Friday, 21 December 2012

Sports commentators and zero sum games

England have beaten India in India at cricket! Which for those of you who know nothing about cricket is about as good as it gets. But, this post was not prompted by Englands success. Instead it was prompted by a discussion I heard on the TMS commentary of the penultimate day of the series.
   A bit of background info first: Cricket, like most sports, relies on an umpire to make decisions – and they sometimes get them wrong. Technology has been progressively introduced over the last decade in order to reduce errors. The latest development is a Decision Review System. India, however, said that they did not want to use the system against England. And the International Cricket Council Regulations say that it can only be used if both sides agree. The commentators were discussing India’s decision not to use the system after England captain Alastair Cook was wrongly given out for the second time in the game. If the Decision Review System had been in use both decisions could have been corrected. On the basis of this the commentators were questioning why a team would not use the system. They basically said that it’s surely to the advantage of both teams to use it.
   This made me chuckle. It made me chuckle because cricket is a zero-sum-game, and in a zero-sum-game there cannot be anything that is advantageous to both sides. So, the claim is perverse (a Colemanballs). Let me explain: A zero-sum-game is one where payoffs add to zero meaning one team can only gain at another expense. Sport contests are effectively zero-sum-games because winning and losing is what it is all about – and only one team can win. You might want to argue at this point that winning fairly, in an exciting contest is preferred to winning by bending the rules in a dull contest, etc. That’s true, and it would mean that sports contests are not strictly zero-sum-games. This, however, is surely a very minor effect. Sport is about winners and losers and so we shall not be far wrong in modelling sports contests as zero-sum.
   In a zero-sum-game, given that one team’s gain is another’s loss, it is simple impossible to do something that benefits both teams. So, the commentators on test match special were wrong to suggest that the Decision review System could help both teams. It’s not uncommon, however, to hear similar sentiments. For example, we hear that the referral system in tennis has helped all players. We hear that putting the roof on to stop the weather effecting a football, rugby, or tennis match will help both teams. This suggests that sports commentators have a slight bias in understanding zero-sum-games.
   Interestingly, however, the bias has its limits. Sometimes commentators are very good at recognising the zero-sum nature of contests. For example, we hear that windy weather will favour the less talented tennis player. Or we hear that rain and mud will benefit the less talented rugby team. These comments are spot on – bad weather has to benefit one player or team, and by making the contest more of a lottery it will help close the gap between the less and more talented.
   So, what’s going on? Things like the review system, referral systems, and putting a roof on are under our control. The weather is out of our control. My conjecture, based entirely on anecdotal evidence, is that people are good at seeing the essential zero-sum nature of things when it comes to events out of our control, but are less good when it comes to things under our control. Why? Having a review system, or putting a roof on the stadium looks like progress – and progress must be good - so, we are biased to think it must help both teams. In truth, progress will almost always help the most talented to the disadvantage of the least talented, because it takes elements of luck and chance out of the equation. Which is bad news for those who favour the underdog.         

