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Martin A. Nowak - One of the best experts on this subject based on the ideXlab platform.

  • a unified framework of Direct and inDirect Reciprocity
    Nature Human Behaviour, 2021
    Co-Authors: Laura Schmid, Krishnendu Chatterjee, Christian Hilbe, Martin A. Nowak
    Abstract:

    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 studied in isolation. Here, we introduce a mathematical framework that allows us to explore both kinds of Reciprocity simultaneously. We show that the well-known 'generous tit-for-tat' strategy of Direct Reciprocity has a natural analogue in inDirect Reciprocity, which we call 'generous scoring'. Using an equilibrium analysis, we characterize under which conditions either of the two strategies can maintain cooperation. With simulations, we additionally explore which kind of Reciprocity evolves when members of a population engage in social learning to adapt to their environment. Our results draw unexpected connections between Direct and inDirect Reciprocity while highlighting important differences regarding their evolvability.

  • Publisher Correction: Partners and rivals in Direct Reciprocity.
    Nature human behaviour, 2018
    Co-Authors: Christian Hilbe, Krishnendu Chatterjee, Martin A. Nowak
    Abstract:

    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.

  • Partners and rivals in Direct Reciprocity.
    Nature human behaviour, 2018
    Co-Authors: Christian Hilbe, Krishnendu Chatterjee, Martin A. Nowak
    Abstract:

    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 beautiful surprises. Recent theoretical research driven by new mathematical tools has proposed a remarkable dichotomy among the crucial strategies: successful individuals either act as partners or as rivals. Rivals strive for unilateral advantages by applying selfish or extortionate strategies. Partners aim to share the payoff for mutual cooperation, but are ready to fight back when being exploited. Which of these behaviours evolves depends on the environment. Whereas small population sizes and a limited number of rounds favour rivalry, partner strategies are selected when populations are large and relationships stable. Only partners allow for evolution of cooperation, while the rivals’ attempt to put themselves first leads to defection. Hilbe et al. synthesize recent theoretical work on zero-determinant and ‘rival’ versus ‘partner’ strategies in social dilemmas. They describe the environments under which these contrasting selfish or cooperative strategies emerge in evolution.

  • Memory-n strategies of Direct Reciprocity.
    Proceedings of the National Academy of Sciences of the United States of America, 2017
    Co-Authors: Christian Hilbe, Martin A. Nowak, Krishnendu Chatterjee, Luis A. Martinez-vaquero
    Abstract:

    Humans routinely use conditionally cooperative strategies when interacting in repeated social dilemmas. They are more likely to cooperate if others cooperated before, and are ready to retaliate if others defected. To capture the emergence of Reciprocity, most previous models consider subjects who can only choose from a restricted set of representative strategies, or who react to the outcome of the very last round only. As players memorize more rounds, the dimension of the strategy space increases exponentially. This increasing computational complexity renders simulations for individuals with higher cognitive abilities infeasible, especially if multiplayer interactions are taken into account. Here, we take an axiomatic approach instead. We propose several properties that a robust cooperative strategy for a repeated multiplayer dilemma should have. These properties naturally lead to a unique class of cooperative strategies, which contains the classical Win–Stay Lose–Shift rule as a special case. A comprehensive numerical analysis for the prisoner’s dilemma and for the public goods game suggests that strategies of this class readily evolve across various memory-n spaces. Our results reveal that successful strategies depend not only on how cooperative others were in the past but also on the respective context of cooperation.

  • Comparing reactive and memory-one strategies of Direct Reciprocity
    Scientific reports, 2016
    Co-Authors: Seung Ki Baek, Hyeong-chai Jeong, Christian Hilbe, Martin A. Nowak
    Abstract:

    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 the right response. However, there are natural bounds on strategic complexity: Humans find it difficult to remember past interactions accurately, especially over long timespans. Given these limitations, it is natural to ask how complex strategies need to be for cooperation to evolve. Here, we study stochastic evolutionary game dynamics in finite populations to systematically compare the evolutionary performance of reactive strategies, which only respond to the co-player's previous move, and memory-one strategies, which take into account the own and the co-player's previous move. In both cases, we compare deterministic strategy and stochastic strategy spaces. For reactive strategies and small costs, we find that stochasticity benefits cooperation, because it allows for generous-tit-for-tat. For memory one strategies and small costs, we find that stochasticity does not increase the propensity for cooperation, because the deterministic rule of win-stay, lose-shift works best. For memory one strategies and large costs, however, stochasticity can augment cooperation.

Bonaventura Majolo - One of the best experts on this subject based on the ideXlab platform.

