Evolution of trust in structured populations

The trust game, derived from a notable economics experiment, has recently attracted interest in the field of evolutionary dynamics. In a prevalent version of the evolutionary trust game, players adopt one of three strategies: investor, trustworthy trustee, or untrustworthy trustee. Trustworthy trustees enhance and share the investment with the investor, whereas untrustworthy trustees retain the full amount, betraying the investor. Following this setup, we propose a two-player version of the trust game, which is analytically feasible. Based on weak selection and pair approximation, we explore the evolution of trust in structured populations, factoring in four strategy updating rules: pairwise comparison (PC), birth-death (BD), imitation (IM), and death-birth (DB). Comparing structured populations with well-mixed populations, we arrive at two main conclusions. First, in the absence of untrustworthy trustees, there is a saddle point between investors and trustworthy trustees, with collaboration thriving best in well-mixed populations. The collaboration diminishes sequentially from DB to IM to PC/BD updating rules in structured populations. Second, an invasion of untrustworthy trustees makes this saddle point unstable and leads to the extinction of investors. The 3-strategy system stabilizes at an equilibrium line where the trustworthy and untrustworthy trustees coexist. The stability span of trustworthy trustees is maximally extended under the PC and BD updating rules in structured populations, while it decreases in a sequence from IM to DB updating rules, with the well-mixed population being the least favorable. This research adds an analytical lens to understanding the evolution of trust in structured populations.Comment: 15 pages, 5 figure

The role of intra- and inter-group Matthew effect in the social dilemma of public goods games

The Matthew effect describes the phenomenon where the rich tend to get richer. Such a success-driven mechanism has been studied in spatial public goods games in an inter-group way, where each individual's social power is enhanced across all groups. For instance, factors like knowledge can exert an advantage across various social contexts. In contrast, certain factors, especially local material goods, only enhance advantages within their current group. Building on this, we further explore the intra-group Matthew effect where the enhancement of social power is calculated separately in each group. Our findings indicate that the intra-group Matthew effect sustains cooperation more at high productivity, while the inter-group Matthew effect promotes cooperation at low productivity. Moreover, the mixture of the intra- and inter-group Matthew effect harms cooperation. This study provides insights into addressing social dilemmas by adjusting wealth accumulation across diverse social groups.Comment: 6 pages, 3 figures, accepted for publication at Physics Letters

Inertia in spatial public goods games under weak selection

Due to limited cognitive skills for perceptual error or other emotional reasons, players may keep their current strategies even if there is a more promising choice. Such behavior inertia has already been studied, but its consequences remained unexplored in the weak selection limit. To fill this gap, we consider a spatial public goods game model where inertia is considered during the imitation process. By using the identity-by-descent method, we present analytical forms of the critical synergy factor $r^\star$, which determines when cooperation is favored. We find that inertia hinders cooperation, which can be explained by the decelerated coarsening process under weak selection. Interestingly, the critical synergy conditions for different updating protocols, including death-birth and birth-death rules, can be formally linked by the extreme limits of the inertia factor. To explore the robustness of our observations, calculations are made for different lattices and group sizes. Monte Carlo simulations also confirm the results

A general epidemic model and its application to mask design considering different preferences towards masks

While most masks have a limited effect on personal protection, how effective are they for collective protection? How to enlighten the design of masks from the perspective of collective dynamics? In this paper, we assume three preferences in the population: (i) never wearing a mask; (ii) wearing a mask if and only if infected; (iii) always wearing a mask. We study the epidemic transmission in an open system within the Susceptible-Infected-Recovered (SIR) model framework. We use agent-based Monte Carlo simulation and mean-field differential equations to investigate the model, respectively. Ternary heat maps show that wearing masks is always beneficial in curbing the spread of the epidemic. Based on the model, we investigate the potential implications of different mask designs from the perspective of collective dynamics. The results show that strengthening the filterability of the mask from the face to the outside is more effective in most parameter spaces, because it acts on individuals with both preferences (ii) and (iii). However, when the fraction of individuals always wearing a mask achieves a critical point, strengthening the filterability from outside to the face becomes more effective, because of the emerging hidden reality that the infected individuals become too few to utilize the filterability from their face to outside fully.Comment: Complexity, 202

