Tuesday, April 26, 2011

Is Trading a Zero-Sum Game?

First of all, let me cite the article that started this whole voyage into game theory. In the appendix of this pdf is a great table of who is competing against whom in a stock transaction.

From there I watched 2 free lectures on the  Academic Earth website on game theory.
Benjamin Polk from Yale lectures on pure game theory.
Kathleen Bawn from UCLA lectures on game theory in politics.

As an aside, how did Clint Eastwood know what to do in the final scene of the "The Good, The Bad & The Ugly"? He followed his own game theory. [ Edit: I have heard another version of the story, where the only way to be assured of survival is to shoot your gun up in the air prematurely. That way the other two know they will not be killed by you. ]

Is trading a zero-sum game? In economics and contract theoryinformation asymmetry deals with the study of decisions in transactions where one party has more or better information than the other. "When two asymmetrically informed risk-neutral agents repeatedly exchange a risky asset for numéraire, they are essentially playing an n-times repeated zero-sum game of incomplete information"

Joseph E. Stiglitz pioneered the theory of screening. In this way the under informed party can induce the other party to reveal their information. They can provide a menu of choices in such a way that the choice depends on the private information of the other party. Examples of situations where the seller usually has better information than the buyer are numerous but include used-car salespeoplemortgage brokers and loan originators, stockbrokersRealtorsreal estate agents, and life insurance transactions.
Examples of situations where the buyer usually has better information than the seller include estate sales as specified in a last will and testament, or sales of old art pieces without prior professional assessment of their value. This situation was first described by Kenneth J. Arrow in an article on health care in 1963.[2]
George Akerlof in The Market for Lemons notices that, in such a market, the average value of the commodity tends to go down, even for those of perfectly good quality. Because of information asymmetry, unscrupulous sellers can "spoof" items (like software or computer games) and defraud the buyer. As a result, many people not willing to risk getting ripped off will avoid certain types of purchases, or will not spend as much for a given item. It is even possible for the market to decay to the point of nonexistence.

But the best white paper on financial applications of game theory I have found is this link. In Corporate pricing, it starts "with a discussion of the use of game theory in corporate finance where to date it has been most successfully applied". It talks about dividends as signals, capital structure, debt and bankruptcy. These include the choice between debt and equity and the amount to pay out in dividends.

In Asset pricing it talks about market microstructure.  "This is the study of the process and outcomes of exchanging assets under explicit trading rules. Where as general equilibrium theory simply assumes an abstract price formation mechanism, the market microstructure literature seeks to explicitly model the process of
price formation." Also covered are market manipulation models and "pricing anomalies such as those associated with P/E or P/B ratios that have received so much attention in recent years, are intimately associated with accounting numbers.  Since these numbers are to some extent the outcome of strategic decisions analysis these techniques seems likely to be a fruitful area of research."

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