Economist's Notebook: On-Line News and the Prisoner's Dilemma

I received this today in my e-mail box:

Dear New York Times Reader,

Today marks a significant transition for The New York Times as we introduce digital subscriptions. It’s an important step that we hope you will see as an investment in The Times, one that will strengthen our ability to provide high-quality journalism to readers around the world and on any platform. The change will primarily affect those who are heavy consumers of the content on our Web site and on mobile applications.

***

If you are a home delivery subscriber of The New York Times, you will continue to have full and free access to our news, information, opinion and the rest of our rich offerings on your computer, smartphone and tablet. International Herald Tribune subscribers will also receive free access to NYTimes.com.

If you are not a home delivery subscriber, you will have free access up to a defined reading limit. If you exceed that limit, you will be asked to become a digital subscriber.

This is how it will work, and what it means for you:

On NYTimes.com, you can view 20 articles each month at no charge (including slide shows, videos and other features). After 20 articles, we will ask you to become a digital subscriber, with full access to our site.

This has been coming for some time now and it will severely hamper my blogging as I rely on The Times for a lot of my content. There is a lot of talk among those who study the news business about this model and if it will work - will people really (finally) pay for content on the web?

NPR recently had a nice piece on The Times of London's experience with a pay wall where they lost about 95% of their audience after instituting it.  So there is every reason to expect the NY Times' experiment to fail as well - though the London Times is still sticking with it and embracing the remaining 5% as the right sort of people (how very British).

To me this is a classic game theory problem: the payoffs to any one news outlet's decision to charge is a function of other news outlets' decisions. To wit, if all the major news organizations decided to charge for on-line content then to read news on-line consumers would have to pay and all the news organizations might be able to sustain healthy readership as there would be no other alternative to those seeking news.

Of course this is not how it works. There are so many sources of news that any one decision to charge sends readers scurrying elsewhere ala The Times of London. But if all of the players could coordinate and contract over charging for the service, they would all be better off.  If there was no one free alternative there would probably be enough custom to go around and keep many papers in newsprint microchips.

This is the classic market failure that we associate with strategic situations in economics and is precisely the point of the prisoner's dilemma game: in strategic situations (where an individual's outcome depends on the decisions of other players) acting in your own self interest can lead to inefficient outcomes. In fact the best outcome is to be the one provider that doesn't charge - gets an amazing amount of visitors and can charge a decent amount for advertising.

Not coincidental, I think, that in the same week as the New York Times institutes a pay-wall, the still free Washington Post unveils a major web-site redesign. Ah the games we play...

Economist's Notebook: Game Theory and Athletic Conferences

In my Managerial Economics class this term we studied strategic interaction in great detail.  We saw how one player's actions can affect others' payoffs and how players can gain advantage through being first movers and making credible commitments.

I thought of all of this today as the news that Colorado has agreed to join the Pac 10 hit the news sites.  This decision by Colorado is likely to set of a cascade of movement across the Big Ten, Big 12, Big East and Mountain West conferences.

Colorado's decision to join the Pac 10 may seem abrupt, but they have employed a classic strategy and gained the first-mover advantage.  You see, there is widespread speculation that Texas, Texas A&M, Texas Tech, Oklahoma and Oklahoma State are going to join the Pac 10 and politicians in Texas were starting to make noise about preventing the Texas schools from joining the Pac 10 unless Baylor was included as well.  As the Pac 10 does not want more than 16 teams, this would have left Colorado out.  Seeing that this was changing the strategic landscape and not wanting to be left out in the cold, Colorado jumped first and gained the first mover advantage.

Now, every other team and conference's payoffs have changed and I expect to see some pretty swift defections right away.  Apparently Nebraska is about to leave the Big 12 and join the Big Ten (which will then become, humorously, a 12 team league).  Missouri may follow suit.  This leaves Kansas, Kansas State, Iowa State and Baylor without a conference and I imagine that the Mountain West which is employing a different strategy - wait and let the payoffs change to the point that you become an attractive option - will open up its arms to these schools.

