Cake cutting I know that you knowThat I know game theory.Think strategically!
Fair division • Covers many situation in life: divorce settlements, negotiations, allocation of carbon permits, etc. • So how do you fairly divide cake? • One option: Moving knife procedure (also applies to football overtime!) • Another approach: I cut, you choose.
Fair division • But is it better to cut or to choose? • If you know a lot about the other person, you should cut. • But if you don’t, you should probably choose. • Information matters: Lots of economic issues involve situations in which parties don’t have the same information and can’t be trusted to share. (Screening, signaling, etc.)
Two game theory questions • 1) Can we predict the outcome of a game? • 2) Is that outcome good? • But what does good mean? • Recall the Big Question… • Under what circumstances does individual optimization lead to outcomes that are good for the group as a whole?
“Good” for cake-cutting (according to Brams and Taylor) • Proportional: Each kid gets at least 1/n of the cake (in his or her estimation). • Envy-free: Nobody covets another’s piece. • Equitable: My value for my share is about the same as your value for your share. • Pareto efficient: It’s not possible to reallocate the cake in a way that makes someone better off without making someone else worse off.
“Good” for cake-cutting (according to Brams and Taylor) • Of these and other components of good, economists often focus on Pareto efficiency. • Pareto efficient: It’s not possible to reallocate the cake in a way that makes someone better off without making someone else worse off. • It’s not that the other ones aren’t important! • It’s just that economists have little insight into the others (like everyone, we have personal opinions, but not professional opinions).