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...

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...

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 ...

Think of how a car park typically works: you pick up a ticket when you drive in and then pay in rough proportion to  how long you park your car. Now think of how a gym typically works: you pay a fee when you go in and can then stay as long as you like.          There is no reason, in principle, why the car park could not charge a lump sum fee and the gym charge for how long you stay there. But they typically don't. And the gym may well even offer a membership package that allows year long unlimited use. How can we make sense of all this?          We need to think in terms of two part tariffs. With a two part tariff the customer is charged a lump sum fee for access to the good and then charged a user fee for each unit of the good consumed. For example, on your mobile phone you may pay a monthly subscription fee and then a fixed fee per text message or call. The car park...

As the dust finally settles on the 2015 UK general election it is interesting to reflect on the big (game theory) question - why did over 30 million people turn up to vote?        A simple model of voting would suggest that hardly anyone should vote. Basically there are non-negligible costs to voting in terms of time. But, the expected benefit of voting seems very, very small. Indeed, since universal suffrage in 1928 there is not a single constituency election in the UK that has been won by one vote. In other words everyone who has voted in a UK general election for the last 70 years or so could have stayed at home and the outcome would have been exactly the same.         With such dismal prospects of making a difference why would anyone vote? Yet people do vote! This is the paradox of voting . And I saw the paradox in full swing at 7am on polling day - people were already turning up in nu...

The conventional way to charge consumers for something is pretty simple - they pay for every unit they buy. But, there are alternatives. One is to charge an up-front fee and then refund customers for every unit they purchase below some threshold. Google's new Project Fi has an element of this built into it, as they explain - 'Let's say you go with 3GB for $30 and only use 1.4GB one month. You'll get $16 back, so you only pay for what you use'.           It is simple to design a pay and refund pricing policy that are theoretically equivalent. For instance, suppose you regularly buy movies from an online website. Also, suppose that you would never buy more than 20 movies a month. Then the following pricing policies are equivalent: Pay: You pay £5 for every movie you download. Refund: You pay a monthly fee of £100 and receive £5 back, per movie, if you download less than 20 movies.  For example, if you b...

In a social dilemma what is good for the group is not necessarily good for the individual. For instance, if Fred donates time and money to charity that costs Fred but benefits society. Similarly, if Fred cycles to work so as to not pollute that costs Fred but benefits society. We know in the lab that many people (typically around 50%) are willing to put the interests of the group ahead of their own. This gives hope when it comes to things like combating climate change. There is, however, an intriguing and unexplained framing effect regarding willingness to cooperate.          Any social dilemma can be framed in two alternative ways. One can frame things in terms of Fred making a contribution to the group or in terms of Fred making a withdrawal from the group . Some things, like giving to charity, are more naturally thought of in terms of contribution. And others, like cycling to work, are more naturally thought of in t...