Behavioral Game Theory

Nash equilibrium is the main game theoretic concept used in economics. Evolutionary stable strategy , or ESS, is the main game theoretic concept using in biology. The issue I want to look at here is the relationship between the two. This is an issue that appears to cause much confusion amongst students (and some academics).          The main thing that I would suggest needs to be recognised is that Nash equilibrium and ESS are fundamentally different. They were conceived completely independently with very contrasting objectives in mind. The Nash equilibrium was developed by John Nash in the 1940/50s as an equilibrium concept for non-cooperative games . And note that the genius of Nash was not so much to develop the Nash equilibrium but to recognise the importance of non-cooperative games. The ESS, by contrast, was developed by John Maynard Smith and George Price in the 1970s as an equilibrium concept for evolutionary games ...

The UK will soon have to decide whether to maintain its Trident nuclear weapon programme. Clearly, the nuclear capability will be maintained. This has not, though, stopped a fairly vociferous debate on the issue. The basic argument in favour of nuclear weapons, and one that we have heard time and time again in the debate, is that nuclear weapons are to deter attack and not be used. This is encapsulated in the concept of mutual assured destruction or MAD. But, just how solid is the MAD argument?            A standard logic goes something like this: If the UK has nuclear weapons then Russia would not attack the UK because the UK would have the capability to destroy Russia. Thomas Schelling, in the Strategy of Conflict , pointed out that there is a basic flaw in this logic. To see why let us set out a hypothetical game tree, see below. Russia moves first by deciding whether to attack the UK. Then the UK decides wheth...

The UK's National Health Service is nudging ever closer to collapse. This fact is blatantly obvious to many. The political will to do anything about it is, however, sadly lacking. It is particularly disappointing that the Conservatives, in a position of strength, seem more interested in tackling the immigration 'problem' that isn't a problem, than getting to grips with the huge and pressing problem that is the health of the nation.          As I have discussed before in this blog the NHS principle of free health care is simply unworkable in the modern world. That inevitably means some people are going to have to pay for treatment. This is already happening with the slow growth of the private system. Things would be much, much better, however, if the NHS would embrace the willingness of many to pay for better treatment. The flu vaccine provides a small but useful illustration of this issue.        ...

Garrett Hardin's 1968  Science article on the Tragedy of the Commons  can easily lay claim to be one of the most cited 'game theory' articles of all time. According to Google Scholar it has a mighty impressive 27,362 citations, and counting. But, as with all well cited articles, it is not entirely clear how many people have actually read the paper. As someone who has neither cited nor read the paper I thought it was about time I educated myself. And, I was surprised by what I found.         Let us start with the modern, textbook conception of the tragedy of the commons. The focus is on common resource goods. These goods are characterised by being non-excludable and (to some extent) rivalrous. Hardin, himself, gave the example of pastureland that can be used for cattle. The pastureland is non-excludable - everyone is free to graze their cattle - and rivalrous - the more cattle that graze the less grass av...

A government commissioned review is currently looking into the way UK charities raise money. Reports this week suggest it will be tough. And it should be! The review follows the high profile case of 92 year old Olive Cooke who took her own life having become exhausted by requests for money from charities. Such requests for money are all too familiar to many. In our household I would say that we average a charity letter per day, a phone call per week, and a fundraiser at the door every month. The Prime Minister was stating the obvious when he said that the behaviour of some charities was 'frankly unacceptable'.           Against this public backlash the charity sector has stood firm. Time and again I have heard spokespeople arguing that charities only do good . The argument essentially seems to be that the funds they raise are spent on worthy causes and so the ends justify the means. The ch...