Sunday, 16 December 2012

Smoking bans and adverse selection

We’ve just got back from a couple of days in France. It was a good trip, but one thing is clear - smoking is a problem in France. I have nothing against people smoking if that’s what they choose to do. What I do have an issue with, is myself and my family having to ‘share’ in their smoking. And for a large part of our trip we had no choice but to share. In public spaces - train platforms, Christmas market, cafes etc. - you could argue it is not so disturbing to be constantly engulfed in cigarette smoke. But, when you cannot escape the smoke in your hotel and hotel bedroom then it starts to get a bit annoying.
    Smoking is, of course, banned in public places in France. And, there are lots of signs to remind people of this fact – the hotel was full of no smoking signs. Its just that the French appear to complete ignore the law. Indeed, during our visit a report was published by government auditors (Cours de Comptes) highlighting the seriousness of the problem – 1 in 3 French adults smoke, tobacco is the most common cause of avoidable death, and enforcement of the legislation is very poor. The report was headline news, but will anything change?
    Well, my purpose here is not to question how smoking can be reduced. Instead I want to talk about the danger of legislation that is not enforced. In the U.K. the ban on smoking in public places is enforced relatively well. If a person smokes in a hotel room then there is a significant probability of punishment. I recently heard, for instance, of someone staying in a hotel where the fire alarm went off in the middle of the night because another guest was smoking – the culprit was fined £100 and thrown out of the hotel. Such threats appear to work – smoking in British hotels does not seem a major problem. An enforced ban on smoking suits me, because I don’t have to put up with cigarette smoke. It is probably not so great for smokers. But, as with any negative externality, its impossible to find a solution that pleases everyone. Current legislation favours non-smokers and, as such, protects non-smokers relatively well.
    What’s happening in France is not about favouring one side over another – its a lot worse than that. To see why, think back to the days before any ban on smoking. Then firms had an incentive to offer a service for both smokers and non-smokers. Hotels, for example, had parts of the hotel with rooms for smokers and parts for non-smokers. This also suited me fine because I didn’t have to put up with a room smelling of cigarette smoke. It can also benefit smokers if smoking rooms having slightly lower demand. The only people that lose out are non-smoking employees that need to clean the rooms of smokers.
    Once a ban on smoking is imposed firms cannot discriminate between smokers and non-smokers. That clearly does nothing to help smokers. The main point, however, is that when the ban is not enforced it harms non-smokers: non-smokers have to put up with cigarette smoke because hotels no longer have the power to distinguish smokers from non-smokers. This can even lead to adverse-selection – non-smokers getting so annoyed that they spend less time in hotels. And employees are clearly no better off either if smokers carry on smoking as before. A non enforced ban on smoking, therefore, helps no one and positively harms non-smokers! 
    That’s not very clever. But, there is nothing special about smoking bans - any law that is not enforced has the potential to harm the very people it was designed to protect. And that clearly does nothing to motivate people to change their ways. It is, therefore, no surprise that smoking has increased in France since the smoking ban was put in place over five years ago. Until France starts enforcing the ban expect the proportion of smokers to increase further, not decrease!

Sunday, 9 December 2012

Starbucks and fairness

Starbucks has been hitting the headlines for all the wrong reasons recently. First up was the news that the company has paid corporation tax only once in 15 years of operating in the U.K. This has seemingly been achieved by making royalty payments, and the like, to parts of the business in lower tax jurisdictions. Customers, taxpayers, and the tabloid media were suitably annoyed. Starbucks’ response was to say that it would ‘voluntarily’ pay £20 million in tax over the next two years. The thought of Starbucks ‘volunteering’ to pay tax seems to have aggravated rather than calmed the situation! On Saturday, tax avoidance campaigners protested outside a number of stores forcing some to temporarily close.
    Starbucks is certainly not alone in avoiding tax - Amazon and Google also usually get a mention. And they are certainly not the first company to ‘annoy’ customers on fairness grounds. For example, an accusation even more damaging than that of tax avoidance is one of using forced labour. The latest accusations came in June when a report by Anti-slavery International claimed that many U.K. high street retailers such as Tesco and Marks and Spencer were selling clothes made by girls working under slave conditions in India. Customers didn’t like this news much either. More generally, customers seem to rebel against any company ‘not playing fair’.
    Making sense of this is difficult if you rely on the standard economic textbook. Fairness is not supposed to matter. Seemingly it does. So, how can we put fairness into the mix?  Let’s start with a diagram that should be familiar to anyone who has done a bit of microeconomics.
    Suppose that the demand for Starbucks coffee is given by curve D. The textbook story is then as follows: We derive Starbucks marginal revenue curve (MR) and their marginal cost curve (MC). Starbucks maximizes profit by finding the point where marginal revenue equals marginal cost MR = MC. So, they should charge £4.00 for a cup of coffee. The last cup of coffee they make costs them £0.75 and so they make £3.15 profit on this. Overall, their average costs (AC) are £1.00 and so they make a profit of £3.00 on every cup of coffee sold.

