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The Market Game, from James Sogi

December 16, 2007 |

Victor Niederhoffer reviewed Luck, Logic & Whies Lies by Bewersdorf which discussed computational methods for optimal and pure strategies for various games based on simplified models. In the even/odd marble guessing game the optimal defense by the simpleton against the smart player to foil the advantage is to use a random choice. This is the basis of using a behaviorally optimal "mixed" strategy to foil the opposition who is guessing your strategy by alternating between two advantageous strategies.

The market could be modeled as a zero sum game with imperfect information. The goal is to find the pure strategies or behaviourly optimal strategies against opposing strategies than the ones already being used and by how much could the winning expectation be increased? The market modeled can be further simplified as a two person game in which one bids, one offers. The initial choice is whether to bid and offer. If the market goes up, bidder wins, if it goes down, bidder loses. If the market was random it would be a coin toss, but due to drift the odds favor the upside. This pure strategy conclusion is not trivial.

However there is more to the game. To profit one must exit. The next decision is when to exit. Analyzing the buy side of the decision tree to model the situation, buyer wins by selling before his opponent with a profit. If he waits too long or for too much, and seller sells before he sells, and price goes down, he loses. The balance is between time and profit. To find the optimal strategy Bewersdorff models an analogous poker betting situation on a decision tree. The optimal strategy requires some sort of mixed strategy for optimal results. He speaks of a realization plan using a sequential form of analysis. A way to solve this involved a linear optimization method developed to solve military procurement. The linear optimization was applied to the decision on what quantities of various products should be produced to maximize profit realization given a choice of resources. The limits of the resources and the limits of capacity or given by a series of inequality formula and are solved by looking at the largest profit distribution. This analysis might be applied to a trade by looking at the profit potential and probability of various time/profit target lags and solving for the optimal. Or it might be applied to leverage calculations. It is solved with the Simplex Algorithm. The method would be to choose two strategies say x period or y period, or x percent or y percent. But therein lies the rub. I have not tested these simplex solving tools.

Larry Williams replies:

Simplex ain't gonna work…

"Simplex is quite good for solving static, linear (and thus rather well-defined) problems."

… markets are not well defined. I suspect hold on to winners with trailing stops and ditch losers is much more elegant.

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