Memory-based involution dilemma on square lattices

When involution affects individuals, their efforts do not augment resources but merely compete for limited resources. From entrance exams to company overtime, such efforts lead to unnecessary costs, undermining group welfare. Meanwhile, the individual advantages or collective disadvantages from this unnecessary effort may accumulate over time, such as the long-term validity of test scores. To identify the role of this memory factor, we propose a memory-based involution game model. In a more competitive environment, our findings suggest: (i) with scant social resources, increasing memory length curbs involution, (ii) with moderate resources, increasing memory length initially intensifies involution but later reduces it, and (iii) with abundant social resources, increasing memory length amplifies involution. Conversely, in a less competitive environment, involution consistently decreases with a larger memory length. Our research provides insights into mitigating involution by considering memory effects.Comment: 9 pages, 7 figures, accepted for publication in Chaos, Solitons & Fractal

When greediness and self-confidence meet in a social dilemma

A greedy personality is usually accompanied by arrogance and confidence. This work investigates the cooperation success condition in the context of biased payoff allocation and self-confidence. The first component allows the organizer in a spatial public goods game to receive a different proportion of goods than other participants. The second aspect influences the micro-level dynamics of strategy updates, wherein players can maintain their strategy with a certain weight. Analytical results are obtained on square lattices under the weak selection limit. If the organizer attempts to monopolize the public goods, cooperation becomes more attainable. If the confidence increases, cooperation is inhibited. Consequently, these elements have conflicting effects on cooperation, and their simultaneous presence can result in a heterogeneous change of the critical synergy factor. Our theoretical findings underscore the subtle implications of a mutual trait that may manifest as greediness or self-confidence under different circumstances, which are validated through Monte Carlo simulations.Comment: 15 pages, 7 figures, accepted for publication in Physica

The conflict between self-interaction and updating passivity in the evolution of cooperation

In social dilemmas under weak selection, the capacity for a player to exhibit updating passivity or interact with its own strategy can lead to conflicting outcomes. The central question is which effect is stronger and how their simultaneous presence influences the evolution of cooperation. We introduce a model that considers both effects using different weight factors. We derive theoretical solutions for the conditions of cooperation success and the cooperation level under weak selection, scanning the complete parameter space. When the weight factors are equally strong, the promoting effect of self-interaction to cooperation surpasses the inhibitory effect of updating passivity. Intriguingly, however, we identify non-monotonous cooperation-supporting effects when the weight of updating passivity increases more rapidly. Our findings are corroborated by Monte Carlo simulations and demonstrate robustness across various game types, including the prisoner's dilemma, stag-hunt, and snowdrift games.Comment: 17 two-column pages, 7 figures, accepted for publication in Chaos, Solitons and Fractal

A reversed form of public goods game: equivalence and difference

According to the public goods game (PGG) protocol, participants decide freely whether they want to contribute to a common pool or not, but the resulting benefit is distributed equally. A conceptually similar dilemma situation may emerge when participants consider if they claim a common resource but the related cost is covered equally by all group members. The latter establishes a reversed form of the original public goods game (R-PGG). In this work, we show that R-PGG is equivalent to PGG in several circumstances, starting from the traditional analysis, via the evolutionary approach in unstructured populations, to Monte Carlo simulations in structured populations. However, there are also cases when the behavior of R-PGG could be surprisingly different from the outcome of PGG. When the key parameters are heterogeneous, for instance, the results of PGG and R-PGG could be diverse even if we apply the same amplitudes of heterogeneity. We find that the heterogeneity in R-PGG generally impedes cooperation, while the opposite is observed for PGG. These diverse system reactions can be understood if we follow how payoff functions change when introducing heterogeneity in the parameter space. This analysis also reveals the distinct roles of cooperator and defector strategies in the mentioned games. Our observations may hopefully stimulate further research to check the potential differences between PGG and R-PGG due to the alternative complexity of conditions