Life is not a game, but there sure are a lot of games in it.

Game Theory

Game theory is a branch of mathematics that studies the behavior of individuals in situations where their decisions impact one another. It has applications in parlor games as well as broader contexts.

Nash Equilibrium

Do you remember the movie “A Beautiful Mind”? It’s based on a true story about John Nash, a mathematician who developed the concept of Nash equilibrium. In game theory, Nash equilibrium is a situation where no player can benefit by changing their strategy, assuming the other players’ strategies remain unchanged. It’s a fundamental concept in understanding strategic interactions between individuals or entities.

Prisoner’s Dilemma

The Nash Equilibrium can be used to find the best strategy for The Prisoner’s Dilemma game, a classic thought experiment in game theory. It’s a scenario where two individuals are arrested and held in separate cells, unable to communicate with each other. Each prisoner is given the option to either cooperate with the other by remaining silent or defect by confessing to the crime. Even though cooperating would yield the lowest total prison time, each individual would receive less prison time by defecting. The equilibrium for the game is for both players to defect.

Bidding Behavior in Real-Time Auctions

We can also use game theory to explain behavior in different types of auctions. In real-time auctions, bidders see only other bidders’ actions, not their motives. This leads bidders to bid irrationally higher than the item’s expected value, based solely on others’ observed behavior, a phenomenon known as the “Winner’s curse”.

Vickrey Auctions

Vickrey auctions, also known as second-price sealed-bid auctions, are a type of non-real-time auction where the highest bidder wins but pays the second-highest bid. This mechanism incentivizes bidders to submit their true valuation of the item, since they know they’ll pay only the second-highest bid if they win.

Change The Game

Game theory can be used to recognize the most likely decisions that each participant will make in different situations. By using a Vickrey auction instead of a standard real-time auction, you’re changing the auction game in a sense to incentivize submitting actual valuation for the items. In climate policy, game theory can be used to design policies that encourage environmentally friendly behavior, and in politics, it can be used to design voting systems that promote fair representation. The systems we put in place have a significant impact on our day-to-day lives, and game theory explains why.