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Stern-judging: A simple, successful norm which promotes cooperation under indirect reciprocity.

Pacheco JM, Santos FC, Chalub FA - PLoS Comput. Biol. (2006)

Bottom Line: We employ an evolutionary game theoretical model of multilevel selection, and show that natural selection and mutation lead to the emergence of a robust and simple social norm, which we call stern-judging.Under stern-judging, helping a good individual or refusing help to a bad individual leads to a good reputation, whereas refusing help to a good individual or helping a bad one leads to a bad reputation.Similarly for tit-for-tat and win-stay-lose-shift, the simplest ubiquitous strategies in direct reciprocity, the lack of ambiguity of stern-judging, where implacable punishment is compensated by prompt forgiving, supports the idea that simplicity is often associated with evolutionary success.

View Article: PubMed Central - PubMed

Affiliation: Centro de Física Teórica e Computacional and Departamento de Física da Faculdade de Ciências, Lisbon, Portugal.

ABSTRACT
We study the evolution of cooperation under indirect reciprocity, believed to constitute the biological basis of morality. We employ an evolutionary game theoretical model of multilevel selection, and show that natural selection and mutation lead to the emergence of a robust and simple social norm, which we call stern-judging. Under stern-judging, helping a good individual or refusing help to a bad individual leads to a good reputation, whereas refusing help to a good individual or helping a bad one leads to a bad reputation. Similarly for tit-for-tat and win-stay-lose-shift, the simplest ubiquitous strategies in direct reciprocity, the lack of ambiguity of stern-judging, where implacable punishment is compensated by prompt forgiving, supports the idea that simplicity is often associated with evolutionary success.

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Multilevel Selection Model for the Evolution of NormsEach palette represents a tribe in which inhabitants (coloured dots) employ different strategies (different colours) to play the indirect reciprocity game. Each tribe is influenced by a single social norm (common background colour), which may be different in different tribes. All individuals in each tribe undergo pairwise rounds of the game (lower level of selection, Level 1), whereas all tribes also engage in pairwise conflicts (higher level of selection, Level 2), as described in the main text. As a result of the conflicts between tribes, norms evolve, whereas evolution inside each tribe selects the distribution of strategies that best adapt to the ruling social norm in each tribe.
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pcbi-0020178-g001: Multilevel Selection Model for the Evolution of NormsEach palette represents a tribe in which inhabitants (coloured dots) employ different strategies (different colours) to play the indirect reciprocity game. Each tribe is influenced by a single social norm (common background colour), which may be different in different tribes. All individuals in each tribe undergo pairwise rounds of the game (lower level of selection, Level 1), whereas all tribes also engage in pairwise conflicts (higher level of selection, Level 2), as described in the main text. As a result of the conflicts between tribes, norms evolve, whereas evolution inside each tribe selects the distribution of strategies that best adapt to the ruling social norm in each tribe.

Mentions: Let us consider a world in black and white consisting of a set of tribes, such that each tribe lives under the influence of a single norm, common to all individuals (see Figure 1). Each individual engages once in the indirect reciprocity game (cf. Methods) with all other tribe inhabitants. Her action as a donor will depend on her individual strategy, which dictates whether she will provide help or refuse to do it depending on her and the recipient's reputation. Reputations are public: this means that the result of every interaction is made available to everyone through the “indirect observation model” introduced in [13] (see also [15]). This allows any individual to know the current status of the co-player without observing all of her past interactions. On the other hand, this requires a way to spread the information (even with errors) to the entire population (communication/language). Consistently, language seems to be an important cooperation promoter [22], although recent mechanisms of reputation-spreading rely on electronic databases (e.g., in e-trade, where reputation of sellers is centralized). Since reputations are either GOOD or BAD, there are 24 = 16 possible strategies. On the other hand, the number of possible norms depends on their associated order. The simplest are the so-called first-order norms, in which all that matters is the action taken by the donor. In second-order norms, the reputation of one of the players (donor or recipient) also contributes to decide the new reputation of the donor. And so on, in increasing layers of complexity (and associated requirements of cognitive capacities from individuals) as shown in Figure 2, which illustrates the features of third-order norms such as those we shall employ here. Any individual in the tribe shares the same norm, which in turn raises the question of how each inhabitant acquired it. We do not address this issue here. However, inasmuch as indirect reciprocity is associated with “community enforcement” [9,10], one may assume, for simplicity, that norms are acquired through an educational process. Moreover, it is likely that a common norm contributes to the overall cohesiveness and identity of a tribe. It is noteworthy, however, that if norms were different for different individuals, the “indirect observation model” would not be valid, as it requires trust in judgments made by co-inhabitants. For a norm of order n, there are possible norms, each associated with a binary string of length 2n. We consider third-order norms (8-bit strings, Figure 2): in assessing a donor's new reputation, the observer has to make a contextual judgment involving the donor's action, as well as her and the recipient's reputations scored in the previous action. We introduce the following evolutionary dynamics in each tribe: during one generation all individuals interact once with each other via the indirect reciprocity game. When individuals “reproduce,” they replace their strategy by that of another individual from the same tribe, chosen proportional to her accumulated payoff [12]. The most successful individuals in each tribe have a higher reproductive success. Since different tribes are “under the influence” of different norms, the overall fitness of each tribe will vary from tribe to tribe, as well as the plethora of successful strategies that thrive in each tribe (Figure 1). This describes individual selection in each tribe (Level 1 in Figure 1).


