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The Forces Behind a Bubble

The stock market has been has been a vehicle for wealth since its inception. With its creation, the infamous “bubbles” associated with reckless speculation of these markets eventually arrived as well. The consequences are often dire as countless individuals lose their investments and the economic repercussions reach beyond the stock market. Whether talking about the tulip mania of 17th century Netherlands or the more recent and relatable housing crisis of less than a decade ago, it is clear that individuals often lose sight of reason and follow the crowd. What we learn in Networks provides an interesting way to analyze this phenomenon.

Specifically, the coordination game offers valuable insight to the possible reasons that a speculative bubble may form. First we will need to set up the game. Let us make ‘a’ the payoff of deciding to choose a certain stock and ‘b’ the payoff of deciding to choose any other stock. We know that ‘p’ is the fraction of an individual’s neighbors that have chosen ‘a’. Furthermore, the threshold rule maintains that an individual will choose ‘a’ if ‘p’ is greater than or equal to. Finally, the network at play here is one that resembles the social network of the real world: fairly uniform and interconnected.

A bubble’s stages of conception are fascinating. A certain stock or commodity must first manage to gain a foothold among the investor community. Either through news or a shift in public opinion, the stock gains popularity and more and more nodes choose ‘a’. At this point, a runaway effect arises and causes the bubble to rapidly inflate. Looking at our model we can see that as the stock catches on, ‘p’ increases as more of a given nodes neighbors have already chosen ‘a’. Moreover, ‘a’ increases relative to ‘b’ as the price of the stock within the bubble increases with each purchase of shares. Looking at our threshold rule we can see that the left side of the inequality increases while the right side decreases. This means that with every passing moment, according to our rules, investing in the bubble becomes increasingly more attractive. The bubble proceeds to grow larger and faster until it inevitably pops. The wisest investors realize that the stock is ridiculously overvalued and proceed to sell, forgoing ‘a’ for ‘b’. The stock eventually returns to its pre-bubble price or usually even lower. Looking at our model again, this causes the left side of the equation to decrease as nodes’ neighbors are now switching to ‘b’ instead of ‘a’. Additionally, the right side increases as the payoff for ‘a’ decreases with its dwindling price. One could argue that the payoff of ‘a’ becomes negative as it becomes clear that its price grossly overstates its value. Within our model, this makes the decision to now sell the stock even easier. No matter what, the right side is now greater than the left side. The left side will always be less than one because ‘p’ is a fraction and the right side will be greater than one because ‘a’ has a negative payoff. Due to this inversion of the inequality, the bubble deflates as rapidly as it grew, and the latest investors are left with empty pockets.

The reason all of this happens is because more than anything, humans fear missing out. They see everyone following a trend and making money, so naturally, they want in. The actual value of the stock is disregarded as the bubble grows until eventually someone has a “Wait a minute” moment and ignites a market-wide sell-off. Despite multiple occurrences and the advice to be a contrarian, people are bound to fall into the trap of the bubble due to their innate desire to not miss an opportunity and the blind trust that they place in crowds.




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November 2012