Christian Hilbe

Max Planck Institute for Evolutionary Biology · Research Group 'Dynamics of Social Behavior'

Direct reciprocity is a powerful mechanism for the evolution of cooperation based on repeated interactions between the same individuals. But high levels of cooperation evolve only if the benefit-to-cost ratio exceeds a certain threshold that depends on memory length. For the best-explored case of one-round memory, that threshold is two. Here, we re...

Human interactions can take the form of social dilemmas: collectively, people fare best if all cooperate but each individual is tempted to free ride. Social dilemmas can be resolved when individuals interact repeatedly. Repetition allows them to adopt reciprocal strategies which incentivize cooperation. The most basic model for direct reciprocity i...

Many human interactions feature the characteristics of social dilemmas where individual actions have consequences for the group and the environment. The feedback between behavior and environment can be studied with the framework of stochastic games. In stochastic games, the state of the environment can change, depending on the choices made by group...

Cooperation is a crucial aspect of social life, yet understanding the nature of cooperation and how it can be promoted is an ongoing challenge. One mechanism for cooperation is indirect reciprocity. According to this mechanism, individuals cooperate to maintain a good reputation. This idea is embodied in a set of social norms called the "leading ei...

Direct reciprocity is the tendency to repay others' cooperation. This tendency can be crucial to maintain cooperation in evolving populations. Once direct reciprocity evolves, individuals have a long‐run interest to cooperate, even if it is costly in the short run. The major theoretical framework to describe reciprocal behavior is the repeated pris...

The field of indirect reciprocity investigates how social norms can foster cooperation when individuals continuously monitor and assess each other’s social interactions. By adhering to certain social norms, cooperating individuals can improve their reputation and, in turn, receive benefits from others. Eight social norms, known as the “leading eigh...

One landmark application of evolutionary game theory is the study of social dilemmas. This literature explores why people cooperate even when there are strong incentives to defect. Much of this literature, however, assumes that interactions are symmetric. Individuals are assumed to have the same strategic options and the same potential pay-offs. Ye...

Social interactions often take the form of a social dilemma: collectively, individuals fare best if everybody cooperates, yet each single individual is tempted to free ride. Social dilemmas can be resolved when individuals interact repeatedly. Repetition allows individuals to adopt reciprocal strategies which incentivize cooperation. The most basic...

Cooperation is a crucial aspect of social life, yet understanding the nature of cooperation and how it can be promoted is an ongoing challenge. One mechanism for cooperation is indirect reciprocity. According to this mechanism, individuals cooperate to maintain a good reputation. This idea is embodied in a set of social norms called the ``leading e...

People tend to have their social interactions with members of their own community. Such group-structured interactions can have a profound impact on the behaviors that evolve. Group structure affects the way people cooperate, and how they reciprocate each other’s cooperative actions. Past work has shown that population structure and reciprocity can...

Many human interactions feature the characteristics of social dilemmas where individual actions can have consequences for the group and the environment. The feedback between behavior and environment can be studied with the framework of stochastic games. In stochastic games, the state of the environment can change, depending on the choices made by g...

Reciprocity is a simple principle for cooperation that explains many of the patterns of how humans seek and receive help from each other. To capture reciprocity, traditional models often assume that individuals use simple strategies with restricted memory. These memory-1 strategies are mathematically convenient, but they miss important aspects of h...

People routinely cooperate with each other, even when cooperation is costly. To further encourage such pro-social behaviors, recipients often respond by providing additional incentives, for example by offering rewards. Although such incentives facilitate cooperation, the question remains how these incentivizing behaviors themselves evolve, and whet...

People tend to have their social interactions with members of their own community. Such group-structured interactions can have a profound impact on the behaviors that evolve. Group structure affects the way people cooperate, and how they reciprocate each other's cooperative actions. Past work has shown that population structure and reciprocity can...

