Game theory applications
Game theory illuminates everything from public goods and auctions to climate agreements and pricing algorithms.
Public goods games
In experiments, players can contribute to a shared pot that is multiplied and split equally. Everyone gains most if all contribute, but each individual does better by contributing nothing and free-riding. Real people contribute about half at first, then contributions fall unless punishment of free-riders is allowed.
The ultimatum game
One player proposes how to split a sum of money; the other accepts (both get the split) or rejects (both get nothing). Narrow self-interest predicts tiny offers accepted. In practice, offers are often 40-50%, and offers below about 20% are frequently rejected, showing that fairness matters.
Auctions
In an English auction, prices rise until one bidder remains. In a sealed-bid second-price (Vickrey) auction, the highest bidder wins but pays the second-highest bid, which makes bidding your true value the best strategy. Online advertising slots and government licences are often sold through carefully designed auctions.
The winner's curse
When an item's value is uncertain and common to all bidders, such as oil drilling rights, the winner is the bidder with the most optimistic estimate and may overpay. Experienced bidders shade their bids down to avoid this winner's curse.
Climate agreements
Reducing emissions is a global public good: each country bears its own costs but shares the benefits. This creates a prisoners' dilemma, where each is tempted to free-ride. International agreements like the Paris Agreement rely on pledges, transparency, and reputation, since there is no global enforcer.
Bargaining
In bargaining, each side's outside option (what it gets if talks fail) shapes the outcome. Improving your outside option, like having another job offer, strengthens your position. Patience also matters: the side less pressed for time can often hold out for a better deal.
Algorithms and tacit collusion
Online sellers increasingly use pricing algorithms that react to rivals' prices instantly. Research suggests learning algorithms can sometimes settle at high prices without explicit agreement, like a repeated game with fast punishment. Competition authorities are studying how to respond.
Worked example
In a public goods game with 4 players, each with 10 tokens, contributions are doubled and split equally. If all contribute 10, the pot is 80 and each gets 20. If one player contributes 0 while others contribute 10, the pot is 60, and each gets 15: the free-rider ends with 25, the contributors with 15. This temptation drives contributions down.
Key takeaways
Public goods games show free-riding, which punishment can reduce. Ultimatum games show people care about fairness. Second-price auctions encourage truthful bidding; common-value auctions risk the winner's curse. Climate change is a global prisoners' dilemma. Outside options and patience shape bargaining. Pricing algorithms raise new questions about tacit collusion.
Flashcard
Contribute to shared pot
Check your understanding
In a second-price sealed-bid auction, what is a bidder's best strategy?