  • Evidence of Direct Reciprocity, but not of inDirect and generalized Reciprocity, in the grooming exchanges of wild Barbary macaques (Macaca sylvanus).
    American journal of primatology, 2017
    Co-Authors: Sandra Molesti, Bonaventura Majolo
    Abstract:

    Reciprocity is one of the mechanisms that have been proposed to explain the exchange of social behaviors, such as grooming, in animals. Reciprocity assumes that individuals act as the donor and recipient of grooming and switch roles over time to balance the benefits and costs of this behavior. Three main patterns of Reciprocity may follow a grooming given: (i) Direct Reciprocity, where the former recipient returns the grooming to the former donor; (ii) inDirect Reciprocity, where another individual returns the grooming to the former donor; and (iii) generalized Reciprocity, where the former recipient returns the grooming to another individual. While there is evidence that Direct Reciprocity plays an important role in various species of animals, the role of inDirect and generalized Reciprocity is less clear and has been rarely analyzed. We tested the role of Direct, inDirect, and generalized Reciprocity in explaining grooming exchanges of wild Barbary macaques, by analyzing the temporal contingency between giving and receiving grooming. We collected the occurrence and latency of the three types of grooming reciprocation during 1 hr long focal sessions run simultaneously on two partners who just stopped grooming (post-grooming session) or who were in proximity (i.e., within 1.5 m) without grooming each other (control session). We ran the analyses on 284 post-grooming and 63 control sessions. The results revealed a temporal contingency of grooming interactions exchanged according to Direct Reciprocity but not according to inDirect or generalized Reciprocity. Our results indicate that grooming distribution in Barbary macaques is partner-specific. We discuss the possible role of cognition and emotions in explaining Direct Reciprocity in animals.

  • Testing the role of Direct, inDirect and generalised Reciprocity in grooming exchanges of wild Barbary macaques
    2013
    Co-Authors: Sandra Molesti, Bonaventura Majolo
    Abstract:

    In non-human primates, grooming is thought to be a costly activity for the donor and beneficial for the recipient. Reciprocity assumes that individuals act as the donor and recipient of grooming and switch roles over time to balance the benefits and costs. Three main patterns of Reciprocity may follow a grooming given by A to B: (1) Direct Reciprocity, where B return the grooming to A; (2) inDirect Reciprocity, where individual C, not involved in the former grooming between A and B, grooms A; and (3) generalized Reciprocity, where B grooms any individual including A. We tested the role of Direct, inDirect, and generalized Reciprocity in explaining grooming exchanges of wild Barbary macaques. We collected the occurrence and latency of the three types of grooming Reciprocity during one hour focal session run simultaneously on two partners who just stopped grooming (post-grooming session) or who were in proximity (i.e. within 1.5 meters) without grooming (control session). We ran the analyses on 284 post-grooming sessions and 63 control sessions. Directly reciprocated grooming from B to A was more likely to occur, and occurred earlier when A had previously groomed B than in control sessions. We found no evidence for inDirect or generalised Reciprocity. Our results indicate that grooming distribution in Barbary macaques is partnerspecific and occurs according to Direct Reciprocity. Such partner specificity can explain the lack of evidence for generalised Reciprocity, whereas inDirect Reciprocity may be too cognitively demanding to occur in macaques.

  • The relative prevalence of Direct, inDirect and generalized Reciprocity in macaque grooming exchanges
    Animal Behaviour, 2012
    Co-Authors: Bonaventura Majolo, Gabriele Schino, Filippo Aureli
    Abstract:

    Reciprocation is thought to favour altruism among nonrelatives. Three types of Reciprocity have been proposed: Direct, inDirect and generalized. All three are theoretically possible, but their role in real biological systems is unclear. We concurrently examined the occurrence of Direct, inDirect and generalized Reciprocity during grooming exchanges in longtailed macaques, Macaca fascicularis. The occurrence of the grooming monkey A gave B predicted the latency and occurrence of the grooming B gave back to A (Direct Reciprocity), the latency of the grooming A received from C (inDirect Reciprocity), but not the grooming B gave C (generalized Reciprocity). The duration of the grooming monkey A gave B predicted the latency and occurrence of the grooming B gave back to A (Direct Reciprocity) but not the grooming A received from C (inDirect Reciprocity) or the grooming B gave C (generalized Reciprocity). Finally, monkeys Directed overall more of their grooming to those individuals that overall groomed them more (Direct Reciprocity), but not to those that groomed other individuals more (inDirect Reciprocity); nor did monkeys that received overall more grooming groom others more (generalized Reciprocity). Overall, we found strong evidence for Direct Reciprocity, limited support for inDirect Reciprocity and no evidence for generalized Reciprocity. Our results support the view that Direct Reciprocity plays a crucial role in the life of primates and suggest inDirect and generalized Reciprocity are rare or absent in nonhuman animals. We argue that Direct Reciprocity may be driven by a system of partner-specific emotional bookkeeping of past social interactions that does not require complex cognitive capacities.