Across many domains of interaction, both natural and artificial, individuals use past experience to shape future behaviors. The results of such learning processes depend on what individuals wish to maximize. A natural objective is one’s own success. However, when two such “selfish” learners interact with each other, the outcome can be detrimental t...

In repeated interactions, players can use strategies that respond to the outcome of previous rounds. Much of the existing literature on direct reciprocity assumes that all competing individuals use the same strategy space. Here, we study both learning and evolutionary dynamics of players that differ in the strategy space they explore. We focus on t...

Social behavior in human and animal populations can be studied as an evolutionary process. Individuals often make decisions between different strategies, and those strategies that yield a fitness advantage tend to spread. Traditionally, much work in evolutionary game theory considers symmetric games: Individuals are assumed to have access to the sa...

In repeated social interactions, individuals often employ reciprocal strategies to maintain cooperation. To explore the emergence of reciprocity, many theoretical models assume synchronized decision making. In each round, individuals decide simultaneously whether to cooperate or not. Yet many manifestations of reciprocity in nature are asynchronous...

Direct and indirect reciprocity are key mechanisms for the evolution of cooperation. Direct reciprocity means that individuals use their own experience to decide whether to cooperate with another person. Indirect reciprocity means that they also consider the experiences of others. Although these two mechanisms are intertwined, they are typically st...

Indirect reciprocity is a mechanism for the evolution of cooperation based on social norms. This mechanism requires that individuals in a population observe and judge each other’s behaviors. Individuals with a good reputation are more likely to receive help from others. Previous work suggests that indirect reciprocity is only effective when all rel...

Cooperation is crucial for the success of social interactions. Given its importance, humans should readily be able to use available cues to predict how likely others are to cooperate. Here, we review the empirical literature on how accurate such predictions are. To this end, we distinguish between three classes of cues: behavioral (including past d...

Evolutionary game theory offers a general framework to describe how humans revise their behavior in strategic environments. To model this adaptation process, most previous work assumes that individuals aim to increase their own short-run payoff. This kind of "selfish learning," however, entails the risk of getting trapped in equilibria that are det...

Psychologists, economists, historians, computer scientists, sociologists, philosophers, and legal scholars explore the conscious choice not to seek information. The history of intellectual thought abounds with claims that knowledge is valued and sought, yet individuals and groups often choose not to know. We call the conscious choice not to seek or...

Psychologists, economists, historians, computer scientists, sociologists, philosophers, and legal scholars explore the conscious choice not to seek information. The history of intellectual thought abounds with claims that knowledge is valued and sought, yet individuals and groups often choose not to know. We call the conscious choice not to seek or...

Humans routinely engage in many distinct interactions in parallel. Team members collaborate on several concurrent projects, and even whole nations interact with each other across a variety of issues, including trade, climate change and security. Yet the existing theory of direct reciprocity studies isolated repeated games. Such models cannot accoun...

Coinfections with multiple pathogens can result in complex within‐host dynamics affecting virulence and transmission. While multiple infections are intensively studied in solitary hosts, it is so far unresolved how social host interactions interfere with pathogen competition, and if this depends on coinfection diversity. We studied how the collecti...

Direct reciprocity is a powerful mechanism for the evolution of cooperation on the basis of repeated interactions1–4. It requires that interacting individuals are sufficiently equal, such that everyone faces similar consequences when they cooperate or defect. Yet inequality is ubiquitous among humans5,6 and is generally considered to undermine coop...

Significance Indirect reciprocity explores how humans act when their reputation is at stake, and which social norms they use to assess the actions of others. A crucial question in indirect reciprocity is which social norms can maintain stable cooperation in a society. Past research has highlighted eight such norms, called “leading-eight” strategies...

In the version of this Review Article originally published, in Fig. 4 an arrow pointing from ALLC to ALLD was mistakenly omitted. This has now been corrected in all versions of the Review Article.

