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Karl Sigmund

Publications and source records attributed to Karl Sigmund.

15 recordsLinked to original sources
PubMed2005

Punishing and abstaining for public goods.

The evolution of cooperation within sizable groups of nonrelated humans offers many challenges for our understanding. Current research has highlighted two factors boosting cooperation in public goods interactions, namely, costly punishment of defectors and the option to abstain from the joint enterprise. A recent modeling approach has suggested that the autarkic option acts as a catalyzer for the ultimate fixation of altruistic punishment. We present an alternative, more microeconomically based model that yields a bistable outcome instead. Evolutionary dynamics can lead either to a Nash equilibrium of punishing and nonpunishing cooperators or to an oscillating state without punishers.

Altruism↗
PubMed2005

The good, the bad and the discriminator--errors in direct and indirect reciprocity.

This paper presents, in a series of simple diagrams, concise results about the replicator dynamics of direct and indirect reciprocity. We consider repeated interactions between donors and recipients, and analyse the relationship between three basic strategies for the donor: unconditional cooperation, all-out defection, and conditional cooperation. In other words, we investigate the competition of discriminating and indiscriminating altruists with defectors. Discriminators and defectors form a bistable community, and hence a population of discriminators cannot be invaded by defectors. But unconditional altruists can invade a discriminating population and 'soften it up' for a subsequent invasion by defectors. The resulting dynamics exhibits various forms of rock-paper-scissors cycles and depends in subtle ways on noise, in the form of errors in implementation. The probability for another round (in the case of direct reciprocity), and information about the co-player (in the case of indirect reciprocity), add further elements to the ecology of reciprocation.

Altruism↗
PubMed2005

Evolution of indirect reciprocity.

Natural selection is conventionally assumed to favour the strong and selfish who maximize their own resources at the expense of others. But many biological systems, and especially human societies, are organized around altruistic, cooperative interactions. How can natural selection promote unselfish behaviour? Various mechanisms have been proposed, and a rich analysis of indirect reciprocity has recently emerged: I help you and somebody else helps me. The evolution of cooperation by indirect reciprocity leads to reputation building, morality judgement and complex social interactions with ever-increasing cognitive demands.

Altruism↗
PubMed2005

Indirect reciprocity, image scoring, and moral hazard.

Whether one-shot interactions can stably sustain mutual cooperation if they are based on a minimal form of reputation building has been the subject of considerable debate. We show by mathematical modeling that the answer is positive if we assume an individual's social network evolves in time. In this case, a stable mixture of discriminating and undiscriminating altruists can be proof against invasion by defectors. This sheds light on current discussions about the merits of different types of moral assessment, an issue where theoretical arguments and experimental findings seem at odds.Unexpectedly, our approach also relates to the proverbial observation that people tend to become more tightfisted with age.

Journal Article↗
PubMed2004

The logic of reprobation: assessment and action rules for indirect reciprocation.

Ever since image-based models for indirect reciprocity were introduced, the relative merits of scoring vs. standing have been discussed to find out how important it is to differentiate between justified and non-justified defections. This is analogous to the question whether punishment can sustain cooperation even when it is costly. We show that an answer to this question can depend on details of the model, for instance concerning the probability distribution of the number of interactions experienced per player. We use extensive individual-based simulations to compare scoring, standing and other forms of assessing defections, and show that several forms of indirect reciprocation can robustly sustain cooperation. By most standards, standing is better than scoring, but nevertheless scoring is able to sustain cooperation in the presence of errors. The model presented here is based on three specifications: each player has a personal list of images of all co-players, a specific way of judging an observed situation, and a specific strategy to decide whether to cooperate or not.

Biological Evolution↗
PubMed2004

Karl Sigmund.

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Biological Evolution↗
PubMed2004

Evolutionary dynamics of biological games.

Darwinian dynamics based on mutation and selection form the core of mathematical models for adaptation and coevolution of biological populations. The evolutionary outcome is often not a fitness-maximizing equilibrium but can include oscillations and chaos. For studying frequency-dependent selection, game-theoretic arguments are more appropriate than optimization algorithms. Replicator and adaptive dynamics describe short- and long-term evolution in phenotype space and have found applications ranging from animal behavior and ecology to speciation, macroevolution, and human language. Evolutionary game theory is an essential component of a mathematical and computational approach to biology.

Adaptation, Biological↗
PubMed2003

Punishment and reputation in spatial public goods games.

The puzzle of the emergence of cooperation between unrelated individuals is shared across diverse fields of behavioural sciences and economics. In this article we combine the public goods game originating in economics with evolutionary approaches traditionally used in biology. Instead of pairwise encounters, we consider the more complex case of groups of three interacting individuals. We show that territoriality is capable of promoting cooperative behaviour, as in the case of the Prisoner's Dilemma. Moreover, by adding punishment opportunities, the readiness to cooperate is greatly enhanced and asocial strategies can be largely suppressed. Finally, as soon as players carry a reputation for being willing or unwilling to punish, highly cooperative and fair outcomes are achieved. This group-beneficial result is obtained, intriguingly, by making individuals more likely to exploit their co-players if they can get away with it. Thus, less-cooperative individuals make more-cooperative societies.

Animals↗
PubMed2002

Replicator dynamics for optional public good games.

The public goods game represents a straightforward generalization of the prisoner's dilemma to an arbitrary number of players. Since the dominant strategy is to defect, both classical and evolutionary game theory predict the asocial outcome that no player contributes to the public goods. In contrast to the compulsory public goods game, optional participation provides a natural way to avoid deadlocks in the state of mutual defection. The three resulting strategies--collaboration or defection in the public goods game, as well as not joining at all--are studied by means of a replicator dynamics, which can be completely analysed in spite of the fact that the payoff terms are nonlinear. If cooperation is valuable enough, the dynamics exhibits a rock-scissors-paper type of cycling between the three strategies, leading to sizeable average levels of cooperation in the population. Thus, voluntary participation makes cooperation feasible. But for each strategy, the average payoff value remains equal to the earnings of those not participating in the public goods game.

Altruism↗
PubMed2002

Volunteering as Red Queen mechanism for cooperation in public goods games.

The evolution of cooperation among nonrelated individuals is one of the fundamental problems in biology and social sciences. Reciprocal altruism fails to provide a solution if interactions are not repeated often enough or groups are too large. Punishment and reward can be very effective but require that defectors can be traced and identified. Here we present a simple but effective mechanism operating under full anonymity. Optional participation can foil exploiters and overcome the social dilemma. In voluntary public goods interactions, cooperators and defectors will coexist. We show that this result holds under very diverse assumptions on population structure and adaptation mechanisms, leading usually not to an equilibrium but to an unending cycle of adjustments (a Red Queen type of evolution). Thus, voluntary participation offers an escape hatch out of some social traps. Cooperation can subsist in sizable groups even if interactions are not repeated, defectors remain anonymous, players have no memory, and assortment is purely random.

Cooperative Behavior↗
PubMed2002

Primer: altruism.

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Altruism↗