Field of Science

Showing posts with label Game Theory. Show all posts
Showing posts with label Game Theory. Show all posts

Freedom and the Public Goods

ResearchBlogging.org

Last post, I used the example of a protest against peanut allergy-related procedures to explore how the American conception of "rights" may be changing. In particular, I suggested that ideas of common or collective good were being displaced by an increasingly narrow and selfish definition of individual liberty.

A few friends pointed out that I may have unfairly maligned libertarians, anarchists, and others wary of government power.  These people aren't necessarily opposed to volunteerism or helping others; they just don't want to be coerced into doing so (or have their money taken for these purposes).  

This is a fair point.  However, it doesn't make me feel much better about the "leave me alone" political philosophy.  I don't think this philosophy will ever be up to solving our common challenges.  To illustrate why, I'd like to bring in a concept from game theory.

The Public Goods Game represents situations in which there is a common resource ("public good") that benefits all members of a group.  The public good might be a clean kitchen, a functioning electrical grid, or a healthy environment.  This good cannot be maintained without contributions from some group members.  Contributions can be in the form of doing something (washing dishes, working in the community garden, donating to NPR) or not doing something (not littering in a public park, not overfishing a lake).

The dilemma is this: everyone benefits from the public good, but contributions are voluntary.  The public goods game has no built-in incentive to contribute, beyond the desire to make things better for everyone.  So "free-riders" can benefit from others' contributions without contributing anything themselves. 

Both theory and experiment predict that cooperation cannot be sustained in such a game.  A typical experimental result looks like this:

Horizontal axis is time (number of game rounds)  SOURCE: Fehr and Gaechter (2000)


Contributions decline over time to virtually nothing. This is not because the participants are inherently selfish.  Indeed, at the start of the game, many people are inclined to contribute.  However, they realize at some point that others are exploiting their generosity.  Not wanting the benefits of their hard work to reward those who don't contribute, people eventually stop contributing altogether.  This unfortunate outcome has a name: the Tragedy of the Commons

Economists and social scientists have identified a few mechanisms that can reverse this tragedy.  If the participants know each other, and also interact in settings aside from the game, then concern for one's reputation can motivate people to contribute (Milinski et al. 2002, Rand et al. 2009).  This helps explain why co-ops can be successful: everyone knows each other.  They can reward or punish others based on their contributions to cooking, cleaning, and other tasks. 

But what about global challenges like climate change, environmental conservation, and sustainable use of resources?  These involve billions of players across the globe, and there are strong financial incentives to exploit the public good for individual gain.  Furthermore, it can be difficult to trace problems like pollution or overfishing to the individuals or companies responsible.  How these large-scale challenges be solved?

Research has identified only one answer. If the game is too large and complex for individual interactions to maintain cooperation, the solution is for the participants to invest in institutions (Gureck et al., 2006; Sigmund et al., 2010).  These institutions must have the power to investigate the actions of individuals, and reward or punish them based on their contributions. In other words, a social contract is needed, together with institutions to enforce it.

Of course, powerful institutions have inherent potential for corruption and abuse.  This is what worries libertarians and anarchists.  I share that concern.  But the solution, in my view, is to build in democratic checks, so that these institutions are as responsive as possible to the people they serve.

It's hardly a perfect solution.  Institutions can become entangled with those they should regulate.  Democratic checks can be co-opted. 

But to solve the largest problems that face humanity, we can't count on good will and personal responsibility alone.

References:

Ernst Fehr, & Simon Gaechter (2000). Cooperation and Punishment in Public Goods Experiments American Economic Review, 90 (4)

Özgür Gürerk, Bernd Irlenbusch, & Bettina Rockenbach (2006). The Competitive Advantage of Sanctioning Institutions Science, 312 (5770), 108-111 DOI: 10.1126/science.1123633

Milinski, M., Semmann, D., & Krambeck, H. (2002). Reputation helps solve the ‘tragedy of the commons’ Nature, 415 (6870), 424-426 DOI: 10.1038/415424a

Rand, D., Dreber, A., Ellingsen, T., Fudenberg, D., & Nowak, M. (2009). Positive Interactions Promote Public Cooperation Science, 325 (5945), 1272-1275 DOI: 10.1126/science.1177418

Sigmund, K., De Silva, H., Traulsen, A., & Hauert, C. (2010). Social learning promotes institutions for governing the commons Nature, 466 (7308), 861-863 DOI: 10.1038/nature09203

Game theory and Obama's mistake

Like many of my fellow lefties, I'm disillusioned with current US politics. In my view, we have a president who pursued an admirable, ambitious agenda for two years, but failed to win sufficient public support for his initiatives, and wasted too much time searching for nonexistent common ground. Now, with midterm elections lost, our president seems ready to abdicate all decision making power to the Republicans, whose ideas (in my judgment, as well as in Obama's) will actively make our country worse.