If I were the Mountain West I would bring on board these four schools and Boise State pronto in the hopes of becoming a BCS conference.  But Kansas basketball battling it out in places like Ft. Collins, Reno, Provo, Laramie and Albuquerque?  Weird.

The most interesting piece is the play of Notre Dame, which has a lucrative deal for its independent football team but risks the rest of its sports getting lost in the conference shuffle.  My bet is that they end up in the Big Ten along with Nebraska, Missouri, Rutgers and one other - Syracuse maybe?

Anyway, this is all an incredibly high stakes game being played at the moment and it is fascinating to observe as a student of game theory.   The one player in all of this that does not seen to have any kind of winning strategy is the Big 12 conference.  It looks like a goner for sure.  Like I said, weird.

Don't know if this is a net positive or negative for Oregon State, but it hardly matters, the status quo is gone.  Little tiny stadiums like those in Corvallis, Pullman and Palo Alto are going to look awfully puny if Austin, Norman, College Station are added to the mix (all over 80,000 capacity).  And now there is the real prospect of two orange and black OSUs in the same conference...

Econ 539-Public Policy Analysis: Game Theory

A big part of the class will be spent studying how and when markets fail and what (if any) are the appropriate policy responses. Though it may seem unusual for a public policy class, an important way that markets can fail is if there is strategic behavior. This is perhaps the most well-known result from game theory: in situations where strategic behavior is important, individually rational, self-interested behavior may not yield an efficient outcome.

For the purposes of this class, we will look closely at only the basic normal form games and see how this result comes about. I will also talk about sequential and repeated games in general and what additional important results come from these situations.

As examples, we will talk about the incentives of Wall Street banks and have a look at this Bob Frank column in the New York Times. We will also discuss another interesting example of game theory at work in my little take on unsigned intersections. (Which reminds me, I haven't been keeping up on the Economist's Notebook thing lately - I'll try to do more)

Paradoxes in Economics: The Ultimatum Game

Economics, with its basis in rational decision making, can lead to paradoxical results. One classic paradox is the ultimatum game whereby one player has an amount of money (say $100) and has to make an offer to share some part of it with the other player. The second player can only say 'yes' and both players get the agreed upon shares, or 'no' and both players get nothing. It is played only once.

The economic solution to the game simple: the first player offers the smallest amount possible (say $1) and the second player agrees (as $1 is better than nothing). In the real world, however, this rarely happens - the second player will often say no to too small an offer as the dis-utility of the feeling of being cheated is worth more than $1. [This by the way, just means we have to be more careful when we describe the 'true' payoffs to players and include psychic costs] The first player is also motivated by the positive utility one gets from being generous.

I was reminded of this last night when I watched a wonderful Argentinean movie "Nine Queens." [I have to travel to Buenos Aires for a conference and this was suggested as a good movie to watch to see a little of the city] You can get the gist of the plot from the trailer (though it is a pretty awful trailer - don't worry the movie is very good), but in it there is a scene that illustrates the ultimatum game perfectly. A forger has made a perfect copy of some extremely rare stamps and is ready to sell them to a wealthy collector when he falls ill and is unable to complete the transaction that absolutely has to happen that day. So he calls a fellow confidence man to help him and offers a 50-50 split. The con man realizing the nature of the game says "no: 90% for me and 10% for you." What is the sickly forger to do? 10% is better than 0, so he agrees. Of course the con man should have realized he could have offered only 1%, but perhaps the dis-utility from the feeling of being taken advantage of may have led to a refusal, so he adjusted.

Its a good movie and highly recommended, especially if you want to practice your spanish with a rapid-fire Argentinean accent. [If not, the sub-titles are fine]

The ultimatum game is one paradox of economics, I'll leave you with another classic: why do you leave a tip after service in a restaurant at which you are not a regular?

Can you think of other paradoxes in economics?