Michael Taborsky - One of the best experts on this subject based on the ideXlab platform.

  • Rats show Direct Reciprocity when interacting with multiple partners
    Scientific reports, 2021
    Co-Authors: Nina Kettler, Manon K. Schweinfurth, Michael Taborsky
    Abstract:

    Direct Reciprocity, where individuals apply the decision rule ‘help someone who has helped you’, is believed to be rare in non-human animals due to its high cognitive demands. Especially if previous encounters with several partners need to be correctly remembered, animals might either stop reciprocating favours previously received from an individual, or switch to the simpler generalized Reciprocity mechanism. Here we tested the decision rules Norway rats apply when interacting with multiple partners before being able to return received help. In a sequential prisoner’s dilemma situation, focal subjects encountered four different partners that were either helpful or not, on four consecutive days. On the fifth day, the focal subject was paired with one of the previous four partners and given the opportunity to provide it with food. The focal rats returned received help by closely matching the quantity of help their partner had previously provided, independently of the time delay between received and given help, and independently of the ultimate interaction preceding the test. This shows that Direct Reciprocity is not limited to dyadic situations in Norway rats, suggesting that cognitive demands involved in applying the required decision rules can be met by non-human animals even when they interact with multiple partners differing in helping propensity.

  • male norway rats cooperate according to Direct but not generalized Reciprocity rules
    Animal Behaviour, 2019
    Co-Authors: Manon K. Schweinfurth, Jonathan Aeschbacher, Massimiliano Santi, Michael Taborsky
    Abstract:

    Reciprocal cooperation may evolve if the costs of help are reliably compensated for by delayed returns provided in future interactions. The associated probabilities and cost–benefit ratios may vary systematically between the sexes, which often display different dispersal strategies and interaction patterns. Whereas female Norway rats, Rattus norvegicus, are known to apply Direct and generalized decision rules of reciprocal cooperation, the rules according to which males reciprocate favours are less well understood. Therefore, we investigated the cooperation propensity of male wild-type Norway rats. Male test rats experienced cooperating partners that provided food to them, or defecting partners that refused to provide help. Afterwards, test rats could donate food to previously experienced or unknown partners, resembling Direct and generalized Reciprocity paradigms, respectively. Male rats cooperated according to Direct Reciprocity, suggesting that this decision rule is similarly important for both sexes. However, whereas females additionally help according to generalized Reciprocity, males did not apply this rule. These results suggest a sex difference in reciprocal decision rules, highlighting the potential importance of different interaction patterns and cost–benefit ratios between the sexes.

  • The influence of social experience on cooperative behaviour of rats (Rattus norvegicus): Direct vs generalised Reciprocity
    Behavioral Ecology and Sociobiology, 2008
    Co-Authors: Claudia Rutte, Michael Taborsky
    Abstract:

    Cooperation among non-kin has been attributed sometimes to reciprocal altruism: Two or more individuals exchange behaviour that benefits the respective partner. According to Direct Reciprocity, cooperation is based on past behaviour of a known partner. In contrast, in generalised Reciprocity, cooperation is based on anonymous social experience where the identity of the partner is irrelevant. In a previous study, female Norway rats ( Rattus norvegicus ) were found to cooperate according to a generalised Reciprocity mechanism. In this study, we tested whether Norway rats would also cooperate as predicted by a Direct Reciprocity mechanism and whether Direct Reciprocity would cause a higher propensity to cooperate than generalised Reciprocity. Focal animals were experimentally manipulated to receive social experience from known or unknown, helpful or defecting partners in an instrumental cooperative task. Our first experiment shows that rats are more helpful towards a partner from which they had received help before than towards a partner that had not helped (i.e. Direct Reciprocity). Our second experiment revealed that after receiving help by others, rats were more helpful towards a partner from which they had received help before than towards a new partner (i.e. Direct Reciprocity generated a higher cooperation propensity than generalised Reciprocity). We conclude that in female Norway rats, the tendency to cooperate is influenced by partner-specific information. To our knowledge, this is the first study to demonstrate Direct Reciprocity in rodents, and it is the first study testing Direct vs generalised Reciprocity in animals.