Let’s take a step back at this point, and revaluate. We know the last customer is willing to pay up to £4.00 for a cup of coffee. We also know Starbucks makes a profit if it charges more than £1.00 for a cup of coffee. So, any price between £1.00 and £4.00 benefits both the customer and Starbucks. This leads to what Game theorists call a bargaining problem. The important question, is what price the customer and Starbucks shall ‘agree’ on? The textbook answer to the question is simple: Starbucks can ask for £4.00 and the customer will pay it. Reality may be somewhat different.
    In particular, research on the ultimatum game suggests that customers are unlikely to be willing to pay £4.00. In the ultimatum game a ‘proposer’ makes an offer of how to split, say, £3.00. The ‘receiver’ can then either accept the offer or reject. If he rejects the offer no deal is done. In the Starbucks example there is a £3.00 surplus (£4.00 – 1.00) to be bargained over. Starbucks sets the price for a cup of coffee, which is an offer of how to split the surplus, and the customer can either accept the offer by buying the coffee, or reject and not buy the coffee.
    Many people in the ultimatum game reject ‘unfair’ offers. Someone, for instance, offered 10 pence out of £3.00 may reject the offer. Similarly, someone charged £3.90 for a cup of coffee may not buy the coffee. Note that this does not contradict the fact that the customer was willing to pay up to £4.00 for a cup of coffee: he is willing to pay £4.00 if the deal is fair, e.g. if Starbucks costs are £3.90; but, this deal does not look fair and so is rejected. 
    This point was nicely illustrated in a paper by Richard Thaler in Management Science *. In one well known example people were asked to imagine they are lying on the beach on a hot day. A friend offers to get a beer and asks you how much you are willing to pay. Some were told the only place to buy a beer is a fancy resort hotel. Others were told it’s at a small run-down grocery store. Thaler found that survey respondents were willing to pay on average $2.65 to buy a beer from a ‘fancy resort hotel’, but only $1.50 from ‘a small, run-down grocery store’.  The basic willingness to buy beer is surely the same in both cases. People just don’t want to be ripped off by the run-down grocery store. 
    The key point here is that the transaction between the customer and Starbucks becomes a bargaining problem where fairness is likely to matter. Thaler suggested that we capture this by distinguishing acquisition and transaction utility. Acquisition utility captures the basic willingness to pay - £4.00 in the Starbucks example. Transaction utility captures the pleasure or otherwise of buying the good, and this is where fairness matters. If the customer feels he is being ripped off being charged £3.90 for a coffee he may decide to do without coffee. 
    Starbucks, and any other firm, therefore, has to strike a compromise between charging a high price and not annoying the customer too much. That’s where tax avoidance comes in. Suppose, Starbucks charge £3.50 for a cup of coffee and the customer is happy with that deal. He then learns that Starbucks is paying no corporation tax. Suddenly, £3.50 may not seem like such a ‘fair’ bargain; the customer may realise, for instance, that Starbucks costs are not as high as he thought they were. This sense of unfairness lowers his transaction utility from buying a coffee at Starbucks. The customer is no longer willing to pay £3.50. 
    Starbucks has two choices at this point: lower prices, or make £3.50 seem fair again. I would be surprised if Starbucks lower prices. So, they need to make £3.50 seem fair. The offer to pay taxes in the future is presumably an attempt to do that. Fairness, however, is a difficult thing to earn. This was beautifully illustrate in a study by Daniel Kahneman, Jack Knetsch and Richard Thaler published in 1986 in the American Economic review **. They found some interesting distinctions between behaviour customers consider fair and that they consider unfair. Our understanding of such issues is, however, incomplete. For example, Kahneman, Knetsch and Thaler found that respondents considered it fair for firms to pass on higher costs in the form of higher prices. What happens if a firm like Starbucks ‘passes on’ higher costs without actually incurring the higher cost? We don’t know. 
    One thing we do know is that any transaction involves an element of bargaining and fairness. Economists have not really taken this issue seriously enough, but the troubles at Starbucks remind us how important an issue it is.

* Richard Thaler (1985) ‘mental accounting and consumer choice’ Marketing Science.
** Daniel Kahneman, Jack Knetsch and Richard Thaler (1986) ‘Fairness as a constraint on profit seeking: Entitlement in the market’ American Economic review.

Tuesday, 4 December 2012

70 years after Beveridge: Credible threats and the welfare state

It is 70 years since the publication of the famous ‘Beveridge Report’. The report set out a revolutionary new model for social insurance that soon led to the instigation of the National Health Service and National Insurance. One of the more interesting ‘anniversary events’ I came across was a program on BBC Radio 4 - ‘The State of Welfare’; it basically assessed social insurance 70 years on from Beveridge. The clear message I got from listening to the program was that the current system fails to deliver a core principle of the Beveridge Report. Beveridge would not have been impressed by all the elements of our current welfare system. So, what went wrong?
    The recommendations in the report were based upon three principles. I’ll skip the first two and focus on the third: ‘The third principle is that social security must be achieved by co-operation between the State and the individual. The State should offer security for service and contribution. The State in organising security should not stifle incentive, opportunity, responsibility; in establishing a national minimum, it should leave room and encouragement for voluntary action by each individual to provide more than that minimum for himself and his family.’ Our current system of social security seemingly fails this principle. The analysis of a simple game can guide us through the main issues.  
     The details of the game are sketched out in the game tree below. The game starts with a citizen choosing whether to work hard or be a slacker; working hard would involve working hard at school, searching for a job, being willing to do a job that’s not very pleasant, etc. If the citizen works hard then he can either be ‘lucky’ or ‘unlucky’; lucky would mean avoiding redundancy, disability, discrimination etc. (Because its out of the control of the citizen or taxpayer whether he is lucky we say that nature decides.) If the citizen works hard and is lucky then everyone is happy. Both the citizen and taxpayer get a payoff of 100, which you can interpret as both being 100% happy.

