Extortion subdues human players but is finally punished in the prisoner's dilemma.

Extortion is the practice of obtaining advantages through explicit forces and threats. Recently, it was demonstrated that even the repeated prisoner's dilemma, one of the key models to explain mutual cooperation, allows for implicit forms of extortion. According to the theory, extortioners demand and receive an excessive share of any surplus, which allows them to outperform any adapting co-player. To explore the performance of such strategies against humans, we have designed an economic experiment in which participants were matched either with an extortioner or with a generous co-player. Although extortioners succeeded against each of their human opponents, extortion resulted in lower payoffs than generosity. Human subjects showed a strong concern for fairness: they punished extortion by refusing to fully cooperate, thereby reducing their own, and even more so, the extortioner's gains. Thus, the prospects of extorting others in social relationships seem limited; in the long run, generosity is more profitable.

Democratic decisions establish stable authorities that overcome the paradox of second-order punishment.

Individuals usually punish free riders but refuse to sanction those who cooperate but do not punish. This missing second-order peer punishment is a fundamental problem for the stabilization of cooperation. To solve this problem, most societies today have implemented central authorities that punish free riders and tax evaders alike, such that second-order punishment is fully established. The emergence of such stable authorities from individual decisions, however, creates a new paradox: it seems absurd to expect individuals who do not engage in second-order punishment to strive for an authority that does. Herein, we provide a mathematical model and experimental results from a public goods game where subjects can choose between a community with and without second-order punishment in two different ways. When subjects can migrate continuously to either community, we identify a bias toward institutions that do not punish tax evaders. When subjects have to vote once for all rounds of the game and have to accept the decision of the majority, they prefer a society with second-order punishment. These findings uncover the existence of a democracy premium. The majority-voting rule allows subjects to commit themselves and to implement institutions that eventually lead to a higher welfare for all.

Consistent strategy updating in spatial and non-spatial behavioral experiments does not promote cooperation in social networks.

The presence of costly cooperation between otherwise selfish actors is not trivial. A prominent mechanism that promotes cooperation is spatial population structure. However, recent experiments with human subjects report substantially lower level of cooperation then predicted by theoretical models. We analyze the data of such an experiment in which a total of 400 players play a Prisoner's Dilemma on a 4×4 square lattice in two treatments, either interacting via a fixed square lattice (15 independent groups) or with a population structure changing after each interaction (10 independent groups). We analyze the statistics of individual decisions and infer in which way they can be matched with the typical models of evolutionary game theorists. We find no difference in the strategy updating between the two treatments. However, the strategy updates are distinct from the most popular models which lead to the promotion of cooperation as shown by computer simulations of the strategy updating. This suggests that the promotion of cooperation by population structure is not as straightforward in humans as often envisioned in theoretical models.

An economic experiment reveals that humans prefer pool punishment to maintain the commons.

Punishment can stabilize costly cooperation and ensure the success of a common project that is threatened by free-riders. Punishment mechanisms can be classified into pool punishment, where the punishment act is carried out by a paid third party, (e.g. a police system or a sheriff), and peer punishment, where the punishment act is carried out by peers. Which punishment mechanism is preferred when both are concurrently available within a society? In an economic experiment, we show that the majority of subjects choose pool punishment, despite being costly even in the absence of defectors, when second-order free-riders, cooperators that do not punish, are also punished. Pool punishers are mutually enforcing their support for the punishment organization, stably trapping each other. Our experimental results show how organized punishment could have displaced individual punishment in human societies.

Stochastic gain in finite populations.

Flexible learning rates can lead to increased payoffs under the influence of noise. In a previous paper [Traulsen, Phys. Rev. Lett. 93, 028701 (2004)], we have demonstrated this effect based on a replicator dynamics model which is subject to external noise. Here, we utilize recent advances on finite population dynamics and their connection to the replicator equation to extend our findings and demonstrate the stochastic gain effect in finite population systems. Finite population dynamics is inherently stochastic, depending on the population size and the intensity of selection, which measures the balance between the deterministic and the stochastic parts of the dynamics. This internal noise can be exploited by a population using an appropriate microscopic update process, even if learning rates are constant.

Impact of fraud on the mean-field dynamics of cooperative social systems.

The evolution of costly cooperation between selfish individuals seems to contradict Darwinian selection, as it reduces the fitness of a cooperating individual. However, several mechanisms such as repeated interactions or spatial structure can lead to the evolution of cooperation. One such mechanism for the evolution of cooperation, in particular among humans, is indirect reciprocity, in which individuals base their decision to cooperate on the reputation of the potential receiver, which has been established in previous interactions. Cooperation can evolve in these systems if individuals preferably cooperate with those that have shown to be cooperative in the past. We analyze the impact of fake reputations or fraud on the dynamics of reputation and on the success of the reputation system itself, using a mean-field description for evolutionary games given by the replicator equation. This allows us to classify the qualitative dynamics of our model analytically. Our results show that cooperation based on indirect reciprocity is robust with respect to fake reputations and can even be enhanced by them. We conclude that fraud per se does not necessarily have a detrimental effect on social systems.

Stochastic gain in population dynamics.

We introduce an extension of the usual replicator dynamics to adaptive learning rates. We show that a population with a dynamic learning rate can gain an increased average payoff in transient phases and can also exploit external noise, leading the system away from the Nash equilibrium, in a resonancelike fashion. The payoff versus noise curve resembles the signal to noise ratio curve in stochastic resonance. Seen in this broad context, we introduce another mechanism that exploits fluctuations in order to improve properties of the system. Such a mechanism could be of particular interest in economic systems.

Self-organized critical neural networks.

A mechanism for self-organization of the degree of connectivity in model neural networks is studied. Network connectivity is regulated locally on the basis of an order parameter of the global dynamics, which is estimated from an observable at the single synapse level. This principle is studied in a two-dimensional neural network with randomly wired asymmetric weights. In this class of networks, network connectivity is closely related to a phase transition between ordered and disordered dynamics. A slow topology change is imposed on the network through a local rewiring rule motivated by activity-dependent synaptic development: Neighbor neurons whose activity is correlated, on average develop a new connection while uncorrelated neighbors tend to disconnect. As a result, robust self-organization of the network towards the order disorder transition occurs. Convergence is independent of initial conditions, robust against thermal noise, and does not require fine tuning of parameters.