The evolution of trust and trustworthiness

Evolution of trust in N-player trust games with loss assessment

Trust plays a crucial role in social and economic interactions, serving as the foundation for social stability and human cooperation. Previous studies have explored the evolution of trust between investors and trustees by constructing trust game models, incorporating factors such as network structure, reputation, and incentives. However, these studies often assume that investors consistently maintain their investment behavior, neglecting the potential influence of the investment environment on investment behavior. To address this gap, we introduce a loss assessment mechanism and construct a trust game model. Specifically, investors first allocate their investment amount to an assessment agency, which divides the amount into two parts according to a certain allocation ratio. One part is used for investment assessment, and the results are fed back to the investors. If the payoff from this portion exceeds the investors' expected value, the remaining amount is invested; otherwise, it is returned to the investors. The results indicate that investors with moderate expectations are more likely to form alliances with trustworthy trustees, thereby effectively promoting the evolution of trust. Conversely, lower or higher expectations yield opposite results. Additionally, we find that as investors' expected values increase, the corresponding allocation ratio should also increase to achieve higher payoffs.

Temporal interaction and its role in the evolution of cooperation

This research investigates the impact of dynamic, time-varying interactions on cooperative behavior in social dilemmas. Traditional research has focused on deterministic rules governing pairwise interactions, yet the impact of interaction frequency and synchronization in groups on cooperation remains underexplored. Addressing this gap, our work introduces two temporal interaction mechanisms to model the stochastic or periodic participation of individuals in public goods games, acknowledging real-life variances due to exogenous temporal factors and geographical time differences. We consider that the interaction state significantly influences both game payoff calculations and the strategy updating process, offering new insights into the emergence and sustainability of cooperation. Our results indicate that maximum game participation frequency is suboptimal under a stochastic interaction mechanism. Instead, an intermediate activation probability maximizes cooperation, suggesting a vital balance between interaction frequency and inactivity security. Furthermore, local synchronization of interactions within specific areas is shown to be beneficial, as time differences hinder the spread of cross-structures but promote the formation of dense cooperative clusters with smoother boundaries. We also note that stronger clustering in networks, larger group sizes, and lower noise increase cooperation. This research contributes to understanding the role of node-based temporality and probabilistic interactions in social dilemmas, offering insights into fostering cooperation.

The effect of multi-tasks mechanism on cooperation in evolutionary game

Human games are inherently diverse, involving more than mere identity interactions. The diversity of game tasks offers a more authentic explanation in the exploration of social dilemmas. Human behavior is also influenced by conformity, and prosociality is a crucial factor in addressing social dilemmas. This study proposes a generalized prisoner's dilemma model of task diversity that incorporates a conformity-driven interaction. Simulation findings indicate that the diversity of multi-tasks and the path dependence contribute to the flourishing of cooperation in games. Conformity-driven interactions also promote cooperation. However, this promotion effect does not increase linearly, and only appropriate task sizes and suitable proportions of conformity-driven interactions yield optimal results. From a broader group perspective, the interplay of network adaptation, task size, and conformity-driven interaction can form a structure of attractors or repellents.

Evolutionary game selection creates cooperative environments

The emergence of collective cooperation in competitive environments is a well-known phenomenon in biology, economics, and social systems. While most evolutionary game models focus on the evolution of strategies for a fixed game, how strategic decisions coevolve with the environment has so far mostly been overlooked. Here, we consider a game selection model where not only the strategies but also the game can change over time following evolutionary principles. Our results show that coevolutionary dynamics of games and strategies can induce novel collective phenomena, fostering the emergence of cooperative environments. When the model is taken on structured populations the architecture of the interaction network can significantly amplify pro-social behavior, with a critical role played by network heterogeneity and the presence of clustered groups of similar players, distinctive features observed in real-world populations. By unveiling the link between the evolution of strategies and games for different structured populations, our model sheds new light on the origin of social dilemmas ubiquitously observed in real-world social systems.