Game Theory, Evolutionary Biology and the Financial Meltdown

Bob Frank (who was my teacher, boss and neighbor in grad school and whom I admire immensely) puts an interesting spin on the credit market meltdown. It is actually a narrative that I have told often using game theory as a setting: no one financial institution could be the one to not engage in the risky behaviors without potentially jeopardizing its survival even though they might have known that by doing so it was jeopardizing its survival. But if all agreed to do so together they woudl all be better off (and so would we). It is a classic prisoner's dilemma.

Frank puts this same narrative in evolutionary biology terms, but we know that evolutionary biology and game theory are very closely linked so it makes sense. But Bob is a master at telling a compelling story...

Though Adam Smith is ­almost universally regarded as the father of modern economics, most economists will eventually see Charles Darwin's ideas as the true intellectual foundation of our discipline. Smith's modern disciples celebrate his invisible hand theory, which says markets harness individual self-­interest to serve society's interests. Smith himself was more circumspect, claiming only that self-interested actions often lead to socially benign outcomes. But that claim is remarkable enough. Competition among greedy producers often yields innovations that result in cheaper and better products for everyone.

It was Darwin, however, who better grasped the complex relationship between individual and social interest. And we must turn to his account if we are to understand the recent meltdown in financial markets. His deep insight was that natural selection favours traits and behaviours according to their effect on individual organisms, not groups. Sometimes individual and group interests coincide. But interests at the two levels often conflict.

Male body mass is a case in point. Most vertebrate species are polygynous, meaning that males take more than one mate if they can. The qualifier is important, because when some take multiple mates, others get none. The latter don't pass their genes along, making them the ultimate losers in Darwinian terms. So it is no surprise that males often battle furiously for access to mates. Size matters in those battles. And hence the evolutionary arms races that produce larger males.

Bull elephant seals often weigh more than five times as much as females. But their size is a handicap, making them far more vulnerable to sharks and other predators. Given an opportunity to vote on a proposal to reduce their weight by half, bulls would have every reason to favour it. But they have no such opportunity. And any bull that weighed much less than others would never find a mate.

Similar conflicts arise when individual rewards depend on relative performance. This payoff structure, common in financial markets, helps explain why those markets sometimes fail catas­trophically. Wealth managers' salaries depend primarily on how well their investments perform in relative terms. Funds offering higher returns immediately attract cash from rival funds. If the invisible hand functioned as Alan Greenspan and other modern disciples of Adam Smith imagined, there would be no problem. Investors would be fully compensated for any additional risk they took in search of higher returns. But human brains forged by natural selection don't work as assumed in economics textbooks.

As our brains were evolving, immediate threats to survival loomed everywhere. Natural selection thus favoured a nervous system keenly sensitive to immediate relative payoffs, much less so to distant ones. Anyone disinclined to seize immediate gains at the risk of having to incur costs in the future would experience low relative rewards in the short run. And when competition was intense and immediate, such individuals often didn't survive to see the long run.

In market settings, a nervous system biased in favour of short-term relative reward is a recipe for disaster. When the price of an asset like housing is rising steadily, unregulated wealth managers can create leveraged investments that generate enormous rates of return. Even in the early years of this decade, many experienced analysts were warning that several mortgage-backed securities were poised to tumble. But investors faced a tough choice: they could earn high returns by continuing to invest in them, or they could move their money elsewhere. Many rejected the latter strategy because it would have required watching friends and neighbours pass them by.

Wealth managers felt compelled to offer the risky investments, since many customers would otherwise desert them. Managers also knew there would be safety in numbers when things soured, since almost everyone had been following the same strategy. The resulting collapse was inevitable.

Adam Smith's invisible hand is a truly extraordinary insight. But when rewards depend on relative performance, it doesn't always deliver.

The financial meltdown that caught Adam Smith's disciples off guard would not have surprised Darwin. One of his central themes was that because much of life is graded on the curve, wasteful arms races create conflict between individual and social interests. The good news is that unlike other animal species, humans can often resolve such conflicts through intelligent regulation.