The problem, as I see it, can be illuminated with a bit of game theory. Consider a two-party government, and suppose each party has three possible strategies:
  • Ideological (I): Fight for initiatives that are consistent with the party's core beliefs, regardless of how popular or achievable these initiatives are.
  • Pragmatic (P): Work toward compromise and incremental accomplishments, in the view that "mixed bag" policies are better than stalemate.
  • Cynical (C): Prioritize winning elections and humiliating political opponents over helping the country and upholding core beliefs.

Either side can choose any of the three strategies, giving us nine possible outcomes. Of course, when it comes to the needs of the country as a whole, some outcomes are better than others.  The following matrix illustrates (in my judgment) how desirable each outcome is for the country's citizens, on a scale of 0 (horrible) to 9 (awesome).
The zeros—the worst possible outcomes—occur when cynics are allowed to set the agenda.  A battle of ideologues vs. cynics isn't much better, but at least the ideologues can stop the worst of the cynics' games.  Ideologues vs. ideologues is mostly a stalemate, but the ideologies may overlap enough to allow for cooperation on some fronts.

If both parties are pragmatic, the country gets a solid 7.  If one is pragmatic and one is ideological, the outcome depends on how successful the ideology is for the country, hence the wide range of possible values (3-9).

However, politicians aren't only concerned with the needs of the country.  They also want to maintain and expand their power.  We must therefore also consider how the choices of the parties affect their own success or failure.

This depends in part on how the country as a whole is doing.  Let's say times are tough right now: unemployment, wars, etc. Then here's (again, in my own judgment) how the various outcomes will affect the party currently in power:
As you can see, none of the options are great for the incumbents, because whatever happens, the public will tend to (rightly or wrongly) blame them for the current problems.  The best they can do is govern well.  However, in a US-like system with a supermajority needed to pass any legislation, progress depends on the cooperation of both parties.  With a pragmatic opposition, the incumbents can accomplish what needs to be done, obtaining 6's.  However, a cynical opposition can play the "stick in the mud" strategy and prevent the government from accomplishing anything.  This is bad for the incumbents, because nothing will improve and they will still take the blame.

Here's how it looks for the opposition:
As you can see, the cynical strategy is highly effective for the opposition party.  They can stop the wheels of government and, assuming things stay bad, they are virtually guaranteed to win the next election.  In game theory terms, C is a Nash equilibrium strategy: C is the best choice no matter what the incumbents do.  Of course, "best" here means best for the party, not the country. 

In my reading of events, the Republican leadership has decided that C is the way to go.  This strategy is examplified by Senate leader Mitch McConnell's statement that "the single most important thing we want to achieve is for President Obama to be a one-term president."  There are elements within the Republican party who are more on ideological side, but I see nothing but cynicism from Boehner and McConnell.

Let's say I'm right.  Then the Democrats are stuck with these options for their own fortunes:
and these payoffs for the country:
Given these options, the worst possible choice for the incumbent party is P.  It's bad for the party because it sets them up to be manipulated by the cynics.  It's also bad for the country, because it hands the initiative to those who would sacrifice the country's interests for their own gain.

But, unfathomably, P is exactly what Obama is choosing.  This is apparent from his statements such as
Can Democrats and Republicans sit down together and come up with a list of solutions to common problems? I think that we will be able to. I’m doing a whole lot of reflecting, and I think there’s going to be some areas where we need to do a better job.
We see it also from his willingness to accept tax cuts on the wealthiest one percent of earners.

The take-away message from our game theory model is this: There are times when it's good to compromise.  If the other side is being pragmatic, or even ideological, compromise can be good for both the country and the party.  But there's no point to playing P if your opponent is playing C!  The correct response to C is I: counter cynicism by fighting for your core beliefs.  Even if the cynics foil your policies, you can thwart their bad ideas and invigorate your supporters.

Some democrats (e.g. Bernie Sanders) have grasped the logic of this situation.  But unfortunately, our president isn't yet among them.

The Human Dimension of Climate Change

A New York Times Magazine article raises an issue I've been thinking a lot about lately.

If you are, as I am, a scientist concerned about global climate change, you may find yourself asking, "What kind of research could I be doing to best contribute to a solution?"

According to some, it may not be to study the climate itself. We may not know enough to predict exactly what will happen when, but we do know that drastic changes are coming whose magnitude will be determined by the actions we take now. It may not even be to study technologies such as alternative energy or policies such as cap-and-trade that can help combat global warming. Because while these policies and technologies are surely necessary, global warming is a problem created by human behavior, and our behavior will need to change if we are to make the individual and group decisions necessary to mitigate it, including the implementation of these policies and technologies. It may therefore be that the most important scientific questions in the fight against global warming are questions about humans, human behavior, and what we can do to change it.

The climate change puzzle presents a number of interesting questions about human behavior. The global environment is the ultimate "commons" game: We have a shared resource, and we can individually decide how much effort to put into preserving it. Only, we don't see the fruit of our individual efforts directly; only the sum total of everyone's efforts determines how well the resource is preserved. In the case of climate change, there are further complications: the effects of our actions now may not be seen for another fifty years, and some argue that the entire problem was fabricated by misguided scientists. Combining these factors, it is not hard to understand why many people feel little incentive to take action against global warming.

