Behavioral Game Theory

Following the tragic death of John Nash in May I thought it would be good to explain some of his main contributions to game theory. Where better to start than the Nash bargaining solution. This is surely one of the most beautiful results in game theory and was completely unprecedented. All the more remarkable that Nash came up with the idea at the start of his graduate studies!          The Nash solution is a 'solution' to a two-person bargaining problem . To illustrate, suppose we have Adam and Beth bargaining over how to split some surplus. If they fail to reach agreement they get payoffs €a and €b respectively. The pair (a, b) is called the disagreement point . If they agree then they can achieve any pair of payoffs within some set F of feasible payoff points . I'll give some examples later. For the problem to be interesting we need there to be some point (A, B) in F such that A > a and B > b. In other words Adam and Beth should be able to gain from agreeing.

A threshold (or step-level) public good is a good that would benefit members of a group but can only be provided if there are sufficient contributions to cover the cost of the good. A local community raising funds for a new community centre is one example. Flatmates trying to get together enough money to buy a new TV is another.          There are some fundamental strategic parameters in any threshold public good game: number of group members (n), the threshold amount of money needed (T), the value of the good if provided (V), and the endowment of money that group members have available to contribute (E). Early experimental studies looked at the role of n, T and V but had little to say about E. This raised the intriguing question of whether E matters. Is it 'easier' to provide a threshold public good if group members are relatively rich or poor?          To find out we needed to run some experiments. In two recently published papers, with Federica Alberti and Anna Stepanov

The minimum effort (or weakest link) game is fascinating - simple, yet capable of yielding profound insight. The basic idea is that there is a group of people who individually have to decide how much effort to put into a group task. Effort is costly for the individual but beneficial for the group. Crucially, group output is determined by the minimum effort that any one group member puts in to the task. A classic example is an airline flight: If any person involved in the flight - pilot, fuel attendant, mechanic, luggage handler etc. - gets delayed, then the flight is delayed, no matter how hard others try.            In experiments the minimum effort game is usually reduced to the matrix in Figure 1. Here subjects are asked to choose a number between 1 and 7 with the interpretation that a higher number is higher effort. Someone choosing effort 1 is guaranteed a payoff of 70. Someone who chooses 2 gets 80 if everyone else chooses 2 or more, but only gets 60 if someone in the group