Analysis of Investment Risks and the Nature of Pyramid Schemes from a Game Theory Perspective
There is a classic example in game theory. Suppose there is 100 dollars, and we set a rule: this 100 dollars can be used for bidding. It is just an ordinary 100 dollars with no special value. The bidding rule is that the highest bidder can take the 100 dollars, but the second-highest bidder also has to pay their bid and gets nothing in return.
Specifically, the first place takes 100 dollars, and the second place loses their bid amount but gets nothing. The problem in game theory is, given such a rule, how will you choose to participate?
If you have not understood these concepts or have not thought them through carefully, you might be tempted to participate in the bidding. But actually, the most rational choice is to not participate. Because the value of this 100 dollars is constant, everyone wants to win, and in the end, the price is likely to be driven up to 100 dollars or even higher. For example, the first place bids 100, and the second place bids 99. The second place would lose 99 dollars and get nothing.
You may ask, why would someone bid up to 99 dollars? In fact, many people initially participate with a try-it-out attitude, for instance, if the starting bid is only 20 cents, thinking of taking a gamble. So you bid 20 cents, I bid 50 cents, you bid 1 dollar, I bid 2 dollars, and everyone keeps increasing their bids. In the end, you bid 98, I bid 99, and eventually, someone bids 100. As a result, the second place incurs a significant loss.
For example, I bid 99 dollars, but now I've lost 99 dollars. If someone bids 100 dollars, usually the other person will choose to bid 101 dollars, which means they would lose one dollar, but at least they can take that 100 dollars. The best way to understand game theory is actually for everyone to agree on a fixed price, and then split the 100 dollars equally.