If the citizen works hard but is unlucky then things are not so good. Consequently, the taxpayer needs to decide whether she will give benefits to the citizen. If she doesn’t then the citizen has payoff 0 – it cannot get any worse. Because of this, the taxpayer feels guilty and so her payoff is only 50 – it’s not nice to see hard working people destitute. If the taxpayer gives benefits then the citizen has payoff 50 and the taxpayer 80. Note that the taxpayer has to pay the benefits, so her payoff is less than 100, but she does not feel guilty, so her payoff is more than 50. 
    Clearly, it pays for the taxpayer to give benefits to an unlucky, hard working citizen. More generally, everyone benefits if there is a national insurance system that helps hard working people who, through no cause of their own, fall on hard times. This is a core principle underlying the Beveridge Report. The problem, however, is that this insurance system, like any other, creates moral hazard. To see why we need to know what happens if the citizen chooses to be a slacker. 
    If the citizen is a slacker then no amount of luck is going to help. So, without benefits the citizen gets 0. The taxpayer feels guilty about this meaning she only gets a payoff of 70. Note that the taxpayer feels less guilty when a slacker gets 0 than when a hard working citizen gets 0. Even so, she feels guilty. And if you’re wondering why she should feel guilty then let me point out the slacker’s secret weapon – he has children. No one wants to see children going without and so our taxpayer feels guilty to see this citizen and, more importantly, his children destitute. 
    If the taxpayer gives benefits then the slacker gets 60 and the taxpayer gets 75. (A slacker on benefits is happier than a hard working person on benefits because he did not have to work hard.) The taxpayer is less happy giving benefits to a slacker than a hard working citizen. Crucially, however, she will still give the benefits. She gets payoff of 75 by giving the benefits and only 70 by not giving benefits; remember those children. It’s emotional blackmail – but blackmail can be effective. 
   Why should the citizen work hard if he can get benefits anyway? Well, the citizen does have some incentive to work hard because the 100 he can get from working hard trumps the 60 he can get from slacking. Everything will depend on the probability of being lucky. Suppose the probability is p. If the citizen works hard his expected payoff is 100p + 50(1 – p) = 50 + 50p. If he’s a slacker he gets payoff 60. It pays to be a slacker if 60 > 50 + 50p or p < 0.2. So, if the probability of being lucky is less than 20% it pays to be a slacker. That’s moral hazard – an unintended consequence of offering national insurance is that it lowers the incentive to work hard.
    The Beveridge Report said that social security ‘should not stifle incentive, opportunity, responsibility’. It seems, however, that our current system is doing exactly that. So, can we do anything about it? Most ‘solutions’ seem to focus on changing incentives. These solutions focus on ‘making work pay’ which puts the emphasis on the payoffs of the citizen (those highlighted blue in the game tree below). We can increase the probability a hard working citizen is lucky, increase the payoff to a hard working unlucky person, or decrease the payoff to a slacker on benefits. Doing any of these three things can tip the balance in favour of hard work.

A ‘solution’ that gets much less attention, but can solve the problem in one easy step, is to change the payoffs of the taxpayer (those highlighted brown below). As things stand, a threat to not pay benefits to slackers is non-credible. A slacker knows that the taxpayer will feel guilty watching his children starve and so he will get his benefits. If we flip things around so that not paying benefits is credible then a slacker knows that anything other than hard work will leave him with 0. Arguably, this is the kind of the system the U.S. has created. It certainly looks like the kind of system that Russia has. So, can we make it credible to give slackers no benefits?

While I said this is the easy solution – it’s not so easy to not feel guilty about those children. It requires a change in preferences – the taxpayer to feel less guilty about slackers having nothing – and a change in expectations – the citizen needs to know that the threat of no benefits is credible. Neither of these is easy to do. Note, however, that if it can be pulled off the taxpayer never needs to feel guilty: Everyone will work hard, and unlucky hard workers will get benefits. There will be no slackers! A harsher social security system can, therefore, end up harming nobody. That’s a concept that seems to be missed in the drift towards a softer welfare system which ‘rewards’ slacking.