A new casino offers the following game: you toss a coin until it comes up heads. If the first heads...

Continue reading...# game theory

## Envy-free Cake Division

Say you and a friend wish to share a cake. What is a “fair” way to split it? Probably you...

Continue reading...## Arrow’s Impossibility Theorem

Elections are democracy in action. People go to polls and express their preferences, and somehow we must aggregate the preferences...

Continue reading...## Vickrey Auction

Suppose you are hosting a silent auction to sell your antique car. The rules are: (1) prospective buyers bid for...

Continue reading...## Deal or No Deal

On the TV show “Deal or No Deal”, a contestant is faced with a number of briefcases (26 in the...

Continue reading...## Two Envelopes Paradox

I have two envelopes, and inside each I have put some money. In fact, one envelope contains twice as much...

Continue reading...## Social Choice and the Condorcet Paradox

How should one select the winner of an election? If there are only two candidates, the answer is clear— choose the...

Continue reading...## Rental Harmony

You and your college friends decide to rent a house together, and the N of you have found a house...

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