Econophysics And The Theory Of Games
What has Econophysics to do with the Theory of Games?
Econophysics is the study of Economics by using analogies and methodologies from Physics, particularly that of Statistical Mechanics. The latter uses probability and statistics to derive aggregate properties (Thermodynamics) from a population of interacting particles/molecules. The macro properties of the population is then related to the microscopic properties of the particles.
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Economics Nobel laureate Markowitz: "I believe that microscopic market simulations have an important role to play in economics and finance. If it takes people from outside economics and finance -- perhaps physicists -- to demonstrate this role, it won't be for the first time that outsiders have made substational contributions to these fields.''
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In a way this was inevitable, since treating the system as an N-particle system is intractable. We know that the N-body problem is impossible to solve for N>=3, let alone for N a large number.
Now apply this analogy in Economics, but replace the particles with economic agents, and we have Econophysics. The economic agents are interacting in transactions, such as order, bid, ask, buy and sell.
Of course since the interactions are quite different from the interactions of particles in Statistical Mechanics, we expect Econophysics to have very different results. Some objects to Econophysics, because physics deals mostly with equilibrium and linear systems, whereas the new Economics is nonlinear and far from equilibrium in distinction to classical Economics which deals with equilibrium conditions in close analogy with mechanical equilibriums, such as the power of supply and demand, but could not tackle the fluctuations in a stock market, which sometimes lead to chaos and crashes. This is why Econophysics is also considered as a Complexity Science studying dynamical systems.
The model of a population of agents interacting in economic transactions can be studied theoretically or experimentally.
Theoretical studies are possible with simple systems only, such as applying the Ising lattice model to a the case where agents at the lattice nodes buy or sell or stay idle randomly with some probabilities.
Experimental means studying data from the real world, or making computer simulations of models.
The study of Econophysics described overlaps greatly with social algorithms (see "Defining Social Algorithm") which deals with the algorithmic aspects of a population of agents. Social algorithms does have to do with Economics.
Game theory enters the scene as the rules of engagement of the agents. So Game Theory is the microscopic model, and Econophysics tries to derive the global properties of the population of agents. In most cases, the agents will have different behaviors, leading to a multi-agent system.
The minority game (MG) is a famous setting used in the study by Challet and Chang.
The game itself is derived from the "El-Farol Bar" game invented at Santa Fe. Players in the "El-Farol Bar" decide to go or not to go to the bar. If they decide to go, and the bar is crowded, the payoff is low.
The minority game involves agents who buy or sell. If there are more agents buying than selling, the price goes up, and if there are more agents selling, the price goes down. Thus the minority always win (just like in the "El-Farol Bar"), hence the name MG.
It is worth looking at MG's setting, partial information and bounded rationality. Agents only have memory of the last M histories, for a finite M. It does not satisfy the Efficient Market Hypothesis, one of its premises being that the whole history is reflected in the present situation (Markov property). Bounded rationality asserts that people make decisions based only on partial information, even if more complete information is available (but may be too hard to find), and does not always look for optimal solutions (uses rules of thumb instead).
About MG, Challet wrote: "Funny enough is this game known in the French speaking part of Switzerland as "Zig-Zag-Zoug" : if three children must elect a leader for their games, they put their right foot close together, say the magical words, and at the end of "Zoug", they remove their right foot or not. The child who is in the minority wins."
Other than in Economics, Game Theory is also used in social and biological sciences.
The famous Iterated Prisoner's Dilemma has an interesting way of explaining how ethics/altruism develops, when each are supposed to act selfishly in their own interests.
Prisoner's Dilemma is also an example where the Nash equilibrium (Nash from "Beautiful Mind" ) does not give the best for players, which is why it is called a dilemma.
The above is a very elementary introduction to Econophysics and Game Theory.
It presents only one view of Econophysics, there are other people who look at Econophysics as everything where Physics and Mathematics are applied to Economics.
Econophysics in this wider sense, include stochastic processes, power laws, fractal market hypothesis, and "Physics of Finance".
The last is a title of a book "Physics of Finance, Gauge modeling in non-equilibrium pricing" by Kirill Ilinski , a physicist now working in finance. Ilinski starts with invariant properties (symmetry groups) of Quantum Electrodynamics, and applies the analogy to Finance. Both Quantum Electrodynamics and Finance become abstract mathematical theories of fibre bundles and differential geometry. Ilinksi derived Black Scholes purely from principles of invariance albeit under certain rather strong assumptions.
Econophysics has received much attention, see the following sample list of web sites dealing with Econophysics to get some idea of it:
Some links on Game Theory:
2 komentar:
Here is a joke about econophysicist, told by Abdol Soofi: A man walking along a road in the countryside comes across a shepherd and a huge flock of sheep. He tells the shepherd, "I will bet you $100 against one of your sheep that I can tell you the exact number in this flock." The shepherd thinks it over; it's a big flock so he takes the bet. "973" says the man. The shepherd is astonished, because that is exactly right. Says "OK, I'm a man of my word, take an animal." Man picks one up and begins to walk away.
"Wait," cries the shepherd, "Let me have a chance to get even. Double or nothing that I can guess your exact occupation." Man says sure. "You are an economist for a government think tank," says the shepherd. "Amazing!" responds the man, "You are exactly right! But tell me, how did you deduce that?"
"Well," says the shepherd, "put down my dog and I will tell you."
so econophysicists know all the tricks for calculation, but do not know the difference between a sheep and a dog
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