Here is Bob on carbon offsets as well.

Econ 101: Nash Equilibrium in a Non-Cooperative Single-Shot Game

Via Greg Mankiw, a wonderful illustration of almost the precise game I used to describe the no stop sign intersection. The outcome is ... predictable.



What would you have done? Are you sure?

Economist's Notebook: Game Theory and Stop Signs

The recent attention to the so-called "Idaho Stop" bill that would allow bicyclists to slow but not stop in residential intersections with stop signs got me thinking about this and about the uncontrolled intersections present in many Portland neighborhoods. How should we think about human behavior in the face of such incentives? In these cases, since the problem is inherently about more than one vehicle (or pedestrian) the interactions are strategic in nature, so game theory is the appropriate modeling framework which to employ.

Before we get to that however, Joseph Rose in The Oregonian claims that having an "Idaho Stop" law is actually safer based on incident data from Idaho pre and post law. [Note to Mr. Rose: correlation is not causation, and even if you think this law is good, please explain how such a law could be responsible for an immediate 14.5 percent reduction in bicycle injuries? I think we are dealing with spurious correlation here] But the rationale for the Idaho stop is the same for cars: if there are no other cars around, why stop fully? Sure a bike is human powered but the physical concept is identical, it takes more energy to stop and start than to maintain momentum, and if we care about climate change why not let cars do it too?

Which brings me the the topic of today: non-controlled intersections. These are intersections without any traffic restrictions - anything goes. Well not really, the right of way goes to the vehicle that gets there first, which is precisely the problem. [By the way, do you know who goes if it is a tie? Yep, the vehicle on the right, just like a 4 way stop] Anyway, most of the intersections around my son's elementary school are uncontrolled even though there are many kids walking to school crossing at these intersections. And if you ever want to see good examples of dangerously aggressive driving, all you need to do is show up at an elementary school at drop off times. These are parents who should be most attentive to child safety, but hey their kid isn't walking so they have nothing personal at stake except for getting to work on time. Anyway, I am constantly amazed at the reckless driving exhibited by these parents and what I have found most striking is that on the rare days that I drive my child to school and slow almost to a complete stop at these intersections to be sure there are no cars or kids around, a car from half a block away will almost always bomb right through at 30 mph. If I had asserted my right of way, we would crash and so this reckless driving is kind of like a credible threat in game theory and the logical thing for me to do is to wait until the car has passed.

I imagine that traffic engineers think that these intersections are actually traffic calming. They force all cars to slow down and proceed cautiously through the intersection. But when you think about the game cars are involved in, it is not at all clear that this is the equilibrium. Here is a depiction of a normal form game (single shot, simultaneous, non-cooperative) that I think describes the incentives. Car 1's payoffs are the first number of the pair and Car 2's payoffs are the second number.

Each car has two strategies available to them: be cautious or aggressive when entering the intersection. If both cars are aggressive, a fender-bender occurs and they both loose 10. If they are both cautious, they have to slow down, but no accident occurs so they both get 0. If one is aggressive and the other cautious, the aggressive one gets to go fast and first through the intersection and gets 10 while the cautious gets 0 again. Economics students will immediately recognize the Nash equilibria - where each car is playing a best response strategy to the other. They are the two aggressive/cautious pairs. The problem is of course when both think its the other that is going to be cautious and both end up aggressive... But anyway, this actually describes pretty well what I observe around my son's school: some drivers being aggressive and bombing through the intersections and others being cautious.

This is not what I believe the traffic engineers think and what's worse it means there are aggressive drivers bombing through intersections when lots of little kiddies are running about. Makes me wonder why, of all places, are the intersections around schools not controlled? And, by the way, if you really want to calm traffic, a four-way stop seems to do a good job.

Economist's Notebook: A Green Game Theoretic Conundrum

Suppose you wished to see a greater proliferation and use of 'green' or natural cleaning products.  Would you, as a consumer, do better buying from companies such as Seventh Generation or Ecover that have been solely devoted to green products since their inception, or would you do better buying the green product from the decidedly non-green company?