Social dilemmas occur when incentives for individuals are misaligned with group interests1-7. According to the 'tragedy of the commons', these misalignments can lead to overexploitation and collapse of public resources. The resulting behaviours can be analysed with the tools of game theory8. The theory of direct reciprocity9-15 suggests that repeat...

People sometimes make their admirable deeds and accomplishments hard to spot, such as by giving anonymously or avoiding bragging. Such ‘buried’ signals are hard to reconcile with standard models of signalling or indirect reciprocity, which motivate costly pro-social behaviour by reputational gains. To explain these phenomena, we design a simple gam...

Reciprocity is a major factor in human social life and accounts for a large part of cooperation in our communities. Direct reciprocity arises when repeated interactions occur between the same individuals. The framework of iterated games formalizes this phenomenon. Despite being introduced more than five decades ago, the concept keeps offering beaut...

Direct reciprocity is a mechanism for cooperation among humans. Many of our daily interactions are repeated. We interact repeatedly with our family, friends, colleagues, members of the local and even global community. In the theory of repeated games, it is a tacit assumption that the various games that a person plays simultaneously have no effect o...

Significance When two populations interact, when does it pay to evolve rapidly, and can it ever be an advantage to evolve slowly? We address these questions using evolutionary game theory. In antagonistic interactions (e.g., host–parasite), we find that faster evolution by any means is beneficial—the “Red Queen” effect. In certain mutualisms, slowe...

Significance Direct reciprocity is one of the fundamental mechanisms for cooperation. It is based on the idea that individuals are more likely to cooperate if they can expect their beneficiaries to remember and to return their cooperative acts in future. Previous computational models, however, often had to restrict the number of past rounds subject...

Direct reciprocity is a major mechanism for the evolution of cooperation. Several classical studies have suggested that humans should quickly learn to adopt reciprocal strategies to establish mutual cooperation in repeated interactions. On the other hand, the recently discovered theory of ZD strategies has found that subjects who use extortionate s...

Brood parasites exploit their host in order to increase their own fitness. Typically, this results in an arms race between parasite trickery and host defence. Thus, it is puzzling to observe hosts that accept parasitism without any resistance. The ‘mafia’ hypothesis suggests that these hosts accept parasitism to avoid retaliation. Retaliation has b...

Significance The origins of life required a means for information-containing molecules to compete with one another for survival and reproduction. Using an analysis based on game theory, we can predict the situations in which cooperation, selfishness, or a mixture of the two is beneficial to the future evolutionary success of RNAs.

Social dilemmas force players to balance between personal and collective gain. In many dilemmas, such as elected governments negotiating climate-change mitigation measures, the decisions are made not by individual players but by their representatives. However, the behaviour of representatives in social dilemmas has not been investigated experimenta...

Direct reciprocity is a mechanism for the evolution of cooperation based on repeated interactions. When individuals meet repeatedly, they can use conditional strategies to enforce cooperative outcomes that would not be feasible in one-shot social dilemmas. Direct reciprocity requires that individuals keep track of their past interactions and find t...

We propose a simple model for why we have more trust in people who cooperate without calculating the associated costs. Intuitively, by not looking at the payoffs, people indicate that they will not be swayed by high temptations to defect, which makes them more attractive as interaction partners. We capture this intuition using a simple four-stage g...

Within the class of memory-one strategies for the iterated Prisoner's Dilemma, we characterize partner strategies, competitive strategies and zero-determinant strategies. If a player uses a partner strategy, both players can fairly share the social optimum; but a co-player preferring an unfair solution will be penalized by obtaining a reduced payof...

Repetition is one of the key mechanisms to maintain cooperation. In long-term relationships, in which individuals can react to their peers' past actions, evolution can promote cooperative strategies that would not be stable in one-shot encounters. The iterated prisoner's dilemma illustrates the power of repetition. Many of the key strategies for th...

Significance Many of the world’s most pressing problems, like the prevention of climate change, have the form of a large-scale social dilemma with numerous involved players. Previous results in evolutionary game theory suggest that multiplayer dilemmas make it particularly difficult to achieve mutual cooperation because of the lack of individual co...

