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Apply Ultimatum Game Theory and Nash equilibrium to Stock Market

(2007-12-04 18:11:05) 下一个
                        

The Great Event has provided us an excellent experimental opportunity to understand Ultimatum Game, Nash equilibrium, and Game Theory. In this event, almost all of students chose to accept proposer’s offer with ignorance of unfairness. It makes me believe that there universally exists rational selfishness, which is a nature of humanity. Fortunately, after closer review of this result, I found there is also a student, who seemed not so selfishness (it’s not me), which reject the offer; I believe that the first reason of doing this is he wants fairness instead of economically greedy, I believe another reason is he wants to reach a win-win position in international business negotiation - reject the unfair offer first in order to have more gain he preferred in latter’s negotiation; or to reach the best result- both prisoners are released in game theory; I also believe he want call for government take the responsibility deal with pollution. In order to reach this result, what we need to do is not so much selfishness; people should take care of what others needs.

Stock market provides a great place to compete not only capital, but also patience, courage, and smart. In the past, people invested in stocks in order to gain profits by getting dividends, but now they grab profits mainly from the fluctuation of price daily. There are many similarities between the result of Great Event and stock market, this provide us an opportunity to apply Ultimatum theory on stock market. We assume there are two people in this game: Mr. Market – our proposer, who always provides offers to our accepter – Mr. Smart, sometimes generous, sometimes greedy. We also assume the offer is rejected when Mr. Smart don’t deal with Mr. Market, that is, when he prefer holding cash to buy or holding shares to sell  if he perceived the price is unfair or unreasonable, on the other hand, the offer is accepted when he decided to buy shares at reasonable lower price (maybe low P/E) or sell shares at considerable higher price (remove liquidation). Even there are many deals exist between these two traders in real life, but we now assume every single deal can be consider as an event which cannot be repeat, if Mr. Smart reject the offer, he will get nothing.

In this article, we just analyze two interesting types of Mr. Smart: extremely risk reverse and extremely risk neutral. They are called “extremely” since the former Mr. Smart wants to take the lowest risk only and the later wants to take the largest profit only. Extremely risk reverse can be divided into two categories: technical analysts and value analysts. The former accepts offer when they make buy-low or sell-high decision based on trends analyses, which assume all the price changes have affected by all the information of the market. They are called extremely risk reverses because they usually try to buy shares at the bottom of the trends and sell them at a little higher price, but not at the head. Once when they identified double heads bottom or shoulder- head bottom for example, they are likely to accept Mr. Market’s offer, no matter how less of the gain (they are greedy but fairness, they leave some profits to later buyer). They are satisfied if their expecting return fall into a fairness range they perceived --still remain some profits after deduct cost and risk premium, and most of these Mr. Smart are day traders. Another type of extremely risk reverse is value analyst; they make their decision whether or not to accept Mr. Market’s offer, is based on the fact that they try to find undervalued stocks by analyzing financial reports, marketing shares, industrial rates etc. It seemed that Mr. Market are stupid and generous now that can provide so low price of shares to Mr. Smart. Mr. Market’s shares seemed not popular enough to attract Mr. Smart’s notice, but on Mr. Smart’s point of view, their true values should much higher than the price Mr. Market’s offer. Therefore, Mr. Smart accepts the offer gladly.

Secondly, except extremely risk reverse, we are interested in another sort of Mr. Smart – extremely risk neutral, which means what Mr. Smarts want is as possible as he can to enlarge his profits, since at the same time, the risk do seem too high to offered the game, but he play only when the probability of to gain is higher than to loss. The best example to explain the application of ultimatum theory to extremely risk neutral, is Mr. Smart prefer to accept Mr. Market’s offer only at the day when Mr. Market’s stock company announce bankrupt. The stock prices have been dropped for some time before because Mr. Market had snooped some unfavorable news on his stocks, he is also cautious on his investment. But now after the announcement, the trends seemed even worse which lead to Mr. Market worry, he is worrying the possible result which if Mr. Smart refused his offer, not only both party get nothing, but also he will suffer a loss. As a result, Mr. Market goes to Mr. Smart’s office frequently try to persuade later accept his offer, and provide more and more lower price (we can omit this process as the theory can not repeat and can not negotiate). The only consideration on whether or not to accept Mr. Market’s offer is whether or not stock price has reached such a lower level seemed worthless (fairness and reasonable). Once Mr. Smart decided to accept the offer, he expects the share price will be rebound at least 100 percent higher than purchase price short later. But Mr. Smart worn this strategy can archive the target only to those historical and large enough companies, and at the same time, Mr. Market should be in the trends of bear. For example, yesterday’s (Nov.26, 2007) rebounding of FFHL in NYSE market raised the price from $2.2 to $4.48.

In conclusion, The Great Event provide an excellent chance to understand Ultimatum game theory, we can use this theory on analyzing stock market. In order to avoid being rejecting, we should also take consideration requirements of others, provide seemed fairness offer as possible as we can; On the other hand, in order to enlarge not only ourselves benefit, but also the other party’s, both parties should express their core benefits extrinctly, balance fairness and greedy.

Reference:

1. Benjamin Graham, The Intelligent Investor: a book of practical counsel, 1998, JSPPH

2. Magee, Edwards, Technical Analysis of Stock Trends, 1996

3. Microsoft Student 2006, Nash Equilibrium, Game Theory, and Ultimatum theory

4. Sigmund, Karl, THE ECONOMICS OF FAIR PLAY, Scientific American, 00368733, Jan. 2002, Vol. 286, Issue 1
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