On the one hand supporting the green companies will hopefully help them get bigger and grab a bigger market share and you would feel reasonably confident that they would stick largely to their green product line since it is such a part of their corporate identity.   This would, in the long run, hopefully lead to their becoming more and more dominant in the cleaning products business and support your original goal.  

On the other hand, you may wish to reward an established company in the hopes that you can prompt them to devote more and more of their energy to green products, will be able to leverage economies of scale and scope to provide a low cost green product that will encourage many new customers to try it.  The risk, I suppose is that they are not really concerned about the greenness of their company but sales and if they can use low priced green products to compete Seventh Generation away, they may just do so and then abandon green products altogether.

Thus was my thought process yesterday when I was confronted with a bottle of Green Works dishwashing soap for $3-something, or the Ecover stuff I usually buy that was $6-something.  I decided to go for the Green Works stuff.  My wife disagreed with me later when I brought it home.  I was convinced by the line of argument that went, if the goal is to get as many people using the stuff as possible, then who cares who makes it, what is important to get the price down to the point where people who only marginally care will switch.  My wife is more persuaded by the whole company ethos argument.  But as an economist I tend believe that good intentions are almost always swamped by market realities, and if you want real change in the habits of American consumer, you have to make it work economically.  Witness the Prius.  It was not until finally a car came along that was affordable, reliable and you didn't have to go the extra yard of plugging in or driving to the Biodiesel station that we saw mass adoption.  

Anyway, apparently the Sierra Club feels the same way I do.  They have taken a lot of flak for their support of Clorox, but I understand where they are coming from.    

Econ 101: Game Theory and Car Dealers

The Oregonian reports today on the Oregon Automobile Dealers Association request to lawmakers that they prohibit the sale of cars on Sundays. Huh? Why on earth would dealers want lawmakers to limit how they operate? Isn't this the antithesis of allowing free markets to produce efficient outcomes?

Actually, in economics, game theory provides some useful insight into situations in which, when strategic interactions exist, the free market might lead to inefficient outcomes.

Let's try and see how auto dealers might be in just such a situation using the canonical example of the prisoner's dilemma game. Even though the title of the game refers to a particular story told with it, the canonical nature of the game is actually in the payoffs and outcomes. Here goes:

Suppose, for simplicity, that there are only two auto dealers. I shall describe their interaction with a payoff matrix (shown below). The two dealers are Honest Moe's and Crazy Larry's. Their strategies are either to stay closed on Sunday or to be open on Sunday. Honest Moe's payoffs from each of the four possible outcomes is the first number written (let's call it weekly profits) and Crazy Larry's is the second. Thus if both Honest Moe and Crazy Larry close on Sunday they will both get 120 and so on.



So what will happen if they are both left to their own devices? Well if Honest Moe knows Larry will close on Sunday, Moe will stay open because he can get 140 instead of the 120 he would get if he stayed closed. If Moe knows Larry will be open on Sunday, then Moe will open on Sunday because 100 is better than 80. The exactly same calculations apply for Larry. So, no matter what the other does, it is always better for each individual dealer to stay open on Sunday. Thus the outcome of the game is that both will be open Sunday and they both will get 100.

But is this the best outcome for the two dealers? No, they would both be better off if they both stayed closed on Sunday. This would give both of them payoffs of 120. This is the essence of the prisoner's dilemma: individual incentives lead this market into a sub-optimal outcome and thus the efficiency of the free market breaks down.

Just agreeing to stay closed on Sunday won't work, because each has an individual incentive to cheat and open up and get 20 more at 140 than at 120. In other words, the very best individual outcome is the be the only one open on Sunday.  So they need the option of opening up in Sunday removed from their choices and then they can both be made better off.

Whether consumers are better off is another story...