Stern-judging: A simple, successful norm which promotes cooperation under indirect reciprocity.

Pacheco JM, Santos FC, Chalub FA - PLoS Comput. Biol. (2006)

Multilevel Selection Model for the Evolution of NormsEach palette represents a tribe in which inhabitants (coloured dots) employ different strategies (different colours) to play the indirect reciprocity game. Each tribe is influenced by a single social norm (common background colour), which may be different in different tribes. All individuals in each tribe undergo pairwise rounds of the game (lower level of selection, Level 1), whereas all tribes also engage in pairwise conflicts (higher level of selection, Level 2), as described in the main text. As a result of the conflicts between tribes, norms evolve, whereas evolution inside each tribe selects the distribution of strategies that best adapt to the ruling social norm in each tribe.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC1761656&req=5

pcbi-0020178-g001: Multilevel Selection Model for the Evolution of NormsEach palette represents a tribe in which inhabitants (coloured dots) employ different strategies (different colours) to play the indirect reciprocity game. Each tribe is influenced by a single social norm (common background colour), which may be different in different tribes. All individuals in each tribe undergo pairwise rounds of the game (lower level of selection, Level 1), whereas all tribes also engage in pairwise conflicts (higher level of selection, Level 2), as described in the main text. As a result of the conflicts between tribes, norms evolve, whereas evolution inside each tribe selects the distribution of strategies that best adapt to the ruling social norm in each tribe.
Mentions: Let us consider a world in black and white consisting of a set of tribes, such that each tribe lives under the influence of a single norm, common to all individuals (see Figure 1). Each individual engages once in the indirect reciprocity game (cf. Methods) with all other tribe inhabitants. Her action as a donor will depend on her individual strategy, which dictates whether she will provide help or refuse to do it depending on her and the recipient's reputation. Reputations are public: this means that the result of every interaction is made available to everyone through the “indirect observation model” introduced in [13] (see also [15]). This allows any individual to know the current status of the co-player without observing all of her past interactions. On the other hand, this requires a way to spread the information (even with errors) to the entire population (communication/language). Consistently, language seems to be an important cooperation promoter [22], although recent mechanisms of reputation-spreading rely on electronic databases (e.g., in e-trade, where reputation of sellers is centralized). Since reputations are either GOOD or BAD, there are 24 = 16 possible strategies. On the other hand, the number of possible norms depends on their associated order. The simplest are the so-called first-order norms, in which all that matters is the action taken by the donor. In second-order norms, the reputation of one of the players (donor or recipient) also contributes to decide the new reputation of the donor. And so on, in increasing layers of complexity (and associated requirements of cognitive capacities from individuals) as shown in Figure 2, which illustrates the features of third-order norms such as those we shall employ here. Any individual in the tribe shares the same norm, which in turn raises the question of how each inhabitant acquired it. We do not address this issue here. However, inasmuch as indirect reciprocity is associated with “community enforcement” [9,10], one may assume, for simplicity, that norms are acquired through an educational process. Moreover, it is likely that a common norm contributes to the overall cohesiveness and identity of a tribe. It is noteworthy, however, that if norms were different for different individuals, the “indirect observation model” would not be valid, as it requires trust in judgments made by co-inhabitants. For a norm of order n, there are possible norms, each associated with a binary string of length 2n. We consider third-order norms (8-bit strings, Figure 2): in assessing a donor's new reputation, the observer has to make a contextual judgment involving the donor's action, as well as her and the recipient's reputations scored in the previous action. We introduce the following evolutionary dynamics in each tribe: during one generation all individuals interact once with each other via the indirect reciprocity game. When individuals “reproduce,” they replace their strategy by that of another individual from the same tribe, chosen proportional to her accumulated payoff [12]. The most successful individuals in each tribe have a higher reproductive success. Since different tribes are “under the influence” of different norms, the overall fitness of each tribe will vary from tribe to tribe, as well as the plethora of successful strategies that thrive in each tribe (Figure 1). This describes individual selection in each tribe (Level 1 in Figure 1).

Bottom Line: We employ an evolutionary game theoretical model of multilevel selection, and show that natural selection and mutation lead to the emergence of a robust and simple social norm, which we call stern-judging.Under stern-judging, helping a good individual or refusing help to a bad individual leads to a good reputation, whereas refusing help to a good individual or helping a bad one leads to a bad reputation.Similarly for tit-for-tat and win-stay-lose-shift, the simplest ubiquitous strategies in direct reciprocity, the lack of ambiguity of stern-judging, where implacable punishment is compensated by prompt forgiving, supports the idea that simplicity is often associated with evolutionary success.

View Article: PubMed Central - PubMed

Affiliation: Centro de Física Teórica e Computacional and Departamento de Física da Faculdade de Ciências, Lisbon, Portugal.

ABSTRACT
We study the evolution of cooperation under indirect reciprocity, believed to constitute the biological basis of morality. We employ an evolutionary game theoretical model of multilevel selection, and show that natural selection and mutation lead to the emergence of a robust and simple social norm, which we call stern-judging. Under stern-judging, helping a good individual or refusing help to a bad individual leads to a good reputation, whereas refusing help to a good individual or helping a bad one leads to a bad reputation. Similarly for tit-for-tat and win-stay-lose-shift, the simplest ubiquitous strategies in direct reciprocity, the lack of ambiguity of stern-judging, where implacable punishment is compensated by prompt forgiving, supports the idea that simplicity is often associated with evolutionary success.

Show MeSH