This post is split out from my main summary of Algorithms to Live By by Brian Christian and Tom Griffiths. Check out that summary to learn more about the book.
Algorithms to Live By discusses the following game theory concepts:
- Recursion
- Equilibrium states – how to change them and when to change them
- Information Cascades
Recursion — anticipating others’ thoughts
When something, such as a machine or a person, tries to simulate another thing as complex as itself, it ends up maxing out its resources and going down a rabbit hole. It’s like that problem of figuring out what your opponent thinks you’re thinking — it can go on for infinite levels. This is called recursion.
In poker, you only want to play one level above your opponent. If you play too many levels above them, you’ll think they know something they actually don’t, which makes you worse at predicting their actions.
Equilibrium states
An equilibrium is a state where neither player wants to change their play given the other players’ moves.
Nobel Prize winner John Nash proved that every two-player game has at least one equilibrium. In theory, knowing what the equilibrium is allows us to predict what the stable, long-term outcome of a new policy or rule is. However, predictions only work if players can find the equilibrium. In the real world, games can be so complex that players may not even be able to find the equilibrium.
Mechanism design
However, that equilibrium may not be a good one. To get a desired outcome, we may need to change the rules of the game — this is called mechanism design. For example, in the classical prisoner’s dilemma, defecting is the best strategy yet is worse for both players. But the rules of the game change if both prisoners are members of a crime syndicate that punishes defectors. Cooperation becomes the best strategy, and makes both prisoners better off.
The counterintuitive and powerful thing here is we can worsen every outcome—death on the one hand, taxes on the other—yet make everyone’s lives better by shifting the equilibrium.
Vickrey auction: the holy grail of mechanism design
In ordinary English (bidding out loud) and Dutch auctions (sealed bid), people have an incentive to bid less than an item’s true value in the hopes of getting a bargain.
That’s not true for a Vickrey auction, a sealed bid auction where the highest bidder wins, but pays what the second-highest bidder put down. The dominant strategy here is to be honest and bid what you truly value the item at, regardless of what other bidders do. Bid too much and you may overpay. Bid too low risks you losing the auction, but it won’t even save you any money.
While it might seem disadvantageous to the seller to sell the item for the second-highest bid, this is offset by the fact that it discourages bidders from shading down their bids.
Price of anarchy
The price of anarchy measures the gap between cooperation (where players work together) and competition (where players independently try to maximise their own outcomes). It allows us to quantify the benefits of centralisation vs decentralisation.
For example, the price of anarchy for traffic is low. This is true for both road and network traffic. It turns out that “selfish routing” (where each player just takes the fastest route for themselves) is only 33% worse than a perfect top-down coordination. So even if all cars are self-driving and perfectly coordinated in the future, it may not lower congestion by much.
Information cascades
We hold our thoughts privately, but our actions convey public information. When one person bids on an auction, their bid is public information. That information may make a second person more likely to bid on the same auction. The first two bids may then encourage a third person to make a bid, and so on. This is an information cascade.
Even if each subsequent bidder has private misgivings, they may discount those when they see many people publicly bidding—they may assume the earlier bidders had better information than their private information, and no one’s private misgivings are ever aired. Such a cascade can cause bubbles and fads, even when everyone is acting rationally.
Something very important happens once somebody decides to follow blindly his predecessors independently of his own information signal, and that is his action becomes uninformative to all later decision makers. Now the public pool of information is no longer growing.
So be cautious in cases where public information exceeds private information and remember that actions are not beliefs. Sticking to your convictions can create a positive externality, adding to the pool of public information. Even if you decide to override your own doubts, perhaps you should find a way to broadcast those doubts to others.