What is... | October 31, 2012

What is game theory?

Game theory is about decision making but not, as the term may suggest, by throwing dice or picking a random card.

Game theory relates to situations when decisions depend on the actions of others. It is also useful for understanding the way individuals and families choose to spend and save.  Although called game theory, it does not involve the type of games that typically spring to mind. Here, a "game" is a mathematical representation of a real-world situation. A person (or "player") in the situation tries to pick a strategy that will get the best result for himself or herself.

But when planning this strategy, the player must consider what other players will do. Because of this, beliefs about moves the player’s opponent will likely make influence the player’s choices. Further, the player must also consider how opponents may adjust their strategies based on what they think the first player will do.

The prisoner’s dilemma
The example of the "prisoner’s dilemma” is often given as an illustration of game theory. In it, two thieves (called Albert and Barbara) burgle a jewellery store and are brought in to the police station and placed in separate cells for questioning. The police have some evidence to charge the pair with previous petty crime but need a confession to charge them for the jewellery heist.

The jail sentences handed down to each will depend on the outcome of the questioning. If neither Albert nor Barbara confesses to the heist, they will each get one year in jail for their previous minor misdeeds. If both confess, they will each be given five years in jail for the major jewellery theft. If one confesses that the pair committed the crime, but the other doesn’t, the confessor will be granted amnesty but the other will face eight years in jail: five for the crime plus three extra for obstructing justice.

Albert considers what Barbara will do: if she keeps quiet, he can confess and avoid prison. But if she confesses, he should confess too, to avoid getting stuck with eight years in jail. Barbara goes through the same thought process. So they each confess and are locked up for five years. But both could have been much better off (if we leave truth and ethics to one side) if they had committed to keep quiet and received a sentence of just one year each.

The prisoner’s dilemma example shows that when individuals follow their dominant strategy, in this case confessing, it doesn’t always lead to the best outcome.

Playing at home
Game theory is not confined to prisons or economics classrooms. In the home, decisions about the division of housework, choice of entertainment and how to spend and invest can all be thought of as “games”. Family members are players and managing the household budget is the game. Many household decisions require cooperation and communication. With this comes the possibility for negotiation, bargaining and – at times – threats.

Couples often vow to share what is theirs. What’s perhaps surprising then is that research suggests having a higher share of pre-marital assets may mean more bargaining power for years to come. A separate study abstract shows that the type of spending mattered. If the increase to the household pool of funds came from a man, the study found increased spending on transport. An increase to female income was associated with increased spending on children’s clothing.

Origins of game theory
Developed by mathematician John von Neumann and economist Oskar Morgenstern, game theory was introduced to the wider public in their 1944 book Theory of Games and Economic Behaviour.  Shortly after, mathematician John Nash built on the theory extensively. Nash’s contribution to the field was great: a Nash Equilibrium describes a set of strategies where no one would be better off by changing his or her position. Nash’s life was portrayed in the 2001 Oscar-winning movie A Beautiful Mind

Many game theory models assume everyone is rational and infinitely intelligent. However, behavioural economist Colin Camerer’s Behavioral Game Theory recognises that while this assumption makes it easier to model interactions mathematically, real life often does not fit this ideal. In October 2012, Al Roth and Lloyd Shapley  were awarded the Nobel Prize in Economics for their matching algorithm work in game theory. The Economist write up is here.

Game theory has been applied in areas as diverse as business, evolutionary biology, voting, auctions, and by people attempting to address environmental degradation. Understanding the fundamentals may even change the way you make everyday decisions.

Nathalie Spencer

Behavioural scientist at ING