The intricate geometry of zero-determinant strategies underlying evolutionary adaptation from extortion to generosity

Chen, Xingru; Wang, Long; Fu, Feng

doi:10.1088/1367-2630/ac932d

Cited by 11 publications

(6 citation statements)

References 42 publications

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“…Social norms play a crucial role in shaping how individuals assess others' reputations and adjust their strategies accordingly [27][28][29][30]. The process of evaluation can be categorized into four distinct levels based on the combination of the donor's and recipient's strategies and reputations.…”

Section: Introductionmentioning

confidence: 99%

Social norms and cooperation in higher-order networks

Ma,

Jiang,

Fang

et al. 2024

Proc. R. Soc. A.

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Recent research has been focused on understanding how cooperation is fostered through various mechanisms in cognitive settings, particularly through pairwise interactions. However, real-world interactions often extend beyond simple dyads, including multiple cliques with both pairwise and higher-order interactions. These complex interactions influence how individuals perceive and adapt their strategies based on social norms. We here introduce a model that explores the evolution of collective strategies and social norms within a heterogeneous environment, encompassing both dyadic and three-body interactions. We find that social norms play a crucial role in promoting cooperation in comparison with simply imitating the most successful neighbour. We also show that the rise of prosocial norms leads to increased cooperation across various social dilemmas, often resulting in shifts from defective to cooperative behaviour. Additionally, we observe that a moderate level of information privacy helps sustaining prosocial norms and curtails antisocial tendencies, even in situations where mutual defection might seem advantageous. Our research thus offers insights into the evolution of cooperation through the lens of social norm diffusion in higher-order networks.

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Section: Introductionmentioning

confidence: 99%

Social norms and cooperation in higher-order networks

Ma,

Jiang,

Fang

et al. 2024

Proc. R. Soc. A.

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show abstract

“…Within the memory-one strategies, they correspond to the 2-dimensional subset with p CC = p DC and p CD = p DD . In addition, there has been work on the replicator dynamics among three strategies [15,49], and on the dynamics among transformed memory-one strategies [50,51]. Here, we wish to explore the dynamics among memory-one strategies directly, using adaptive dynamics [52,53].…”

Section: Introductionmentioning

confidence: 99%

Adaptive dynamics of memory-one strategies in the repeated donation game

2023

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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 is the repeated donation game, a variant of the prisoner’s dilemma. Two players interact over many rounds; in each round they decide whether to cooperate or to defect. Strategies take into account the history of the play. Memory-one strategies depend only on the previous round. Even though they are among the most elementary strategies of direct reciprocity, their evolutionary dynamics has been difficult to study analytically. As a result, much previous work has relied on simulations. Here, we derive and analyze their adaptive dynamics. We show that the four-dimensional space of memory-one strategies has an invariant three-dimensional subspace, generated by the memory-one counting strategies. Counting strategies record how many players cooperated in the previous round, without considering who cooperated. We give a partial characterization of adaptive dynamics for memory-one strategies and a full characterization for memory-one counting strategies.

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“…Within the memory-1 strategies, they correspond to the 2-dimensional subset with p CC = p DC and p CD = p DD . In addition, there has been work on the replicator dynamics among three strategies [14,44], and on the dynamics among transformed memory-1 strategies [45,46]. Here, we wish to explore the dynamics among memory-1 strategies directly, using adaptive dynamics [47,48].…”

Section: Introductionmentioning

confidence: 99%

Adaptive dynamics of memory-1 strategies in the repeated donation game

LaPorte

Hilbe

Nowak

2023

Preprint

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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 model to study reciprocity is the repeated donation game, a variant of the repeated prisoner’s dilemma. Two players interact over many rounds, in which they repeatedly decide whether to cooperate or to defect. To make their decisions, they need a strategy that tells them what to do depending on the history of previous play. Memory-1 strategies depend on the previous round only. Even though memory-1 strategies are among the most elementary strategies of reciprocity, their evolutionary dynamics has been difficult to study analytically. As a result, most previous work relies on simulations. Here, we derive and analyze their adaptive dynamics. We show that the four-dimensional space of memory-1 strategies has an invariant three-dimensional subspace, generated by the memory-1 counting strategies. Counting strategies record how many players cooperated in the previous round, without considering who cooperated. We give a partial characterization of adaptive dynamics for memory-1 strategies and a full characterization for memory-1 counting strategies.Author summaryDirect reciprocity is a mechanism for evolution of cooperation based on the repeated interaction of the same players. In the most basic setting, we consider a game between two players and in each round they choose between cooperation and defection. Hence, there are four possible outcomes: (i) both cooperate; (ii) I cooperate, you defect; (ii) I defect, you cooperate; (iv) both defect. A memory-1 strategy for playing this game is characterized by four quantities which specify the probabilities to cooperate in the next round depending on the outcome of the current round. We study evolutionary dynamics in the space of all memory-1 strategies. We assume that mutant strategies are generated in close proximity to the existing strategies, and therefore we can use the framework of adaptive dynamics, which is deterministic.

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The intricate geometry of zero-determinant strategies underlying evolutionary adaptation from extortion to generosity

Cited by 11 publications

References 42 publications

Social norms and cooperation in higher-order networks

Social norms and cooperation in higher-order networks

Adaptive dynamics of memory-one strategies in the repeated donation game

Adaptive dynamics of memory-1 strategies in the repeated donation game

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