The article focuses on Columbia's Center for Research on Environmental Decisions, which performs experiments on people's decision-making processes. One finding jumped out at me as interesting and perhaps counter-intuitive: we tend to make better decisions as groups rather than as individuals. For example, one researcher studied decisions made by farmers in Southern Uganda as they listened to rainy-season radio broadcasts. If they listened to it in groups, they would typically discuss it afterwards and come to consensus on the best planting strategy in response to the weather. They ended up more satisfied with their yields than other farmers who listened to the broadcasts individually.

Our response to climate change will obviously involve a great variety of individual and group decisions, but it may be that if we can force more of the critical decisions to be made in group settings, where participants have not made up their minds beforehand (research shows this is crucial) we may find ourselves more able to put aside the parts of our human nature that would impede progress, and make the decisions that are in all of our best interests.

The Prisoner's Dilemma

You and an acquaintance are charged (and rightfully so!) as co-conspirators in a train robbery. You are being interviewed separately by the police. You can either rat your buddy out or keep silent and do more time. Your acquaintance has the same choices.

If one of you rats and the other remains silent, the one who cooperated with the police gets off free and the other serves 10 years. If you both keep silent, they can only convict on a lesser charge (for lack of evidence), so you each do a year. If you both rat on each other, you each do five years.

Both you and your acquaintance know this information. Assuming neither of you cares what happens to the other, and there are no recriminations in the outside world (we'll revisit both of these assumptions later), what is likely to happen?

Under the assumptions we've made, neither of you has any incentive to help the other. No matter what the other guy does, you get a better result by ratting on him. You both come to the same conclusion, so you both do five years.

This game is one of the most famous examples in game theory. It presents something of a dilemma: By each choosing the option that serves them best, the two "players" in the game end up with a result (5 years each) that is worse than if they had each kept silent. Choosing the best option individually leaves them worse off as a whole.

The game is traditionally phrased in terms of prisoners, but it applies pretty well to any situation when people have an opportunity to screw someone else over for their own benefit. If it truly is better in each situation to screw the other person, then everyone will end up screwing everyone else (in a bad way), and everyone will be worse off.

I think of this game when I drive up my street after a snowstorm, looking for a parking spot. People on my block (and all over Boston, from what I've seen) have the perverse idea that if they dig their car out of the snow, they "own" the spot they parked it in until the snow melts. They mark their spots with chairs or traffic cones. I've thought about doing the same. On the one hand, I think it's ridiculous for people to "claim" spots, just because they happened to park there before the storm. On the other hand, if everyone else does it and I don't, I can't park anywhere. If everyone else has chosen the selfish option, why shouldn't I? Classic Prisoner's Dilemma.

So does this bode ill for humankind? Is this a game-theoretic "proof" that we're all going to stab each other in the back? To answer these questions, let's look back at the assumptions we made.

First, we assumed that you don't care what happens to the other person. If you do care, you'd be much more likely to keep silent, which would end with a better result for both of you. A little selflessness helps everyone.

We also assumed that there were no consequences to your actions beyond what was spelled out in the game. A lot of ways you can screw others for your own benefit, such as breaking into your neighbor's house, are illegal. Laws can't deal with all prisoner's dilemma situations, but they can eliminate some of the worst ones.

There is a third, hidden assumption that we made: we assumed the game would only be played once. If the game is played over and over many times, is it possible for more cooperative strategies to emerge successful? This question was addressed by David Axelrod in The Evolution of Cooperation who found that, while selfishness is the best short-term strategy, cooperative strategies will win in the long run if the game is played enough times. More specifically, he identified four hallmarks of successful strategies: (here I quote Wikipedia)

  • Nice: The most important condition is that the strategy must be "nice", that is, it will not defect before its opponent does. Almost all of the top-scoring strategies were nice; therefore a purely selfish strategy will not "cheat" on its opponent, for purely utilitarian reasons first.

  • Retaliating: However, Axelrod contended, the successful strategy must not be a blind optimist. It must sometimes retaliate. An example of a non-retaliating strategy is Always Cooperate. This is a very bad choice, as "nasty" strategies will ruthlessly exploit such softies.

  • Forgiving: Another quality of successful strategies is that they must be forgiving. Though they will retaliate, they will once again fall back to cooperating if the opponent does not continue to play defects. This stops long runs of revenge and counter-revenge, maximizing points.

  • Non-envious: The last quality is being non-envious, that is not striving to score more than the opponent (impossible for a ‘nice’ strategy, i.e., a 'nice' strategy can never score more than the opponent).

Are these principles to live by? Perhaps. Axelrod and others think the success of these kinds of strategies may help explain the evolution of altruistic behavior in animals. At any rate, it seems to suggest that nice guys can get ahead, if they're willing to be mean at the right moments.