Interpersonal trust: Asymptotic analysis of a stochastic coordination game with multi-agent learning

We study the interpersonal trust of a population of agents, asking whether chance may decide if a population ends up with high trust or low trust. We model this by a discrete time, stochastic coordination game with pairwise interactions occurring at random in a finite population. Agents learn about the behavior of the population using a weighted average of what they have observed in past interactions. This learning rule, called an "exponential moving average," has one parameter that determines the weight of the most recent observation and may, thus, be interpreted as the agent's memory. We prove analytically that in the long run, the whole population always either trusts or doubts with the probability one. This remains true when the expectation of the dynamics would indicate otherwise. By simulation, we study the impact of the distribution of the payoff matrix and of the memory of the agents. We find that as the agent memory increases (i.e., the most recent observation weighs less), the actual dynamics increasingly resemble the expectation of the process. We conclude that it is possible that a population may converge upon high or low trust between its citizens simply by chance, though the game parameters (context of the society) may be quite telling.

Stochastic pairwise preference convergence in Bayesian agents

Beliefs inform the behavior of forward-thinking agents in complex environments. Recently, sequential Bayesian inference has emerged as a mechanism to study belief formation among agents adapting to dynamical conditions. However, we lack critical theory to explain how preferences evolve in cases of simple agent interactions. In this paper, we derive a Gaussian, pairwise agent interaction model to study how preferences converge when driven by observation of each other's behaviors. We show that the dynamics of convergence resemble an Ornstein-Uhlenbeck process, a common model in nonequilibrium stochastic dynamics. Using standard analytical and computational techniques, we find that the hyperprior magnitudes, representing the learning time, determine the convergence value and the asymptotic entropy of the preferences across pairs of agents. We also show that the dynamical variance in preferences is characterized by a relaxation time t^{★} and compute its asymptotic upper bound. This formulation enhances the existing toolkit for modeling stochastic, interactive agents by formalizing leading theories in learning theory, and builds towards more comprehensive models of open problems in principal-agent and market theory.

Language-based game theory in the age of artificial intelligence

Understanding human behaviour in decision problems and strategic interactions has wide-ranging applications in economics, psychology and artificial intelligence. Game theory offers a robust foundation for this understanding, based on the idea that individuals aim to maximize a utility function. However, the exact factors influencing strategy choices remain elusive. While traditional models try to explain human behaviour as a function of the outcomes of available actions, recent experimental research reveals that linguistic content significantly impacts decision-making, thus prompting a paradigm shift from outcome-based to language-based utility functions. This shift is more urgent than ever, given the advancement of generative AI, which has the potential to support humans in making critical decisions through language-based interactions. We propose sentiment analysis as a fundamental tool for this shift and take an initial step by analysing 61 experimental instructions from the dictator game, an economic game capturing the balance between self-interest and the interest of others, which is at the core of many social interactions. Our meta-analysis shows that sentiment analysis can explain human behaviour beyond economic outcomes. We discuss future research directions. We hope this work sets the stage for a novel game-theoretical approach that emphasizes the importance of language in human decisions.

Information synergy maximizes the growth rate of heterogeneous groups

Collective action and group formation are fundamental behaviors among both organisms cooperating to maximize their fitness and people forming socioeconomic organizations. Researchers have extensively explored social interaction structures via game theory and homophilic linkages, such as kin selection and scalar stress, to understand emergent cooperation in complex systems. However, we still lack a general theory capable of predicting how agents benefit from heterogeneous preferences, joint information, or skill complementarities in statistical environments. Here, we derive general statistical dynamics for the origin of cooperation based on the management of resources and pooled information. Specifically, we show how groups that optimally combine complementary agent knowledge about resources in statistical environments maximize their growth rate. We show that these advantages are quantified by the information synergy embedded in the conditional probability of environmental states given agents' signals, such that groups with a greater diversity of signals maximize their collective information. It follows that, when constraints are placed on group formation, agents must intelligently select with whom they cooperate to maximize the synergy available to their own signal. Our results show how the general properties of information underlie the optimal collective formation and dynamics of groups of heterogeneous agents across social and biological phenomena.

