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The evolutionary foundations of fairness is one of the most hotly debated questions in evolutionary anthropology. Reciprocate cooperation (in a large sense) generates collective benefits and, beyond explaining its mere existence, it is also essential to understand how evolution has shaped the way these benefits are divided. Fairness is the fact that, among the many ways to distribute collective benefits, we tend to favor impartial distributions and request our partners to do the same (e.g. 50/50 divisions in symmetric interactions). The evolution of fairness raises a particularly difficult question for theoreticians, as it actually entails dealing with the so-called issue of “equilibrium selection”. The principle of reciprocity per se is underdetermined (this is known in game theory as the “folk theorem”), which fundamentally stems from the fact that a very wide range of cooperative agreements are better than being alone. Influential authors have thus claimed that this problem is actually so difficult that it requires, almost unavoidably, the operation of some form of group selection . Here, we offer an alternative solution. We show that the indeterminacy of reciprocate cooperation vanishes if one considers properly the outside options of individuals. In reality, the question is not whether a given interaction is better than being alone, but whether a given interaction is better than another interaction, possibly with a different partner [2,3]. We will present an overview of our modeling results in this field [4,5], together with the results of a model built specially to deal with the issue of equilibrium selection. We show that fairness evolves naturally when individuals have varied social opportunities, because the issue of each interaction is then constrained by the fact that it must bring at least the same benefit than other interactions. In particular, if two individuals have the same outside opportunities, they can agree upon an interaction only if it brings the same benefit to both of them. The indeterminacy of reciprocity is hence in large part an artifactual consequence of the way models are usually built, and the evolution of fairness does not require any form of group selection.