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Another classic auction format, the “Dutch auction” or “descending auction,” gradually lowers an item’s price until someone is willing to buy it.
In an English auction, bidders alternate raising the price until all but one of them drop out.
An enormously influential paper by the economists Sushil Bikhchandani, David Hirshleifer, and Ivo Welch has demonstrated that under the right circumstances, a group of agents who are all behaving perfectly rationally and perfectly appropriately can nonetheless fall prey to what is effectively infinite misinformation. This has come to be known as an “information cascade.”
Cramer’s incredulity is his private information holding up against the public information.
Investors are said to fall into two broad camps: “fundamental” investors, who trade on what they perceive as the underlying value of a company, and “technical” investors, who trade on the fluctuations of the market.
But while this critique is typically leveled at computers, people do the same kind of thing too, as any number of investment bubbles can testify. Again, the fault is often not with the players but with the game itself.
For one, be wary of cases where public information seems to exceed private information, where you know more about what people are doing than why they’re doing it, where you’re more concerned with your judgments fitting the consensus than fitting the facts. When you’re mostly looking to others to set a course, they may well be looking right back at you to do the same. Second, remember that actions are not beliefs; cascades get caused in part when we misinterpret what others think based on what they do.
Last, we should remember from the prisoner’s dilemma that sometimes a game can have irredeemably lousy rules.
And if you’re the kind of person who always does what you think is right, no matter how crazy others think it is, take heart. The bad news is that you will be wrong more often than the herd followers. The good news is that sticking to your convictions creates a positive externality, letting people make accurate inferences from your behavior. There may come a time when you will save the entire herd from disaster.
Here, algorithmic game theory gives us a way to rethink mechanism design: to take into account not only the outcome of the games, but also the computational effort required of the players.
However, in a Vickrey auction, the winner ends up paying not the amount of their own bid, but that of the second-place bidder.
In fact, there is no better strategy than just bidding your “true value” for the item—exactly what you think the item is worth.
This makes the Vickrey auction what mechanism designers call “strategy-proof,” or just “truthful.” In the Vickrey auction, honesty is literally the best policy.
In a Vickrey auction, on the other hand, honesty is the dominant strategy. This is the mechanism designer’s holy grail. You do not need to strategize or recurse.
In fact, a game-theoretic principle called “revenue equivalence” establishes that over time, the average expected sale price in a first-price auction will converge to precisely the same as in a Vickrey auction. Thus the Vickrey equilibrium involves the same bidder winning the item for the same price—without any strategizing by any of the bidders whatsoever.
In a landmark finding called the “revelation principle,” Nobel laureate Roger Myerson proved that any game that requires strategically masking the truth can be transformed into a game that requires nothing but simple honesty.
And the revelation principle just expands this idea: any game that can be played for you by agents to whom you’ll tell the truth, it says, will become an honesty-is-best game if the behavior you want from your agent is incorporated into the rules of the game itself.
And if that’s not possible, you can at least exercise some control about which games you choose to play.
Seek out games where honesty is the dominant strategy. Then just be yourself.
I firmly believe that the important things about humans are social in character and that relief by machines from many of our present demanding intellectual functions will finally give the human race time and incentive to learn how to live well together. —MERRILL FLOOD
First, there are cases where computer scientists and mathematicians have identified good algorithmic approaches that can simply be transferred over to human problems.
