Continuous Cooperation

In a prisoner’s dilemma, two sides have an incentive to defect, even though mutual defection is worse for both sides than mutual cooperation. It is well known that in theory and in reality people cooperate more when then expect to interact over more repetitions, and when they care more about the future.

It is hard to make people live longer, or care more about the future. It can be just as helpful, however, and often much easier, to make people interact more frequently. In the limit of continuous interaction, people should cooperate the most. My once co-author Ryan Oprea has a paper with Daniel Friedman in the latest AER, showing this:

We study [lab experiment] prisoners’ dilemmas played in continuous time with flow payoffs accumulated over 60 seconds. In most cases, the median rate of mutual cooperation is about 90%. Control sessions with repeated matchings over 8 subperiods achieve less than half as much cooperation, and cooperation rates approach zero in one-shot control sessions.

They introduce some new theory to explain details of this behavior:

Inspired by a strand of existing theoretical literature, we postulated a particular class of epsilon equilibria and derived formulas predicting how cooperation rates respond to adjustment lags and to payoff parameters. These predictions accounted well for the Continuous, Grid-8 and (trivially) One-Shot data. They also nicely explained a set of second-round data from Grid-n sessions, which varied the number of subperiods from 2 to 60. Thus the formulas correctly predict defection in one shot games, cooperation in continuous time and intermediate results on the path between the two. The underlying intuition is simple. When your opponent can react very quickly, defecting from mutual cooperation is likely to earn you the temptation paypoff only briefly and may cost you the cooperation payoff for the rest of the period.

So do online firms cooperate more when they can vary their prices more frequently? What rapidly-changeable actions would help nations to cooperate more?

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  • So do online firms cooperate more when they can vary their prices more frequently?

    Is the idea here that price competition is like the prisoner’s dilemma, with cooperation = price collusion?

    • David

      Isn’t it?

  • Tom W. Bell

    Densely populated cities.

    • Karl Hallowell

      Densely populated cities.

      The problem is that the continuous interaction has to be with the same parties. Densely populated cities, if small enough, could have that. But large cities can and do lead to nomadic defectors who roam around hunting unconditional cooperators. So if you build up populations of cooperating people, what keeps the con men from cleaning them out?

      That’s in part why crime, impoliteness, political corruption, and other signs of defection occur IMHO.

      • Tom W. Bell

        Good point, KH. Substitute “neighborhoods” for cities, with Jane Jacobs in mind, and it works better.

  • Dremora

    It is hard to make people live longer, or care more about the future.

    Just imagine if we could cure aging or restore brain-injured people from backup. And offer them lush holiday experiences in multi-sensory virtual environments. What better motivator could there be to become a responsible world citizen who follows the law and helps punish defectors.

  • haig

    reputation systems

  • Zaine

    It’s not very practical, but countries under a shared group identity, like a more powerful U.N., could each have a set of representatives from all other member countries present and active in their respective governments. The representatives would all provide their input on minor (or major, but lack of tension is the intent) governmental decisions; exempli gratia France, Spain, Australia, the U.K., Russia, China, etcetera all have present in U.S. Congress representatives, each sharing their country’s perspective and input on the issues of the day’s docket, and vice versa.

    The purpose would be everyday, unobstructive cooperation; interaction as close to the continuous model as I can conceive.

  • PJF

    Nuclear weapons.

    • Karl Hallowell

      The euphemism for that is “shared destiny”. If defection means we all suffer, then there’s greater interest for most parties to cooperate and enforce cooperation. But it also means that those who do choose to defect (or at least try to) may have greater power and advantage in doing so than they otherwise would have in the absence of shared destiny.