What should you do if everyone else is using eco-friendly fuels? Should you use them too? No! As the environment will still be saved if you use carbon-based fuels and you get an advantage over everyone else, you must use carbon-based fuels if everyone else is using eco-friendly fuels.
Suppose everyone else uses carbon fuels, then should you use eco-friendly fuels? Of course not! Why should you? It’s not as if the earth will be saved just because you choose to use eco-friendly fuels. And if you’re the only one not using carbon fuels, you’ll be a loser compared to everyone else.
Therefore, for you, using carbon fuels is a dominant strategy. This means that it’s a strategy that makes you better off no matter what the other party is doing.
This logic of course holds true for everyone else as well. The outcome is that, each person behaving rationally dooms the earth collectively. This counter intuitive result where rational decisions lead to disaster is commonly known as the “Prisoner’s Dilemma.” There’s no way that we can save the earth if the only solution is cooperation.
The prisoner’s dilemma can be overcome if there is a law against carbon fuels. This way, the cost of using carbon fuels goes up (as the law can punish you), and the payoffs in the diagram change.
There is another solution to the prisoner’s dilemma. Game theory assumes that everyone is rational. However, people don’t think rationally. I certainly don’t. I use a bicycle instead of a car because of an illogical and stupidly misplaced sense of civic duty. I feel that my actions actually have an effect on the environment when they really don’t. The paradox is that when everyone behaves illogically, it is possible for a good outcome to ensue!
So maybe rationality isn’t all that it’s hyped up to be. We will explore this idea in later articles where I will show that nature has deliberately made us illogical precisely for the purpose of avoiding the Prisonner’s Dillemma. There is hope for our planet after all!
By Bhagwad Jal Park, on July 21st, 2008
In this two part article, I will demonstrate using game theory that it is not possible for the the human race to cooperate to save the earth from global warming. No matter how dire the situation or how clearly it is demonstrated that the earth will be doomed if we all don’t stop polluting, it can never happen.
To demonstrate this however, I will need to elaborate on the concepts of the Nash equilibrium that I introduced earlier. To recap, it simply means that given the strategies that everyone else is playing, each person is happy with their own decision.
Image Credit: Onken Bio-pot
The Nash equilibrium implies stability. It’s a stable solution to the game, inasmuch that people have no incentive to change their strategy. In the movie A Beautiful Mind, despite the implication, the solution given by Russell Crowe (the actor playing John Nash) is not a Nash equilibrium!
The situation, if you remember, was that Nash and his two pals were in a bar, and four women walked in, one of whom was truly stunning. Nash proposed to his friends that if everyone hit on the beautiful babe, then the rejected men (two of them) would fail to score with even the other women who would not like being “second choice.” As a result, only one out of the three would get laid. His solution was that they all hit on the other women and thus increase their chance of collectively scoring.
The movie implies that this was what set Nash thinking and laid the path for his paper on Nash equilibriums. However, you will recognize that the above situation was not a Nash Equilibrium. If everyone has hit on the other women, then no one has hit on the stunning babe. Consequently, each man would regret not hitting on her (since no one else has) and would be dissatisfied with his choice. In a Nash equilibrium, everyone is happy with their choice, given that everyone else has made theirs.
 Image Credit: John Nash
In a given game, it is possible for multiple Nash equilibriums to be present or no Nash equilibriums at all. If this is the case, then it is not possible to predict the outcome of the game. There are various types of games including coordination games, trust games, outguessing games, and chicken games. Out of these, outguessing games and chicken games have no Nash equilibriums, whereas trust games have multiple Nash equilibriums. Hence, for these games, it is not possible to predict the outcome. In coordination games, however, there is just one Nash equilibrium, and so, it is possible to predict the outcome for coordination games.
In the next article, I will demonstrate that when it comes to saving the planet, there is only one Nash equilibrium – that of everyone using carbon based fuels and is, therefore, the only stable outcome for rational beings like us! It is a completely new sort of game that deserves special attention…and one that dooms us all.
By Bhagwad Jal Park, on July 12th, 2008
In my previous post, you read about Nash equilibriums and the formation of cartels. You also read about how cartels tend to be unstable and susceptible to treachery by its members.
This week we will look at De Beers – one of the most successful cartels ever. In fact, it is so successful that it operates completely behind the scenes and has shifted public opinion to accommodate its internal needs.
Simply put, diamonds are not rare. They are expensive yes, but they exist freely on earth. However, like any other commodity, they do follow the laws of supply and demand. The supply has been artificially constrained so that there is no proliferation of diamonds in the market. Because of this, the prices of diamonds are higher than they would be in a free market.
So why is the cartel put together and led by De Beers stable? One would have thought that according to the laws of game theory, it should have broken apart by a defecting member. There are two reasons for this. First of all, most of the cartel members have major holdings by De Beers themselves. This means that there are even fewer players than it looks. Fewer players makes it less likely that there will be a defection.
