Game Theory, Reinhard Selten and Trembling Hand Equilibrium

“I attended workshop on Game Theory at Jerusalem in 1965, It had only 17 participants, but among them all the important researchers in game theory, with few exceptions. Game theory was still a small field. We had heated discussions about Harsanyi’s new theory of games with incomplete information. This was the beginning of my long cooperation with John C. Harsanyi.”

-Reinhard Selten

Reinhard Justus Reginald Selten is a German economist, who won the 1994 Nobel Memorial Prize in Economic Sciences, which he shared with John Harsanyi and John Nash.

Selten further refined Nash equilibrium and came with concept of trembling hand. Game theory assumes that players are rational and not capable of making mistakes.

Selten felt that there exists a small probability of other person making a mistake through what he called “slip of hand” or tremble, wherein a person may choose wrong strategy by mistake.

“My first contact with game theory was a popular article in Fortune Magazine which I read in my last high school year. I was immediately attracted to the subject matter and when I studied mathematics I found the fundamental book by von Neumann and Morgenstern in the library and studied it.”

-Reinhard Selten

Suppose there are two individuals working on a project, a member should take into consideration a possibility of other member unintentionally making an error (a “tremble”).By acknowledging such possibility that other member may take wrong decision, the member chooses a trembling hand perfect equilibrium that takes into account this probability and protects the member should the other member make a mistake.

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There are two students (player A and player B) who wish to join engineering college; they have option of joining civil or mechanical engineering. If you look at payoff matrix, it has two Nash equilibriums.

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Player B feels that player A may tremble i.e. there exists a possibility that player A may end up opting for civil engineering while filling form (can happen due to oversight). Suppose probability of oversight is 5%. Suppose player A trembles and opts for civil engineering.

Then expected value for player B is 5% of 4 + 95% of 5= 4.95, so player B will opt only for mechanical engineering ensuring payoff of 5 for himself and in process player A will also benefit.

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