Matthew R. Zefferman - One of the best experts on this subject based on the ideXlab platform.

  • Direct Reciprocity Under Uncertainty Does Not Explain One-shot Cooperation, but Demonstrates the Benefits of a Norm Psychology
    2014
    Co-Authors: Matthew R. Zefferman
    Abstract:

    Humans in many societies cooperate in economic experiments at much higher levels than would be expected if their goal was maximizing economic returns, even when their interactions are anonymous and one-shot. This is a puzzle because paying a cost to benefit another in one-shot interactions gives no Direct or inDirect benefits to the cooperator. This paper explores the logic of two competing evolutionary hypotheses to explain this behavior. The "norm psychology" hypothesis holds that a player9s choice of strategy reflects socially-learned cultural norms. Its premise is that over the course of human evolutionary history, cultural norms varied considerably across human societies and through a process of gene-culture co-evolution, humans evolved mechanisms to learn and adopt the norms that are successful in their particular society. The "mismatch" hypothesis holds that pro-social preferences evolved genetically in our hunter-gatherer past where one-shot anonymous interactions were rare and these preferences are misapplied in modern laboratory settings. I compare these hypotheses by adopting a well-known model of the mismatch hypothesis and show that selection for one-shot cooperation in the model is an artifact of agents being constrained to only two strategies: Tit-for-Tat and Always Defect. Allowing for repentant and forgiving strategies reverses selection away from one-shot cooperation under all environmental parameters. Direct Reciprocity does not necessarily lead to cooperation, but instead generates many different normative equilibria depending on a group9s idiosyncratic evolutionary history. Therefore, an agent whose behavior is evoked solely from non-cultural environmental cues will be disadvantaged relative to an agent who learns the locally successful norms. Cooperation in one-shot laboratory experiments is thus more easily explained as the result of a psychology evolved for learning social norms than as a genetic mismatch.

  • Direct Reciprocity under uncertainty does not explain one-shot cooperation, but demonstrates the benefits of a norm psychology
    Evolution and Human Behavior, 2014
    Co-Authors: Matthew R. Zefferman
    Abstract:

    article i nfo Article history: Initial receipt 23 October 2013 Final revision received 17 April 2014 Humans in many societies cooperate in economic experiments at much higher levels than would be expected if their goal was maximizing economic returns, even when their interactions are anonymous and one-shot. This is a puzzle because paying a cost to benefit another in one-shot interactions gives no Direct or inDirect benefits to the cooperator. This paper explores the logic of two competing evolutionary hypotheses to explain this behavior. The ``norm psychology'' hypothesis holds that a player's choice of strategy reflects socially- learned cultural norms. Its premise is that over the course of human evolutionary history, cultural norms varied considerably across human societies, and through a process of gene-culture co-evolution, humans evolved mechanisms to learn and adopt the norms that are successful in their particular society. The ``mismatch'' hypothesis holds that pro-social preferences evolved genetically in our hunter-gatherer past where one-shot anonymous interactions were rare and these preferences are misapplied in modern laboratory settings. I compare these hypotheses by adopting a well-known model of the mismatch hypothesis and show that selection for one-shot cooperation in the model is an artifact of agents being confined to only two strategies: Tit-for-Tat and Always Defect. Allowing for repentant and forgiving strategies reverses selection away from one-shot cooperation under all environmental parameters. Direct Reciprocity does not necessarily lead to cooperation, but instead generates many different normative equilibria depending on a group's idiosyncratic evolutionary history. Therefore, an agent whose behavior is evoked solely from non- cultural environmental cues will be disadvantaged relative to an agent who learns the locally successful norms. Cooperation in one-shot laboratory experiments is thus more easily explained as the result of a psychology evolved for learning social norms than as a genetic mismatch.

  • Direct Reciprocity Under Uncertainty Does Not Explain One-Shot Cooperation, But It Can Explain Norm Psychology
    2013
    Co-Authors: Matthew R. Zefferman
    Abstract:

    Humans in many societies cooperate in economic experiments at much higher levels than would be expected if their goal was maximizing economic returns even when interactions are anonymous and one-shot. This is a puzzle because paying a cost to benefit another player in one-shot interactions has no Direct benefit to the cooperator. This paper explores the logic of two competing evolutionary hypotheses to explain this behavior. The "norm psychology" hypothesis holds that a player's choice of strategy is heavily influenced by socially-learned cultural norms. Its premise is that over the course of human evolutionary history, cultural norms varied considerably across human societies and through a process of gene-culture co-evolution, humans evolved mechanisms to learn and adopt the norms of their particular society. The "evolutionary mismatch" hypothesis holds that pro-social preferences evolved genetically in our hunter-gatherer past where one-shot anonymous interactions were rare and these evolved "protocols" for cooperation are misapplied in modern, laboratory, conditions. I compare these hypotheses by adopting a well known model of the mismatch hypothesis. I show that the cooperation generated by the model is based on a flawed assumption - that the best thing to do is cooperate in a repeated game. I show that repeated games generate a great diversity of behavioral equilibria, in support of the norm psychology hypothesis's premise. When interaction is repeated, adopting local norms is a more evolutionarily successful strategy than automatically cooperating. If various groups are at different behavioral equilibria, then cultural selection between groups tends to select for cooperative behavior.

