Theoretical and empirical research highlights the role of punishment in promoting collaborative efforts 1,2,3,4,5 .However, both the emergence and the stability of costly punishment are problematic issues. How can punishers invade a society of defectors by social learning or natural selection, and how can second-order exploiters (who contribute to the joint effort but not to the sanctions) be prevented from drifting into a coercion-based regime and subverting cooperation? Here, we compare the prevailing model of peer-punishment 6,7,8 with pool-punishment, which consists in committing resources, prior to the collaborative effort, to prepare sanctions against free-riders. Pool punishment facilitates the sanctioning of second-order exploiters, since these are exposed even if everyone contributes to the common good. In the absence of such second-order punishment, peer-punishers do better than pool-punishers, but with second-order punishment, the situation is reversed. Efficiency is traded for stability. Neither other-regarding tendencies or preferences for reciprocity and equity, nor group selection or prescriptions from higher authorities are necessary for the emergence and stability of rudimentary forms of sanctioning institutions regulating common pool resources and enforcing collaborative efforts.Many economic experiments on 'public goods games' (PG games) have shown that a substantial fraction of players are willing to incur costs in order to impose fines on exploiters, i.e., those who do not contribute to the joint effort 1,2,3,4,5,6,7,8 . As a consequence, the threat of punishment looms credibly enough to increase the average level of pro-social contributions. However, the sanctioning system is itself a public good. Thus punishers are often seen as altruistic, since others benefit from their costly efforts 9,10,11,12,13 . Conversely, those who refrain from punishing exploiters are 'secondorder free-riders'. Among self-interested agents, second-order free-riding should spread and ultimately cause the collapse of cooperation.A solution is to also punish second-order free-riders 14 . But such 'second-order punishment' risks being subverted by third-order free-riders in turn, leading to infinite regress. Moreover, if everyone contributes to the public good, second-order free riders will not be spotted. Their number can grow through neutral drift, ultimately allowing defectors to invade with impunity.We show how a simple mechanism can overcome this objection. There exists a variety of sanctioning systems. Most experiments on PG with punishment have considered peer punishment: after the PG game, individuals can impose fines on exploiters, at a cost to themselves. Interestingly, the first experiment on PG with punishment 15 considered a different mechanism. Here, players decide whether to contribute to a 'punishment pool' before contributing to the PG. This can be viewed as a first step towards an institutionalized mechanism for punishing exploiters, and compared with the self-financed contract enforcement games in ...

Evolutionary game theory describes systems where individual success is based on the interaction with others. We consider a system in which players unconditionally imitate more successful strategies but sometimes also explore the available strategies at random. Most research has focused on how strategies spread via genetic reproduction or cultural imitation, but random exploration of the available set of strategies has received less attention so far. In genetic settings, the latter corresponds to mutations in the DNA, whereas in cultural evolution, it describes individuals experimenting with new behaviors. Genetic mutations typically occur with very small probabilities, but random exploration of available strategies in behavioral experiments is common. We term this phenomenon ''exploration dynamics'' to contrast it with the traditional focus on imitation. As an illustrative example of the emerging evolutionary dynamics, we consider a public goods game with cooperators and defectors and add punishers and the option to abstain from the enterprise in further scenarios. For small mutation rates, cooperation (and punishment) is possible only if interactions are voluntary, whereas moderate mutation rates can lead to high levels of cooperation even in compulsory public goods games. This phenomenon is investigated through numerical simulations and analytical approximations.cooperation ͉ costly punishment ͉ finite populations ͉ mutation rates E volutionary game dynamics describes how successful strategies spread in a population (1, 2). Individuals receive a payoff from interactions with others. Those strategies that obtain the highest payoffs have the largest potential to spread in the population, either by genetic reproduction or by cultural imitation. For example, from time to time, a random focal individual could compare its payoff with another, randomly chosen role model. The role model serves as a benchmark for the focal individual's own strategy. Depending on the payoff comparison, the focal individual either sticks to its old strategy or it imitates the role model's strategy. We focus here on the simplest choice for a payoff comparison, which is the following imitation dynamics (3): If the role model has a higher payoff, the focal individual switches to the role model's strategy. If the role model has a lower payoff, the focal individual sticks to its own strategy. If both payoffs are identical, it chooses between the 2 strategies at random. The imitation dynamics can be obtained from other dynamics with probabilistic strategy adoption in the limit of strong selection (4). When only 2 strategies are present, the dynamics becomes deterministic in following the gradient of selection. In infinite populations, it leads to deterministic dynamics closely related to the classical replicator equation (5, 6). In both cases, the dynamics remains stochastic if the payoff differences vanish. For large populations and in the absence of mutations, the replicator dynamics is a useful framework to explore the general dynamics of t...

A vast amount of empirical and theoretical research on public good games indicates that the threat

Punishment of free-riders is generally viewed as an important factor in promoting cooperation. But since it is often costly to sanction exploiters, the emergence of such a behavior and its stability raise interesting problems. Players who do not contribute to the sanctions, but profit from the increased level of cooperation caused by them, act as "second-order exploiters" and threaten the joint enterprise. In this paper, we review the role of voluntary participation in establishing and upholding cooperation with or without punishment. In particular, we deal with two distinct forms of punishment, namely peer punishment and pool punishment, and compare their stability and their efficiency. The emergence and upkeep of collaborative undertakings can strongly depend on whether participation is voluntary or mandatory. The possibility to opt out of a joint enterprise often helps in curbing exploiters and boosting pro-social behavior.Keywords Evolutionary game theory · Public goods games · Cooperation · Costly punishment · Social dilemma · Voluntary interactions For online experimentation, we refer to http://www.hanneloredesilva.at/sanctions and the VirtualLabs at

Cooperation in joint enterprises poses a social dilemma. How can altruistic behavior be sustained if selfish alternatives provide a higher payoff? This social dilemma can be overcome by the threat of sanctions. But a sanctioning system is itself a public good and poses a second-order social dilemma. In this paper, we show by means of deterministic and stochastic evolutionary game theory that imitation-driven evolution can lead to the emergence of cooperation based on punishment, provided the participation in the joint enterprise is not compulsory. This surprising result-cooperation can be enforced if participation is voluntary-holds even in the case of 'strong altruism', when the benefits of a player's contribution are reaped by the other participants only.