Author Bio

One of the games which is repeatedly used as an example in game theory is called the Prisoner’s Dilemma. In this game, two prisoners are caught and they are each given the choice to cooperate with each other or turn on each other. This game has been used to simulate various real life scenarios including many economical situations and in essence describe any un-trusted transaction between people.

In 1984, Robert Axelrod conducted an experiment in which he asked scientists to play in a tournament of repetitive prisoners dilemma with one another – by creating the repetition of the game Axelrod made it possible for people to adapt their strategies and also created a memory in the game such that each player plays the next iteration with the knowledge of the strategy his opponent played in the previous iteration.

The winning strategy was found to be “tit-for-tat”, which leads to a balance of cooperation between the two prisoners.

Axelrod then conducted another tournament where he disclosed the winning strategy. The surprising thing he found was that even though everyone knew the winning strategy, it still remained the winning strategy. So collaboration on the strategy did not affect the game in any way.

Another variation of the prisoner’s dilemma is called an assurance game and is most commonly known as “Hunt a Stag.” In this game, two hunters can choose to collaborate and hunt a Stag (large and tasty adult deer) or split and hunt a rabbit alone (smaller but just as tasty).  The difference between this game and the Prisoner’s Dilemma is that players are allowed to communicate and choose to collaborate.

So creating a proper mechanism for communication and trust between players is essential for collaboration.

One other commonly used game is called the tragedy of the common. This game is played by several players that share the same resources. In this game it has been shown that if the players act independently in their own best interest they would eventually deplete the resource, which is not in their long term best interest. Elinor Ostrum, a political scientist, has researched the matter looking at various communities around the world that share resources. She actually found that it’s true and that most communities have depleted their resources, which was not in their best interest. But she also found something else; there were many communities that didn’t deplete the common resources and managed to sustain a long-term preservation of these resources. By looking closely at communities that succeeded vs. communities that failed she discovered that communities that succeeded in preserving these resources managed to establish institutions for collective actions, and that collaboration was the main reason for the positive outcome.

Robert (Yisrael) Aumann and Thomas Schelling received the Nobel Prize in 2005 for their work on collaboration in games (“The tile of Aumann’s work is “Conflict and cooperation through the lens of game theory”) and addressed the question of which games would promote collaboration and why people chose to collaborate. Part of Aumann’s findings was that multi-player repetitive or infinite games promote cooperation between players because people learn to collaborate in time.

Another contributing factor to cooperation is introduced by some irrationality in the players, meaning that perfection and uniform thinking does not lead to collaboration. There is a need for some of the players to act differently than others given the same situation in order to promote collaboration or, as George S Patton described it, “If everyone is thinking alike, then somebody isn’t thinking.” — George S. Patton.

So if we look at all of these examples we can see that in multi player infinite games with some irrational behavior (like trading for example) sharing and collaboration are always in our best interest. In my mind we still haven’t begun to realize the true potential of collaboration and the payoffs it would yield but we can clearly identify that collaboration, in the eyes of game theory, leads to greater success.

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Be sure to read the full risk disclosure before trading Forex.  Please note that Forex trading involves significant risk of loss. It is not suitable for all investors and you should make sure you understand the risks involved before trading. Performance, strategies and charts shown are not necessarily predictive of any particular result. And, as always, past performance is no indication of future results.

Author Bio

Probably one of the earliest applications of psychology to the financial world was the Prospect Theory in 1979.  Two psychology professors, Amos Taversky and Daniel Kahnman, proved that people when faced with a financial decision will not necessarily make the most logical selection. This is because of the way we think about our prospects and not the big picture scenario when making financial choices. Kahnman was awarded the 2002 noble prize in economic for his work in the field.

What they proved is that people are affected by losses more than they are affected by wins when they are required to make a financial decision. For example, when a person is asked to choose between receiving $100 or tossing a coin to receive $210 most people would prefer to take the $100 even though the most cost effective option would be to toss the coin (This is because the probability of winning is 0.5 so the utility function for tossing the coin is 0.5*$210 = $105 which is greater than the other option of $100). Another interesting thing they have found is that that the opposite behavior happens when they are faced with losing money. Most people would prefer to toss a coin with the 50/50 chance of losing $210 as opposed to just giving away $100, which again is not the logical option.

So to make a long story short – people like to make as much money as possible without risk and take more risk than necessary when they’re about to lose money.

We can see one application of this in real life trading where most traders tend to close winning positions sooner, take their profit and avoid additional risk. On the other hand they could leave loosing positions longer, take additional risk for the chance that the market would change direction (which rarely happens) and they wouldn’t loose as much.

There are many other applications of this behavior in real life trading. Stay tuned for the next post in this series, coming soon.

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Be sure to read the full risk disclosure before trading Forex.  Please note that Forex trading involves significant risk of loss. It is not suitable for all investors and you should make sure you understand the risks involved before trading. Performance, strategies and charts shown are not necessarily predictive of any particular result. And, as always, past performance is no indication of future results.

Author Bio

In the following few posts I’ll try to give a few examples of how game theory is applied to trading the forex market hoping to shed some light on the mathematical aspect of trading and the value of collaboration in this market.

The most common statement I hear from traders is “The forex market is an efficient zero-sum game market and therefore sharing information may expose my edge.”

So what is a zero-sum game and how do I know if the above statement is true? Let’s start by talking about game theory and the different types of mathematical games.

Game theory is relatively young and quite complex branch of mathematics applying math to structurally define strategic situations in games. Mathematical games are most commonly defined by the number of players, duration of the game, game sum (more on this in a minute), simultaneous/sequential, and information flow. So for example chess is a two player, finite, zero-sum, sequential perfect information game because there are two players, the game ends when one of the players wins, only one player can win, the players take turns in playing and each player sees the actions of the other trader. (This is what defines perfect information flow.)

Economy, in general, is a multi player, infinite, positive-sum (Hold on, I promise I will explain why this is), simultaneous, imperfect information game.

Zero-sum games are games where a win by one player means a loss by the other player; the term has little to no relevance when describing multiplayer infinite games. The reason economy is a positive-sum game is because it’s an infinite game where value is built throughout time due to value growth in the overall economy.

So what about retail forex trading? Is forex a zero-sum game?

The short answer is that it doesn’t really matter because it’s an infinite, multiplayer game. The long answer is that it’s not a zero-sum game and it largely depends on the way the broker operates. Brokers that operate as a dealing desk, for example, (also known as market makers) mathematically resemble the way a bookie operates in a horse race. This becomes a negative-sum game because mathematically the players in the game are all traders using the same broker.

So what is the best strategy to play in a multiplayer infinite game with imperfect information – like the retail forex market? – More on that in future posts …

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Be sure to read the full risk disclosure before trading Forex.  Please note that Forex trading involves significant risk of loss. It is not suitable for all investors and you should make sure you understand the risks involved before trading. Performance, strategies and charts shown are not necessarily predictive of any particular result. And, as always, past performance is no indication of future results.