Econ 101: Game Theory and Politics

A decent description of modern economics is the study of behaviour in the face of incentives. Game theory is a branch of economics where we study behavior in strategic settings. In this, and in many other areas, economists have confirmed that understanding incentives goes long way toward explaining behavior.

And here is the thing with games: the rules of the game create the incentives. So once we know the game's rules, we internalize these rules, devise strategies that serve to maximize likely outcomes given these rules, and then play the game based on these strategies. At the risk of picking on one candidate too much, it is quite infuriating for someone like Hillary Clinton to say (and I paraphrase): "if the Democratic primaries were run under the same rules as the Republican primaries, I would have already won the nomination."

Oh please, if the rules had been different at the outset, Obama would have had another set of strategies and Hillary would have probably lost then too. We all understand this whether I dress it up as economics or not. What is sad it that she would even use this argument - to whom does she think this appeals? The micro-trending population of poor losers?

This is also true of statements like "well, I won the big states." Yes, but the democratic primary is not the general election - the game is entirely different. It is a false analogy.

Games are defined by their rules - different rules, different game. End of story.

Econ 101: The Prisoner's Dilemma

[This post was motivated by a question in the comments to my post on self-fulfilling expectations]

One of the most canonical examples in all of modern economics is the game theory story of the prisoner’s dilemma. The reason this has become so well-known and almost always used as the very first example of game theory in economics classes is because of the power of the result. It very simply and elegantly shows how, in strategic situations, the basic efficiency of free markets fails.

A little background: in economics perhaps the most powerful result of all is what is known as the first welfare theorem. The first welfare theorem states that when markets are free and complete (which is a technical term but actually implies some fairly strong conditions), the resulting equilibrium is efficient. This is also related to the invisible hand which states that economic agents, by solely pursuing their own self-interest, will maximize social welfare. Now, there are lots of things that make this not true in reality, the most common are the existence of externalities, public goods and asymmetric information. But, the prisoner’s dilemma shows us that it is also not true in strategic situations. Strategic situations are where the actions of one player determine the ‘payoffs’ of the other players. (NB: you can think of this as a type of externality, but a in a specific and complicated way – more complicated than the standard externality stories) To give a simple example if we are roommates and you are considering purchasing a new iPhone, the joy you get from that purchase may depend on you being the first to own one and show it off to our friends. If I buy one before you, then the enjoyment you get from yours diminishes. So my actions have affected your payoffs from the purchase of an iPhone. We are now no longer in the pure free market case which assumes that others decisions have no affect on your costs or benefits from market transactions.

The Game: there are infinite variations on the same story but they all follow similar lines. Suppose that two people are arrested of a crime. The police put them in two separate interrogation rooms where they cannot see or talk to each other. The police have enough evidence to get convictions only for a lesser charge which would lead to 1 year jail terms, but if one confesses to the crime they can convict the other of the more serious crime and in this case the confessor gets probation only (o years in jail) and the other person gets a 5 year jail sentence. If they both confess then they both get convicted and sentenced to 3 years in jail. It is assumed that they both know all of this and they know the other person knows as well (and technically each knows that the other knows that the other knows, and on, and on, and on…). They also have to make their final decision without knowing what the other has done.

So now consider the choices of each person. If they decide to not confess they get: 1 year in jail if the other does not confess and 5 years if the other confesses. If they decide to confess then they get 0 years in jail if the other does not confess and 3 years if the other confesses. So no matter what one person thinks the other person will do, confess is always the better choice. So they both confess and the result is that they both spend 3 years in jail.

Note, however, that there is a better out come for both, the one where both don’t confess and get only 1 year in jail. So the result of the prisoner’s dilemma game is sub-optimal because both could be made better off by not confessing. But acting in their own self-interest leads to this poor outcome – contrary to the invisible hand in free and complete markets.

So you see the power of the story: in strategic situations, all the efficiencies of free markets are no longer guaranteed. You could easily change the story to my iPhone story or any other more standard market stories and motivate this more obviously, but the essence is always the same.