Behavioral Game Theory

My holiday reading started with the book Behavioral Economics: A History by Floris Heukelom. The book provides a interesting take on how behavioral economics has grown from humble beginnings to the huge phenomenon that it now is. A nice review of the book has been written by Andreas Ortmann and so I will not delve too deeply into general comment here, other than to say I enjoyed reading the book.  But in terms of more specific comment, one theme running throughout the book is the distinction between behavioral economics and experimental economics. Heukelom makes clear that he thinks there is a very sharp distinction between these two fields. Personally I have always thought of them both as part of one big entangled blob. There are people who clearly prefer to label themselves a behavioral economist or an experimental economist but this seemed to me more a matter of personal preference than any grand design. So, what is the difference between behavioral and experimental economics

Prospect theory is most well known for its assumption that gains are treated differently to losses. Another crucial part of the theory, namely that probabilities are weighted, typically attracts much less attention. Recent evidence, however, is suggesting that probability weighting has a crucial role to play in many applied settings. So, what is probability weighting and why does it matter? The basic idea of probability weighting is that people tend to overestimate the likelihood of events that happen with small probability and underestimate the likelihood of events that happen with medium to large probability. In their famous paper on ' Advances in prospect theory ', Amos Tversky and Daniel Kahneman quantified this effect. They fitted experiment data to equation where  γ is a parameter to be estimated. In interpretation, p is the actual probability and  π (p)  the weighted probability. The figure below summarizes the kind of effect you get. Tversky and Kahneman found

Officially, Richard Thaler won the Nobel Prize in Economics because he 'has incorporated psychologically realistic assumptions into analyses of economic decision-making. By exploring the consequences of limited rationality, social preferences, and lack of self-control, he has shown how these human traits systematically affect individual decisions as well as market outcomes'.  An interesting thing about this quote is that nudge doesn't get a mention; indeed, it only just about scrapes it into the Academy's official  press release . (In the more detailed popular information document it doesn't appear until page 5 of 6.) This is in stark contrast to the popular press: the BBC leads with 'Nudge' economist wins Nobel Prize, the Telegraph leads with 'Nudge' guru wins the Nobel Prize, and so on. To read the papers you would think that Nudge is all there is to it. There is no doubt that Nudge has been a huge success and made Thaler famous (at least

In my last post I looked at dishonesty in the banking industry. Sticking with a similar theme, this time I will at dishonesty across different countries.        Let us start with a study by David Pascual-Ezama and a long list of co-authors on 'Context dependent cheating: Experimental evidence from 16 countries'. They asked 90 students in 16 different countries to perform a very simple task: toss a black and white coin and record the outcome. If the coin came up white the student obtained a red Lindt Lindor Truffle. If it came up black they got nothing. Crucially, the coin toss took place in private and so the student could report whatever outcome they wanted. If they wanted a chocolate then they simply had to report white. (The study contrasted three different methods of reporting - form put in a box, form given to the experimenter or verbally telling the experimenter - but I will skip those details here.)           The chart below summarizes the country wide outcomes by f

The film 'A Good Year' starts with a ruthless financial trader called Max, played by Russell Crowe, manipulating bond markets in order to out-maneuver his competitors and make a quick, big profit. But, by the end of the film Max has decided to pack it all in and live out a more fulfilling life in rural France. Could that happen? Can someone really transition from a ruthless, selfish trader to a compassionate, loving family man in the space of a few days?         A study by Alain Cohn, Ernst Fehr and Michel Marechal, publisehd in 2014 in Nature, suggests it might be possible. They used a standard coin tossing task to measure the dishonesty of 128 employees from a large, international bank. The task works as follows: A subject is asked to toss a coin 10 times and record whether the outcome was heads or tails. Depending on the outcome the subject can win $20 per toss. The crucial thing to know is that the subject records whether or not they won for each toss and there is no wa

Suppose you offer someone called Albert a gamble - if the toss of a coin comes up heads then you pay him £100 and if it comes up tails he pays you £100. The evidence suggests that most people will not take on that gamble. If Albert also turns down the gamble, what does that tell you about Albert's preferences?          One thing we can conclude is that Albert is risk averse. In particular, the gamble was fair because Albert's expected payoff was 0 and, by definition, if someone turns down a fair gamble then they are exhibiting risk aversion. It is hard to argue with a definition and so we can conclude that Albert is risk averse. The more interesting question is why he displays risk aversion?            The micro-economic textbook would tell us that it is because of diminishing marginal utility from money. A diagram helps explain the logic. Suppose that Albert has the utility function for money depicted below. In this specific case I have set the utility of £m as the square