The labour party is seemingly about to appoint a leader, Jeremy Corbyn, who almost everyone considers unelectable as prime minister. The apparent 'problem' with Mr Corbyn is that he is too left wing. But, according to simple political choice theory this should be an asset rather than a problem. So, where is the catch?       Let us look first at the basic theory. To win an election a candidate (or party) needs majority support. Now, we all know that wealth is highly asymmetrically distributed - the top 1% own most of our wealth, the top 10% own even more, and so on. The flip side of this asymmetry is that the poorest 50% are a relatively homogeneous bunch that should, in principle, easily be able to gang up on the rich. To be a more specific, they could vote for redistribution of wealth from the rich to the poor and the rich would be powerless to do anything about it.        In some countries the theory seems to work pretty well. Both Vladimir Puti...

The ultimatum game is one of the most well known and well studied games. Yet there still seems much confusion and misunderstanding over the basic theory behind the game. This is worrying because it means one of the key lessons we can learn from the ultimatum game goes unrecognised.        In the ultimatum game a proposer and responder need to decide how to split, say, $10. The proposer moves first by making a take-it-or-leave-it-offer. The responder then either accepts the offer or rejects it. If he accepts it the deal is done. If he rejects both get nothing. For example, the proposer could offer $3. If the offer is accepted the proposer gets $7 and the receiver $3. If it is rejected both get $0.        What is going to happen? In the experimental lab the almost universal outcome is that the proposer offers $5 and this is accepted. We also know, although the evidence for this is less unequivocal, that offers of less than $5 can be rejected. ...

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...

The prisoners dilemma is familiar to any student of game theory. One of its appealing properties is its seeming simplicity - there is an 'obvious' way to play the game. What is obvious in theory does not, however, always show up in reality. So, does that mean people are dumb or the theory is dumb? The conventional approach seems to be to say that people are dumb. But, I think its the theory that needs a rethink. Here is one reason why:           The table below gives an example of the prisoners dilemma. Alice and Barney are two work colleagues who have to produce a project together. If they cooperate they will finish the project in one hour. If they do not cooperate it will take them 10 hours. If Barney cooperates and Alice defects then Alice gets away with doing nothing while Barney spends 15 hours. Vice versa if Alice cooperates and Barney defects.    So, what should Alice do? If Barney cooperates then...

Labour's pitch for the upcoming UK general election has been simple - let's talk about the National Health Service. Particularly headline grabbing was the '100 days until the election, 100 days to save the NHS as we know it'  campaign. To focus on the NHS may seem like a simple winning strategy for Labour given the rollercoaster of 'NHS in crisis' stories hitting the news in recent months. But, I think labour strategists may have badly misjudged this one. After years of dodging the issue the British public may finally waking up to the idea that we can only preserve the 'NHS as we know it' with some pretty radical change.        The NHS is a publicly provided health care system that is centrally funded and free at the point of delivery. Labour is broadly committed to maintaining that status quo. They reject private involvement in providing health care. And they ...

The wait is final over to discover who will broadcasting Premier League football from 2016 onwards. There is no surprise this time in the successful bidders - Sky and BT. But there is surprise at the price they have paid - a huge £5.1 billion. That equates to over £10 million per game. This figure is 70% up on last time and above all analyst forecasts. Surely it is time to talk of the winners curse?         The winners curse is the idea that a winner of an auction may well end up losing money. The intuition is simple enough in that the winner of an auction is likely to be the most optimistic as to how much the prize is worth; that optimism may be misplaced. In the past, TV rights have provided some textbook examples of the winners curse. So, do we have another example?         One reason to doubt Sky and BT have overbid is the fact they know p...

The basic idea behind revealed preference is incredibly simple: we try to infer something useful about a person's preferences by observing the choices they make. The topic, however, confuses many a student and academic alike, particularly when we get on to WARP, SARP and GARP. So, let us see if we can make some sense of it all.           In trying to explain revealed preference I want to draw on a  study  by James Andreoni and John Miller published in Econometrica . They look at people's willingness to share money with another person. Specifically subjects were given questions like:  Q1. Divide 60 tokens: Hold _____ at $1 each and Pass _____ at $1 each.  In this case there were 60 tokens to split and each token was worth $1. So, for example, if they held 40 tokens and passed 20 then they would get $40 and the other person $20. Consider another question: Q2. D...