Our paper on a super-rational solution to the tragedy of the commons published in Scientific Reports

I am very pleased to announce that a paper that I worked on with collaborators Jun-Zhou He, Rui-Wu Wang, and Yao-Tang Li has been published in the open-access journal Scientific Reports. The paper, entitled “Asymmetric interaction paired with a super-rational strategy might resolve the tragedy of the commons without requiring recognition or negotiation“, considers how a different approach to determining optimal behavior in an evolutionary game might lead to a different predicted outcome.

Our paper builds on previous work we have done on asymmetric interactions. Although most interactions in nature are asymmetrical — the payoffs for one individual are not identical to the payoffs for another — a lot of game theory assumes symmetrical interaction; our paper considered a very simple public goods game in which one player (“strong”) enjoyed greater potential payoffs than the remaining players (“weak”). We have shown previously (He et al. 2012) that asymmetrical interactions do influence the probability of altruism, with the more “weak” individuals predicted to be more likely to altruistically provide a public good. This is a somewhat paradoxical outcome, as the “strong” individual has less-to-lose and more-to-gain from providing the public good than the “weak” individuals. A key novelty to the approach of this paper is its consideration of the “degree of asymmetry”: how different the cost-to-benefit ratio is when comparing “strong” and “weak” players. Analysis of this parameter produces another paradoxical result: greater degrees of asymmetry lead to even less probability of cooperation from the “strong” player.

The paper published today tinkers with an important assumption of our previous work. As is done in most game theory, our 2012 paper assumed rational behavior on the part of all interacting individuals. Is it possible that the paradoxes we illuminated actually stem from the assumption of rationality? Although assuming rational behavior is pretty standard, there is an alternative assumption: super-rationality. I will not get deeply into the difference here, but I like to think about these two different strategic approaches as being “cynical” and “optimistic” (with full acknowledgement that ascribing these human states-of-mind has the potential to cause more confusion than clarity). Rationality is “cynical”; it asks the question “what strategy assures that I won’t do worse relative to a player playing any other strategy?”. Super-rationality is “optimistic”: it asks the question “what strategy — if also played by other players — would lead to the best absolute outcome?”. In evolutionary games, rationality is generally assumed to the be the “correct” assumption as it cannot be undermined (more on that assumption below). We decided to see what would happen if we assumed that individuals interacting in this public goods game behaved super-rationally.

Tinkering with this very fundamental assumption produced dramatic changes in predicted behaviors. Assuming super-rationality, the predicted behavior of the “strong” individual dramatically changes:

Past a certain group size, the “strong” super-rational player actually becomes more likely to provide a public good.

Interestingly, increasing asymmetry still makes cooperation less likely in the “strong” individual:

In the construction of this model, super-rationality increases the probability of cooperation in “strong” individuals, but does not fully prevent asymmetries from undermining the incentive for “strong”-individual cooperation.

What I find most interesting is the effect of assuming super-rationality on the overall probability that someone (either the one “strong” player or the many “weak” players) will provide the collective good:

There’s almost a compensatory effect of assuming super-rationality: under conditions where “strong”-individual cooperation is less likely, the “weak”-individual cooperation becomes more likely. In very small groups, public-goods creation is driven by the “weak” individuals, whereas in larger groups public-goods creation is driven by the “strong” individuals. What is also fascinating is that it appears that you need to pass a critical group size in order to maintain very high levels of cooperation, and that a small degree of asymmetry actually increases overall levels of cooperation.

Overall, public-goods creation is more likely assuming super-rationality:

Given that group-outcome is built into the super-rational assumption, this is not really a surprising prediction. But of course neither is the prediction of rationality, which assumes benefits for the individual trump all other concerns.

Our model is admittedly very simple. Not every social interaction is going to be captured by a “one strong player, many weak players” scenario. But our work represents a first step, and I am excited to present these results. It would be interesting to extend this work to a more general scenario, one in which the degree of asymmetry varies more continuously throughout the population.

Game theory — whether you are approaching a particular game with rational or super-rational assumptions — is non-mechanistic. In employing a game-theoretic approach, we do not claim to know the evolutionary mechanism by which an optimal strategy evolves; instead, we assume that it evolves based on being an optimum. And herein lies the conflict between the rational and super-rational assumptions: depending on how you define optimal behavior, you get very different predictions about what behavior will evolve. Our paper explains how some existing forms of cooperation — including intra-specific mutualisms — might be more stable than predicted by previous theory. In this sense, we offer an alternative theory, and one that is more parsimonious with reality. But we do not offer any mechanistic explanation for why a super-rational approach to solving this evolutionary game would make more sense than the rational approach that predicts the breakdown of cooperation (in fact, most evolutionary biologists assume that super-rationality is the wrong assumption, which made this paper a bit harder to get published!). I am excited to look at this issue more mechanistically, to consider what kinds of evolutionary mechanisms would lead to what appears to be a super-rational outcome in many social systems that involve high levels of cooperation.