As the run-up to the UK's snap general election continues, the Conservative party appear content to talk about one thing and one thing only - strong and stable leadership for Brexit negotiations. Throughout the campaign Theresa May has been particularly keen to claim that 'every vote for me strengthens my hand in the Brexit negotiations'. This claim seems to be going down well with voters. But does it make any sense?           In bargaining theory the disagreement point is of critical importance. In the Brexit negotiations we can think of the disagreement point as the outcome if no deal is done between the UK and the EU and so the UK simply leaves the EU in March 2019 and starts from scratch. Most experts seem to agree that no deal would be bad - very bad for the UK and bad for the EU. That means that a deal is essential. It also means that the UK starts from a bad negotiating position.          To put some analysis to this consider the figure below. This plots the pa

Tomorrow the government will trigger Article 50 and start the formal process of getting the UK out of the EU. So, how did we get in this mess in the first place? I think the Condorcet Paradox provides an interesting angle on the problem. In particular, I want to look at preferences for Remain versus Soft Brexit, i.e. leave the EU but still remain in the single market or other collaborations centered on the EU, and Hard Brexit, i.e. walk completely away from the EU.            The one thing we know for sure is that in the referendum last June around 52% of people voted Leave and 48% voted Remain. What does that tell us? In my recollection the referendum campaign primarily focused on the question of Soft Brexit versus Remain. No doubt some would disagree with that. But things like the customs union only started being talked about after the vote. Instead we heard a lot during the campaign about the Norway or Swiss model of Soft Brexit. True the Leave camp made promises like 'take b

In a paper , recently published in the International Journal of Game Theory , my wife and I analyze a game called a forced contribution threshold public good game. A nice way to illustrate the game is to look at the difficulties of getting rid of an incompetent manager.          So, consider a department with n workers who all want to get rid of the manager. If they don't get rid of him then there payoff will be L. If they do get rid of him then there payoff will be H > L. But, how to get rid of him? He will only be removed if at least t or more of the workers complain to senior management. For instance, if a majority of staff need to complain then t = n/2.         If t or more complain then the manager is removed and everyone is happy. The crucial thing, though, is what happens if less than t complain. In this case the manager will remain and any workers that did complain will face recrimination. To be specific suppose that the cost of recrimination is C. Then potential payo

Attitudes to risk are a key ingredient in most economic decision making. It is vital, therefore, that we have some understanding of the distribution of risk preferences in the population. And ideally we need a simple way of eliciting risk preferences that can be used in the lab or field. Charles Holt and Susan Laury set out one way of doing in this in their 2002 paper ' Risk aversion and incentive effects '. While plenty of other ways of measuring risk aversion have been devised over the years I think it is safe to say that the Holt and Laury approach is the most commonly used (as the near 4000 citations to their paper testifies).           The basic approach taken by Holt and Laury is to offer an individual 10 choices like those in the table below. For each of the 10 choices the individual has to go for option A or option B. Most people go for option A in choice 1. And everyone should go for option B in choice 10. At some point, therefore, we expect the individual to switch

In a standard economic experiment the anonymity of subjects is paramount. This is presumably because of a fear that subjects might behave differently if they knew others were 'watching them' in some sense. In the real world, however, our actions obviously can be observed much of the time. So, it would seem important to occasionally step out of the purified environment of the standard lab experiment and see what happens when we throw anonymity in the bin.         A couple of experiments have looked at behavior in public good games without anonymity. Let me start with the 2004 study of Mari Rege and Kjetil Telle entitled ' The impact of social approval and framing on cooperation in public good games '. As is standard, subjects had to split money between a private account and group account, where contributing to the group account is good for the group. The novelty is in how this was done.       Each subject was given some money and two envelopes, a 'group envelope&

The linear public good game is, as I have mentioned before on this blog, the workhorse of experiments on cooperation. In the basic version of the game there is a group of, say, 4 people. Each person is given an endowment of, say, $10 and asked how much they want to contribute to a public good. Any money a person does not contribute is theirs to keep. Any money that is contributed is multiplied by some factor, say 2, and shared equally amongst group members.          Note that for every $1 a person does not contribute they get a return of $1. But, for every $1 they do contribute they get a return of $0.50 (because the $1 is converted to $2 and then shared equally amongst the 4 group members). It follows that a person maximizes their individual payoff by contributing 0 to the public good. Contributing to the public good does, however, increase total payoffs in the group because each $1 contributed is converted to $2. For example, if everyone keeps their $10 then they each get $10.

Few, if any, have contributed as much to game theory as Thomas Schelling. Or, to perhaps be more accurate, surely nobody has more powerfully shown the value of applying game theory to understand the world around us. As we reflect on Schelling's contribution to knowledge, following his death in December , I think it is particularly useful to look back on one of his less touted but fundamental observations - conflict is rarely a zero-sum game.           To put Schelling's insight in perspective it is important to recognise that the early development of game theory was hugely influenced by zero-sum games. These are games in which total payoffs always sum to zero meaning that one player's gain must be another player's loss. Sporting and parlour games, like chess and bridge, are naturally modelled as zero-sum because they are about winning and losing. Zero-sum games also have some nice theoretical properties which mean they are particularly amenable to analysis. For this