Chapter 6: Cake Cutting (pages 67-78)
Summary in haiku form
That I know game theory.
Think strategically!
Summary in one paragraph
Game theory, the study of strategic interactions between optimizing individuals, has applications as diverse as warfare and business and biology and, yes, games like poker. One application of game theory is to fair division problems such as the “I cut, you choose” solution to the cake-cutting problem, where we can see the importance of information: sometimes you want to be the cutter and sometimes you want to be the chooser.
Notes on specific pages
p68-69: Regarding artificial intelligence, see “Poker Bots Invade Online Gambling” (NY Times, March 13 2011). Also incredibly fun is an interactive feature called “Rock-Paper-Scissors: You vs. the Computer” (NY Times, March 4 2011).
Links to books on cake-cutting
Links to moving knife procedure
p69: John Nash shared the 1994 Nobel Prize (with John Harsanyi and Reinhard Selten) “for their pioneering analysis of equilibria in the theory of non-cooperative games.” His life was the topic of Sylvia Nasar’s 1998 book A Beautiful Mind, which in 2001 was made into an Academy-Award-winning film of the same name starring Russell Crowe. For a more true-to-life video, check out PBS’s A Beautiful Madness (buy it here, teacher’s guide here), which includes interviews with Nash.
Chapter 7: Pareto Efficiency (pages 79-88)
Summary in haiku form
Pareto efficiency
Is only one part.
Summary in one paragraph
It’s probably impossible for everyone to agree on the definition of a “good outcome”, but economists pay lots of attention to one part of “good”: Pareto efficiency, which occurs when an outcome is so good that it’s not possible to make one person better off without making someone else worse off (in other words, when there are no Pareto improvements over it). Pareto efficient outcomes may not be good—for example, it’s Pareto efficient to cut the cake so that one child gets the whole cake—but Pareto inefficient outcomes are in a meaningful sense bad: if it’s possible to make someone better off without making anyone worse off, why not do it? One way to promote Pareto efficiency is to provide opportunities to trade, e.g., with tradable fishing permits or tradable pollution permits. The Coase theorem says that people have an incentive to trade until they have exhausted all possible gains from trade, and if that happens then we have reached a Pareto efficient outcome!
Notes on specific pages
Links to Pareto
ITQs
Carbon cap-and-trade
Chapter 8: Simultaneous-Move Games (pages 89-102)
Summary in haiku form
The prisoners’ dilemma.
It’s a tragedy!
Summary in one paragraph
All games—most obviously games like rock-paper-scissors—can be described using a payoff matrix that lists the players’ strategies and the outcomes of the different strategy combinations. An important game is the prisoners’ dilemma, which is a two-player game in which players have dominant strategies that lead to a Pareto inefficient outcome. Generalizing the prisoners’ dilemma to more than two players produces the Tragedy of the Commons, a game that describes overfishing and overpollution and traffic congestion and many other problems. These situations are classic instances in which individual optimization does not lead to good outcomes for the group as a whole. There is, however, a glimmer of hope: competition between two sellers is a prisoners’ dilemma situation for the sellers, but it drivers sellers to provide consumers with good-quality products and low prices!
Notes on specific pages
Links to PD
Links to TOC games
Climate change
Links to Hardin
p99: An interesting article on fisheries (in this case shark fisheries) is “Soup Without Fins? Some Californians Simmer” (NY Times, March 5 2011).
Chapter 9: Auctions (pages 103-116)
Summary in haiku form
Auction equivalences
You’ll save time online.
Summary in one paragraph
Auctions are used in many important situations (and in less important situations like eBay) because they can help reveal how much something is worth, because they can help prevent collusion, and because they can help sell perishable items fast. There are many different kinds of auctions, but it turns out that there is a strategic equivalence between ascending auctions and second-price sealed-bid auctions: in both cases bidding your true value—your maximum willingess to pay—is a dominant strategy. There is also a strategic equivalences between descending auctions and first-price sealed-bid auctions—in both cases you want to shade your bid below your true value—and a deeper result called the Revenue Equivalence Theorem proves that in many situations all four types of auctions will yield the same expected revenue for the seller.
Notes on specific pages
Links to eBay auction page
William Vickrey shared the 1996 Nobel Prize (with James Mirrlees) “for their fundamental contributions to the economic theory of incentives under asymmetric information.”
Links to Aalsmeer Flower Auction
Chapter 10: From Some to Many (pages 117-126)
Summary in haiku form
Of grains of sand on the beach…
Buyers and sellers.
Summary in one paragraph
The strategic complications of game theory disappear when we move to a world of competitive markets in which buyers and sellers are small relative to the market as a whole. This means that buyers and sellers are all price-takers: individually they are too small to affect the market as a whole, so strategic behavior is pointless. The result is a straightforward analysis that applies to many kinds of markets and leads to an optimistic conclusion: competitive markets lead to Pareto efficient outcomes, which is an important part of good!
Notes on specific pages
Links to Tolstoy