Secondly, the real partners of De Beers in the cartel are the Russians. They mine small diamonds from Siberia and channel them through De Beers. The Russians know that if they put their diamonds directly into the market, the prices will drop. And that will be bad for them in the long run.
This brings us to an important point on cartels. The long run. Game theory predicts that if a “Prisoner’s Dilemma“-like game is repeated indefinitely with no end in sight, then the logical outcome, assuming that all participants are intelligent, is cooperation. What this means is that there is a better chance of a member cooperating if the game is repeated continuously.
This happens because if the game is repeated, then all other players will know that the person who defected last time is untrustworthy and can make life hard for them. Also, if it is known beforehand that each party will do in the next game what the other party did in the last game, then it is in each party’s best interests not to renege on the cartel since they will be punished for it in the next game.
Other firms can punish the defector by pricing them out of the market as well. This means that everyone collectively lowers their price temporarily so that the remaining firm is driven out of business. This usually happens to new entrants who are a threat to already established cartels.
Nevertheless, in my opinion, this only means that the cartel will survive longer. When there are a large number of participants, the temptation can be too great for individual members to resist, and cartels are always breaking and reforming again. However, if I’m in a cartel with someone else who I know has defected the last time, I might lose faith in him and decide to defect before he does. So again, the cartel breaks up.
It’s a complex dynamic, and in the long run, it’s all about trust. In fact, this leads us to another interesting idea. Perhaps altruism, self-interest, and honesty are rational strategies and not employed only by the soft-hearted. We’ll discuss that in another blog.
By Bhagwad Jal Park, on July 10th, 2008
One of the neatest developments in economics is the formulation of game theory. Even though its strategies and recommendations have been known to people throughout history, game theory puts these strategies on a theoretical structure. One of the situations thrown up by game theory is a Nash equilibrium.
Assume that there are competing players in a situation (call it a game). Each player has to choose which strategy to adopt. The outcome of that strategy is going to depend on what other people choose. In such a situation, a Nash equilibrium is formed when each player knows what strategies the other player is going to adopt and will gain nothing by changing his/her choice.
Let us take an example of chess. If you watch a Grandmaster play chess against someone who is well beneath him or her in playing stature, you will probably be surprised that the Grandmaster will take longer to beat the novice than an expert would take, although the expert is still much superior to the novice but far inferior to the Grandmaster.
Grandmaster Chess. Photo by Kryten. Taken from Everystockphoto.com
The reason for this is that when you try and finish off an opponent quickly, you leave gaps in your own defenses. These gaps are not easy to spot, but Grandmasters are in a position to take advantage of them. Therefore, it is in the interests of anyone who is playing a Grandmaster to take their time and not rush. So if there are two Grandmasters playing each other, each knows that the other will adopt the strategy of non-rush and will therefore play non-rush themselves. Because of this, Grandmasters are in the habit of taking their time, securing their defenses, and playing slowly.
However, when the expert plays the novice, he has no problems about tearing the poor novice apart because he knows that the novice can’t take advantage of the weaknesses that he leaves behind while attacking. If the expert were to play the Grandmaster, however, he would be a fool to rush into the attack.
In the case of the two Grandmasters, the Nash equilibrium consists of both players choosing the strategy of non-rush because they know that their opponent will do the same. It would be foolish to attack a Grandmaster hastily because they would be building their own defenses, and if you don’t do the same, you will be left in an untenable position. Therefore, the strategies of two Grandmasters playing each other are stable. Each will not change their own strategy if the other continues to maintain theirs.
In a cartel, a group of players who control the supply of a certain product get together and agree to keep the price of that particular product high. There are two strategies here – high prices and not so high prices. It’s easy to see why all the cartel members benefit in the long run if each follows the strategy of high prices. However, it is unstable because it is not a Nash equilibrium.
This is because of the fact that if one of the cartel members changes their strategy to not so high prices, that person will get all the customers who will no longer buy from the other players since they are following the high prices strategy. This will lead to a dramatic gain of business for the player who changes his strategy to not so high prices. Naturally, this situation can’t last. The moment the other players find out that one of them has changed their strategy, it is no longer in their best interests to adhere to the strategy of high prices. Thus, they change their strategy to not so high prices as well, and the cartel breaks.
OPEC Headquarters in Vienna
Cartels are so unstable precisely because of the threat of betrayal. And the more people that make up the cartel, the more unstable it becomes since there are more chances of any one person changing their strategy.
Cartels like OPEC have stood the test of time because, firstly, there are not too many players. And secondly, they all recognize that they’re here for the long term and that if one of them breaks the cartel by adopting not so high prices, then all others will follow suit, and they will be back to square one with lower prices.
Indeed, the only real reason for any cartel to stay together is if they are in the long run together and realize that united they stand and divided they fall.
Editor’s note: Last year a German watch magazine did an interview with John Nash. Read more about it at Amateur Economist. Thanks to Chris Meisenzahl for the link!
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