Investment Risks from a Game Theory Perspective

There is a classic example in game theory. Suppose we have 100 dollars, and we set a rule: this 100 dollars can be used for bidding. It is just an ordinary 100 dollars, without any special value. The bidding rule is that the highest bidder can take this 100 dollars, but the second-highest bidder also has to pay their bid but gets nothing in return.

Specifically, the first place takes 100 dollars, and the second place has to deduct what they bid but gets nothing. The question in game theory is, given such a rule, how would you choose to participate?

If you haven't studied these concepts or thought carefully, you might be tempted to participate in the bidding. However, the most rational action is actually not to participate. Because the value of this 100 dollars is constant, everyone wants to win, and in the end, the price might 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 might ask, why would someone bid up to 99 dollars? In fact, many people start with a 'let's give it a try' mentality; for instance, the starting bid is only 20 cents, thinking to take a gamble. So you bid 20 cents, I bid 50 cents, you bid 1 dollar, I bid 2 dollars, and everyone keeps raising the price. In the end, you bid 98, I bid 99, and eventually someone bids 100. This way, the second place will incur a significant loss.

This example illustrates that under certain game rules, the most rational choice is actually not to participate at all.

For instance, if I bid 99 dollars, I have now lost 99 dollars. If someone bids 100 dollars, usually the other person would choose to raise it to 101 dollars; this way, although they lose a dollar, at least they can take that 100 dollars. The best way to understand game theory is actually for everyone to agree on a pricing and then split the 100 dollars.

But in reality, the game doesn't work so rationally. Usually, as it goes on, people lose their rationality. For example, you bid 99, I bid 100, you bid 101, I bid 102, then you bid 103, and in the end, it might escalate to over five hundred. The result is a lose-lose situation. Typically, it takes this extent for the game to stop.

Therefore, game theory tells us that after studying the rules clearly, the most rational choice is actually not to participate. $SOL $XRP $BNB