The Game theory behind what is happening to GameStop saga


The GameStop saga has hit the stock market, and some people think that this event is a game changer in the stock market which had traditionally been dominated by large hedge funds taking advantage of individual investors.


Long story put short, GameStop stock has attracted short selling by big hedge funds, because the game retail industry had been declining as everyone now buys games online and uses steam downloading. The problem was that the stock was too much shorted, and some investors thought it was excessive.


Individual investors responded by longing GameStop stock, saying that if they buy and hold the line, these mega hedge funds have to cover their short sales, a phenomenon known as short squeeze. A short squeeze occurs when a stock or other asset jumps sharply higher, forcing traders who had bet that its price would fall, to buy it in order to forestall even greater losses.

Source: Investopedia


Will individual investors prevail over these powerful and greedy Wall Street hedge funds? Nobody knows for sure, but most likely the answer is no in the short run.


An example from the game theory, Prisoner’s Dilemma, illustrates why two completely rational individuals might not cooperate, even if it appears that it is in their best interests to do so.

Prisoner's Dilemma


The Prisoner’s Dilemma sets out a hypothetical situation, in which two prisoners face the following scenarios and outcomes:


  • Scenario (1), both prisoners cooperate: They both stay silent, and they will only serve 1 year in jail (both get satisfactory result);
  • Scenario (2), one prisoner defect but the other cooperates: A prisoner says he has not committed crime while B prisoner says he has committed crime. The outcome is that B does not have to go jail while A serves 3 years in jail (only the defector gets satisfactory result); and
  • Scenario (3), both prisoners defect: They both confess their crime, and they will be sentenced to go to jail for 2 years (they both get shorter jail terms because they confessed, but this is less optimal result than it would have been had they cooperated in the first place. Clearly, scenario 1 is better than scenario 3).




As the outcomes from the three scenarios show, prisoners have the incentive to defect rather than cooperate, because they will be rewarded better by defecting regardless of what the other prisoner does. Even if a prisoner choose to cooperate, if the other prisoner defects, then he ends up losing so much more.


This is why they will not get optimal outcome even if they are completely rational human beings. Now, let’s look at GameStop investor’s dilemma.


GameStop Investor's Dilemma


Assuming that the two prisoners in previous case represent a group of individual investors, they face the following scenarios and outcomes:


  • Scenario (1), the individual investors cooperate: All individual investors buy and hold the GameStop stock, and the hedge fund will lose huge amount of money as the stock price does not fall. The investors earn huge amount of money as hedge funds lose;
  • Scenario (2), some individual investors defect but some cooperate: Some individual investors short the stock when the stock price is reasonably high, while other individual investors still buy and hold. Those who shorted stock exits with some profits while those who hold will be punished by falling stock price as hedge funds recover; and
  • Scenario (3), all individual investors defect: All individual investors short the stock, and the hedge fund comfortably recovers their stocks. All the individual investors reap benefit, but their benefit is less than it would have been if they had all held the stock for a long time for hedge funds to die out.


Individual investors have the incentives to cooperate by longing and not selling the stock, because this will drive up the price of the stock and hedge funds will not be able to cover their shorts, resulting in a huge loss (their loss is calculated by [the price at which they sold the GameStop stock] – [the price at which they bought the GameStop stock] If the stock price keeps going up, they will eventually go bust).


However, they will not be able to cooperate if some individual investors defect by choosing to sell their stocks, giving other people more incentive to sell before the stock price drops further. In the short run, therefore, everyone has incentive to short the stock because if other investors short first, then he or she loses more.


This is why institutions or anyone powerful enough to punish defectors are needed to systematically aim for optimal results in the long run. Examples include Saudi Arabia and OPEC, whereby OPEC is an institution for all oil countries to cooperate and promote member countries’ collective interest. And if any member country tries to defect, then Saudi Arabia punishes it by adjusting supply of crude oil.


Individual investors started rebellion against Wall Street hedge funds courageously. While their intention is noble, economic theory shows that rational human beings are more prone to defect rather than cooperate.


Right now, individual investors lack in such institution or powerful individuals to sustain their maneuver in the long run, unfortunately.


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