Learning in time

The story behind “A quantitative description of the transition between intuitive altruism and rational deliberation in iterated Prisoner’s Dilemma experiments” by ​Riccardo Gallotti and Jelena Grujić

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This paper exists because of three encounters. 

How Jelena met the problem

I met at a conference David Rand, who had a theory (then published in Nature) that people are intuitively altruistic because it takes longer for them to do something against the common interest. Two years before, I had run a massive Game Theory experiment where we collected the decision times although they had no use for the paper the experiments were designed for. It would have been cool if those data could confirm David’s theory, but they did not. The problem seemed more complicated than “short decision times mean intuition and long decision time mean deliberation”. I started looking for a model, but there was nothing out in the Game Theory literature and my attempts were going nowhere when I met Riccardo.

How Riccardo met the model

I met Jelena at a workshop where I got fascinated by her awesome experiment. We were both PhD students. I had an idea about some universal characteristics of human time consumption that I wanted to test on her data. I did it: I was wrong. But, these days, I had a flatmate doing his PhD in Neuroscience. By chance, I found myself reading a paper by Anne Churchland showing how decisions between two alternatives were mapped in the "race" between the activity of two neurons. I thought “I can model this” and did reproduce the statistics of Jelena's experiment with a Montecarlo simulation. I called Jelena and shortly we discovered that my model was the Drift Diffusion Model, among  the oldest in the book in Neuroscience but totally unknown at the time in Game Theory.

An illustration of the Drift Diffusion model: starting from an initial condition z · a, the agents accumulate random evidence in favour of one of two alternative decisions. The x = a threshold is associated to cooperation and the x = 0 threshold to defection. Once the amount of evidence reaches one of the thresholds, the associated decision is made. The arrows indicate the presence of a negative drift towards defection, as we observe in the multiplayer experiment. The two curves with shaded area represent the two parts of the probability distribution for the response times, one for the cooperation the other for defection, which are expected to differ in both shape and area.

How we met Reviewer #1

We felt our result was groundbreaking and decided to try big. We were working on our paper in the free time of our first postdocs. It took us a lot, mostly trapped in the submit-deskreject-reformat cycle characteristics of high impact submissions. We got to reviews in Nature Communications, where the feedback was mixed from enthusiastic to critical. Reviewer #1 was a clear expert in DDM and told us how we had to improve the paper methodology to the standards of Neuroscience. Our physicist’s souls were bleeding by the request of increasing the number of the parameters from 2 to 4, but eventually we realized the referee was right. 

Evolution of the Drift Diffusion Model parameters in a multiplayer and a pairwise experiments. (a) In the first round, the threshold a the same in both experiments. For the pairwise experiment we then observe a decreasing trend, while for the multiplayer experiment we observe an increase in the second round, followed by a progressive drop in the course of the experiments. (b) The absolute value of the drift speed v also starts from a common value approximatively zero. Its absolute value progressively increases for both experiments, showing how players process the information faster. The sign differs between the two experiments, because for the multiplayer case the gathered information suggests to defect while for the pairwise interaction it suggests to cooperate. The random phase of the multiplayer experiment has higher v, which is consistent with the fact that the setup of the random phase is easier. (c) Both experiment suggest an initial bias towards cooperation z=55%. The bias then changes progressively in the direction of the average behaviour of the other participants: positive bias for the cooperation in the pairwise experiment, negative bias for the defection in the multiplayer experiment. In the multiplayer experiment, after each phase the bias resets to its initial value of 55%, suggesting a resilience in the human bias towards cooperation. (d) The non decision time t0 drops after a few rounds to a constant value of 0.6 sec for the multiplayer experiment and 0.3 sec for the pairwise experiment. At the first round of the second and third phases of the multiplayer experiment, we observe a clear outlier, possibly accounting for the fact that the individuals were not ready for the next phase.

The new method allowed us to clearly discern between intuition and deliberation as they can be associated with two different parameters of the DDM. Under this new lens, we could observe that people are intuitively cooperative, but not naive! Indeed, although initially people’s intuitive decision is to cooperate, if the deliberation goes in the direction of defection, the bias will also change toward defection. 

In summary

Thanks to data Jelena was not supposed to record, a paper Riccardo was not supposed to read, our open minded and outgoing attitude at conferences, and the great contribution of an anonymous referee, we finally have published the paper that accompanied us for seven years, helped us grow as scientists, motivated us into continuing along this path, and also made us good friends.

Riccardo Gallotti

Researcher, Fondazione Bruno Kessler

Interdisciplinary physicist, interested in human behaviour.