The evolution of extortion in repeated games

In evolutionary biology and the social sciences, repeated games serve as a fundamental tool to describe individual behavior in long-term relationships. When playing a repeated game, subjects can condition their next moves on the outcome of previous interactions, which may give rise to reciprocal cooperation and mutualistic symbioses. However, for the most commonly used metaphor for repeated interactions, the infinitely iterated prisoner`s dilemma, it was recently shown that a sophisticated player could also apply a strategy that permits manipulation and extortion of opponents. Such extortion strategies have three important properties: (1) they ensure that the payoffs of the players are linearly related, (2) they incentivize the co-player to cooperate, and (3) they ensure that any surplus of cooperation is unevenly distributed among the players, such that the co-player`s payoff is lower by a fixed percentage. Evolutionary theory suggests that behaviors that lead to a relative advantage are likely to spread; it is therefore natural to ask whether extortionate behaviors can emerge and succeed in evolving populations. Recent work has shown that their prospects are limited: in reasonably large populations, extortion strategies are not stable and they promote (rather than inhibit) the evolution of cooperation. However, if the population size is small, or if the players originate from distinct populations that evolve at different rates, then extortion is a major force in the evolutionary dynamics. The present project intends to assess the role of extortion strategies in general repeated games. In particular, we will use evolutionary game theory to clarify under which conditions extortion evolves, and what are the consequences for the evolution of cooperation. Moreover, we aim to show that the realm of extortion is not restricted to pairwise interactions; instead, such strategies do also exist for large-scale collective actions, for an arbitrary number of players. In this way, we hope to shed new light on the emergence of conditionally cooperative behaviors in the repeated public goods game and the volunteer`s dilemma. This new angle on repeated games could then be used to re-evaluate existing data on human behavior in social experiments.

Researchers from various disciplines aim to understand under which conditions humans cooperate. As one potential explanation, it has been argued that humans are able to engage in reciprocal relationships. In repeated encounters, they learn to cooperate only with those group members who have also cooperated in the past. Until four years ago, most people in the field have believed that in this way, repeated games would almost automatically lead to cooperation. However, in 2012, William Press and Freeman Dyson made a remarkable discovery; they demonstrated with a beautiful mathematical proof that simple repeated games allow for extortion. A sophisticated player who is aware of such extortionate strategies, they argued, would be able to unilaterally exploit her peers. Their discovery seriously questioned whether direct reciprocity could really promote cooperation at all - as indicated by a comment of the MIT technology review starting with 'The world of game theory is currently on fire'. The aim of our project for the Schrödinger scholarship was two-fold. First, we showed that the extortionate strategies discovered by Press & Dyson are not restricted to the setup of the infinitely repeated prisoners dilemma. They exist in any repeated social dilemma (irrespective of the number of players, and irrespective of whether or not the game has an infinite horizon). As the second aim of our project, we intended to quantify the performance of such extortionate players using both, computer simulations and behavioral experiments. With the computer simulations, we mimicked a simple evolutionary process: we considered a virtual population of individuals who could freely choose how to play the repeated prisoners dilemma, assuming that over time they would learn to adopt strategies that are more successful. Using these computer simulations, we observed that extortion can only evolve if (i) either the population is very small, or if (ii) some players are able to commit themselves to playing an extortionate strategy (i.e., if there are some players who stick to their extortionate strategy even if it is not quite beneficial at the moment). In a behavioral experiment we tested this second prediction by letting students play against a computer program. The computer program was either committed to play an extortionate strategy or to play a cooperative strategy (the students were not aware of the nature of their opponent). Although theory predicts that extortion should succeed in such encounters, our results suggest that generosity fares much better than extortion. According to this experiment, humans oppose being exploited even if this comes at a personal cost.In addition, the Schrödinger scholarship has also allowed me to initiate new collaborations, addressing for example why people have evolved natural instincts to cooperate, or why they sometimes would be modest about their achievements.