Small bots, big impact: solving the conundrum of cooperation in optional Prisoner's Dilemma game through simple strategies

Cooperation plays a crucial role in both nature and human society, and the conundrum of cooperation attracts the attention from interdisciplinary research. In this study, we investigated the evolution of cooperation in optional Prisoner's Dilemma games by introducing simple bots. We focused on one-shot and anonymous games, where the bots could be programmed to always cooperate, always defect, never participate or choose each action with equal probability. Our results show that cooperative bots facilitate the emergence of cooperation among ordinary players in both well-mixed populations and a regular lattice under weak imitation scenarios. Introducing loner bots has no impact on the emergence of cooperation in well-mixed populations, but it facilitates the dominance of cooperation in regular lattices under strong imitation scenarios. However, too many loner bots on a regular lattice inhibit the spread of cooperation and can eventually result in a breakdown of cooperation. Our findings emphasize the significance of bot design in promoting cooperation and offer useful insights for encouraging cooperation in real-world scenarios.

Optimization of institutional incentives for cooperation in structured populations

The application of incentives, such as reward and punishment, is a frequently applied way for promoting cooperation among interacting individuals in structured populations. However, how to properly use the incentives is still a challenging problem for incentive-providing institutions. In particular, since the implementation of incentive is costly, to explore the optimal incentive protocol, which ensures the desired collective goal at a minimal cost, is worthy of study. In this work, we consider the positive and negative incentives for a structured population of individuals whose conflicting interactions are characterized by a Prisoner's Dilemma game. We establish an index function for quantifying the cumulative cost during the process of incentive implementation, and theoretically derive the optimal positive and negative incentive protocols for cooperation on regular networks. We find that both types of optimal incentive protocols are identical and time-invariant. Moreover, we compare the optimal rewarding and punishing schemes concerning implementation cost and provide a rigorous basis for the usage of incentives in the game-theoretical framework. We further perform computer simulations to support our theoretical results and explore their robustness for different types of population structures, including regular, random, small-world and scale-free networks.

Generic catastrophic poverty when selfish investors exploit a degradable common resource

The productivity of a common pool of resources may degrade when overly exploited by a number of selfish investors, a situation known as the tragedy of the commons. Without regulations, agents optimize the size of their individual investments into the commons by balancing incurring costs with the returns received. The resulting Nash equilibrium involves a self-consistency loop between individual investment decisions and the state of the commons. As a consequence, several non-trivial properties emerge. For N investing actors we prove rigorously that typical payoffs do not scale as 1/N, the expected result for cooperating agents, but as (1/N)². Payoffs are hence reduced with regard to the functional dependence on N, a situation denoted catastrophic poverty. We show that catastrophic poverty results from a fine-tuned balance between returns and costs. Additionally, a finite number of oligarchs may be present. Oligarchs are characterized by payoffs that are finite and not decreasing when N increases. Our results hold for generic classes of models, including convex and moderately concave cost functions. For strongly concave cost functions the Nash equilibrium undergoes a collective reorganization, being characterized instead by entry barriers and sudden death forced market exits.

Effects of sex and sex-related facial traits on trust and trustworthiness: An experimental study

The ability to trust others, including strangers, is a prerequisite for human cooperation. Economically it is not rational to trust strangers, as trust can be easily exploited. Still, generally, the level of trust toward strangers is relatively high. Trust is closely related to trustworthiness: when trusting others, one expects them to reciprocate. Some individuals elicit more trust than others. Apparently, humans use subtle cues for judging the trustworthiness of their interaction partners. Here, we report on an experiment that investigates trust and trustworthiness in a population of 176 mainly Dutch students. The aims of our study were: (1) to investigate how the sex of interaction partners and their facial appearance (femininity/masculinity) affect the degree of trust and trustworthiness, compared to fully anonymous conditions; (2) to test whether individuals who elicit trust in their interaction partners are trustworthy themselves. Each subject of our experiment played five one-shot Trust Games: one with an anonymous interaction partner, and four "personalized" games after seeing a 20 s silent video of their interaction partner (twice same-sex, and twice opposite-sex). The degree of facial sexual dimorphism was investigated with geometric morphometrics based on full-face photographs. Our results revealed that, despite the already high level of trust in the anonymous setting, the personalization of interactions had a clear effect on behavior. Females elicited more trust in partners of both sexes. Interestingly, females with more feminine faces elicited less trust in both male and female partners, while males with more masculine facial shape were more trusted by females, but less trusted by males. Neither sex nor facial femininity/masculinity predicted trustworthiness. Our results demonstrate that (1) sex and sex-related facial traits of interaction partners have a clear effect on eliciting trust in strangers. However, (2) these cues are not reliable predictors of actual trustworthiness.

