Here we see a very different, cyclic pattern of investment and deinvestment. After initially getting the ball rolling for the investment scheme, and encouraging ordinary investors to join, speculators quickly begin to withdraw their funds, initially taking out more than they themselves put in. This has the effect of making the ordinary investors the only agents in the population who remain invested. Then as speculators see that the investments made are as large as or larger than the previous year, they again throw their own funds into the game. This pattern then repeats itself in a cyclic fashion, but deinvestment is never as extreme as in the initial drop.

IV. Possible Extensions

A realistic feature in this type of investing that we did not include, but which could be added later, is to allow for increasing returns. In such a scenario, investors would be allowed to leave accrued interest in the investment account, increasing the total account balance upon which future interest is accrued. Such a feature could potentially lead to larger and/or longer lasting bubbles. Additional real-world features that could be included in future versions are larger numbers of wealthy and poor potential investors. In the version presented above, the total money supply is normally distributed, but we could use a distribution with fatter tails, or even a bimodal distribution to represent more exaggerated levels of wealth inequality. The distribution of wealth could also be assumed to be correlated with the type of agent. Finally, and we think most importantly, in future extensions we could allow for agent learning. In the current framework Ordinary Investors and Speculators only have a memory of a single period. And we do, in fact, see investing in periods after the fund has crashed. Building some feature about the investment fund's reputation into agent decision-making would likely lead to more realistic dynamics.

V. Other Social Science Applications

Other potential social science applications include situations in which (i) an agent seeks to convince a population of other agents to pay some cost of support based on the promise of future returns, (ii) one class of agents in the population has some stake in convincing the others to offer that support, and (iii) another class of agents is potentially willing to pay the cost of support in the hope of future returns.

One such situation could be the gain and loss of public support for elected officials. In this situation, the public official would be the agent attempting to convince the mass public to pay some cost of support (e.g., voting, foregoing a vote for someone else), and would do so by making campaign promises in regard to particular policy areas. Political activists would represent the class of the public with a stake in convincing others in the population to offer that support. The stake here may be in the form of a job in the official's administration, the potential financial gain from a future government contract, etc. Ordinary citizens would represent the class of the population that is potentially willing to offer support, but expects to gain some sort of policy action in return. When a public official is elected based on particular policy promises, and those promises cannot be fulfilled, past supporters will pull their support. At this point, the political activists may abandon their exaggerated support for this particular official. The investment in this official's line of goods fails when she is thrown out of office.

Collective actions of a few big players and speculators can also create supernormal returns in the art market, in which winning bids in art auctions influence the value of all works of the artist. Particularly in the contemporary art market, it is argued that auctioneers, dealers and collectors who have large collections of an artist's works, work cooperatively in order to inflate the bids made in auctions. This mechanism can create a bubble that yields supernormal returns until the rise in the prices of artworks cannot be sustained. In such a scenario, art dealers would represent the agent attempting to convince a population to pay a cost of support; serious art collectors would represent those in the population who have a stake in convincing others in the population to pay the cost of support; and ordinary art investors would be the potential investor class.