Seung Ki Baek - One of the best experts on this subject based on the ideXlab platform.

  • Five rules for friendly rivalry in Direct Reciprocity
    Scientific reports, 2020
    Co-Authors: Yohsuke Murase, Seung Ki Baek
    Abstract:

    Direct Reciprocity is one of the key mechanisms accounting for cooperation in our social life. According to recent understanding, most of classical strategies for Direct Reciprocity fall into one of two classes, `partners' or `rivals'. A `partner' is a generous strategy achieving mutual cooperation, and a `rival' never lets the co-player become better off. They have different working conditions: For example, partners show good performance in a large population, whereas rivals do in head-to-head matches. By means of exhaustive enumeration, we demonstrate the existence of strategies that act as both partners and rivals. Among them, we focus on a human-interpretable strategy, named `CAPRI' after its five characteristic ingredients, i.e., cooperate, accept, punish, recover, and defect otherwise. Our evolutionary simulation shows excellent performance of CAPRI in a broad range of environmental conditions.

  • Five rules for friendly rivalry in Direct Reciprocity
    2020
    Co-Authors: Murase Yohsuke, Seung Ki Baek
    Abstract:

    Direct Reciprocity is one of the key mechanisms accounting for cooperation in our social life. According to recent understanding, most of classical strategies for Direct Reciprocity fall into one of two classes, `partners' or `rivals'. A `partner' is a generous strategy achieving mutual cooperation, and a `rival' never lets the co-player become better off. They have different working conditions: For example, partners show good performance in a large population, whereas rivals do in head-to-head matches. By means of exhaustive enumeration, we demonstrate the existence of strategies that act as both partners and rivals. Among them, we focus on a human-interpretable strategy, named `CAPRI', which is described by five simple rules. Our evolutionary simulation shows excellent performance of CAPRI in a broad range of environmental conditions.Comment: 35 pages, 8 figure

  • Automata representation of successful strategies for social dilemmas
    2020
    Co-Authors: Murase Yohsuke, Seung Ki Baek
    Abstract:

    A social dilemma appears when defection is individually favored than cooperation although the latter is collectively optimal. A class of successful strategies of Direct Reciprocity were recently found for the iterated prisoner's dilemma [Yi et al., J. Theor. Biol. (2017)] and for the three-person iterated public goods game [Murase and Baek, J. Theor. Biol. (2018)]. A successful strategy forms a cooperative Nash equilibrium in the presence of implementation error while assuring that the long-term payoff never becomes less than the co-players' regardless of their strategies, when the error rate is small. Although we have a list of actions prescribed by the successful strategies, the rationale behind them have not been fully understood. In this paper, we wish to provide a better understanding for the successful strategies by converting them into automata with a minimal number of states. Each of the states becomes interpretable in this representation, whereby one can gain insight into the underlying mechanism.Comment: 19 pages, 7 figure

  • Comparing reactive and memory-one strategies of Direct Reciprocity
    Scientific reports, 2016
    Co-Authors: Seung Ki Baek, Hyeong-chai Jeong, Christian Hilbe, Martin A. Nowak
    Abstract:

    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 the right response. However, there are natural bounds on strategic complexity: Humans find it difficult to remember past interactions accurately, especially over long timespans. Given these limitations, it is natural to ask how complex strategies need to be for cooperation to evolve. Here, we study stochastic evolutionary game dynamics in finite populations to systematically compare the evolutionary performance of reactive strategies, which only respond to the co-player's previous move, and memory-one strategies, which take into account the own and the co-player's previous move. In both cases, we compare deterministic strategy and stochastic strategy spaces. For reactive strategies and small costs, we find that stochasticity benefits cooperation, because it allows for generous-tit-for-tat. For memory one strategies and small costs, we find that stochasticity does not increase the propensity for cooperation, because the deterministic rule of win-stay, lose-shift works best. For memory one strategies and large costs, however, stochasticity can augment cooperation.