In many species, mutual cooperation is stabilized by forms of policing and peer punishment: if cheaters are punished, there is a strong selective pressure to cooperate. Most human societies have complemented, and sometimes even replaced, such peer punishment mechanisms with pool punishment, where punishment is outsourced to central institutions suc...

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...

Mafia like behavior, where individuals cooperate under the threat of punishment, occurs not only in humans, but is also observed in several animal species. Observations suggest that avian hosts tend to accept a certain degree of parasitism in order to avoid retaliating punishment from the brood parasite. To understand under which conditions it will...

Significance Humans usually punish free riders but refuse to sanction those who cooperate but do not punish. However, such second-order punishment is essential to maintain cooperation. The central authorities established in modern societies punish both free riders and tax evaders. This is a paradox: would individuals who do not engage in second-ord...

Business leaders are increasingly responsible for the societal and environmental impacts of their actions. Yet conceptual views on responsible leadership differ in their definitions and theoretical foundations. This study attempts to reconcile these diverse views and uncover the phenomenon from a business leader’s point of view. Based on rational e...

Business leaders are increasingly expected to take on responsibility for the environmental and societal impact of their actions. Yet, conceptual views on responsible leadership differ considerably in their degrees of stakeholder inclusion and definitions of responsibility, and are nurtured by diverse theoretical points of departure. We seek to inte...

Direct reciprocity is a mechanism for the evolution of cooperation. For the iterated prisoner's dilemma, a new class of strategies has recently been described, the so-called zero-determinant strategies. Using such a strategy, a player can unilaterally enforce a linear relationship between his own payoff and the co-player's payoff. In particular the...

In collective-risk dilemmas, a group needs to collaborate over time to avoid a catastrophic event. This gives rise to a coordination game with many equilibria, including equilibria where no one contributes, and thus no measures against the catastrophe are taken. In this game, the timing of contributions becomes a strategic variable that allows indi...

Iterated games are a fundamental component of economic and evolutionary game theory. They describe situations where two players interact repeatedly and have the ability to use conditional strategies that depend on the outcome of previous interactions, thus allowing for reciprocation. Recently, a new class of strategies has been proposed, so-called...

While empirical evidence highlights the importance of punishment for cooperation in collective action, it remains disputed how responsible sanctions targeted predominantly at uncooperative subjects can evolve. Punishment is costly; in order to spread it typically requires local interactions, voluntary participation, or rewards. Moreover, theory and...

Humans are characterized by a high propensity for cooperation. The emergence and stability of this trait is one of the hottest topics in evolutionary game theory, and leads to a wide variety of models offering a rich source of complex dynamics based on social interactions. This chapter offers an overview of different approaches to this topic (such...

Experimental economics has repeatedly demonstrated that the Nash equilibrium makes inaccurate predictions for a vast set of games. Instead, several alternative theoretical concepts predict behavior that is much more in tune with observed data, with the quantal response equilibrium as the most prominent example. However, here we show that this equil...

Classical replicator dynamics assumes that individuals play their games and adopt new strategies on a global level: Each player interacts with a representative sample of the population and if a strategy yields a payoff above the average, then it is expected to spread. In this article, we connect evolutionary models for infinite and finite populatio...

Cooperation in public good games is greatly promoted by positive and negative incentives. In this paper, we use evolutionary game dynamics to study the evolution of opportunism (the readiness to be swayed by incentives) and the evolution of trust (the propensity to cooperate in the absence of information on the co-players). If both positive and neg...

In search of strategies that boost cooperation in the iterated prisoner's dilemma game (IPD), Contrite Tit for Tat is a promising candidate. It combines the necessary rigor in handling selfish strategies with contrition whenever the player has exploited its coplayer inadvertently. This paper shows that, contrary to conventional wisdom, Contrite Tit...