A Model of Trust

Trust is central to a large variety of social interactions. Different research fields have empirically and theoretically investigated trust, observing trusting behaviors in different situations and pinpointing their different components and constituents. However, a unifying, computational formalization of those diverse components and constituents of trust is still lacking. Previous work has mainly used computational models borrowed from other fields and developed for other purposes to explain trusting behaviors in empirical paradigms. Here, I computationally formalize verbal models of trust in a simple model (i.e., vulnerability model) that combines current and prospective action values with beliefs and expectancies about a partner’s behavior. By using the classic investment game (IG)—an economic game thought to capture some important features of trusting behaviors in social interactions—I show how variations of a single parameter of the vulnerability model generates behaviors that can be interpreted as different “trust attitudes”. I then show how these behavioral patterns change as a function of an individual’s loss aversion and expectations of the partner’s behavior. I finally show how the vulnerability model can be easily extended in a novel IG paradigm to investigate inferences on different traits of a partner. In particular, I will focus on benevolence and competence—two character traits that have previously been described as determinants of trustworthiness impressions central to trust. The vulnerability model can be employed as is or as a utility function within more complex Bayesian frameworks to fit participants’ behavior in different social environments where actions are associated with subjective values and weighted by individual beliefs about others’ behaviors. Hence, the vulnerability model provides an important building block for future theoretical and empirical work across a variety of research fields.

Evolution of cooperation and trust in an N-player social dilemma game with tags for migration decisions

We present an evolutionary game model that integrates the concept of tags, trust and migration to study how trust in social and physical groups influence cooperation and migration decisions. All agents have a tag, and they gain or lose trust in other tags as they interact with other agents. This trust in different tags determines their trust in other players and groups. In contrast to other models in the literature, our model does not use tags to determine the cooperation/defection decisions of the agents, but rather their migration decisions. Agents decide whether to cooperate or defect based purely on social learning (i.e. imitation from others). Agents use information about tags and their trust in tags to determine how much they trust a particular group of agents and whether they want to migrate to that group. Comprehensive experiments show that the model can promote high levels of cooperation and trust under different game scenarios, and that curbing the migration decisions of agents can negatively impact both cooperation and trust in the system. We also observed that trust becomes scarce in the system as the diversity of tags increases. This work is one of the first to study the impact of tags on trust in the system and migration behaviour of the agents using evolutionary game theory.

Artificial intelligence development races in heterogeneous settings

Regulation of advanced technologies such as Artificial Intelligence (AI) has become increasingly important, given the associated risks and apparent ethical issues. With the great benefits promised from being able to first supply such technologies, safety precautions and societal consequences might be ignored or shortchanged in exchange for speeding up the development, therefore engendering a racing narrative among the developers. Starting from a game-theoretical model describing an idealised technology race in a fully connected world of players, here we investigate how different interaction structures among race participants can alter collective choices and requirements for regulatory actions. Our findings indicate that, when participants portray a strong diversity in terms of connections and peer-influence (e.g., when scale-free networks shape interactions among parties), the conflicts that exist in homogeneous settings are significantly reduced, thereby lessening the need for regulatory actions. Furthermore, our results suggest that technology governance and regulation may profit from the world's patent heterogeneity and inequality among firms and nations, so as to enable the design and implementation of meticulous interventions on a minority of participants, which is capable of influencing an entire population towards an ethical and sustainable use of advanced technologies.

Criticality and Griffiths phases in random games with quenched disorder

The perceived risk and reward for a given situation can vary depending on resource availability, accumulated wealth, and other extrinsic factors such as individual backgrounds. Based on this general aspect of everyday life, here we use evolutionary game theory to model a scenario with randomly perturbed payoffs in a prisoner's dilemma game. The perception diversity is modeled by adding a zero-average random noise in the payoff entries and a Monte Carlo simulation is used to obtain the population dynamics. This payoff heterogeneity can promote and maintain cooperation in a competitive scenario where only defectors would survive otherwise. In this work, we give a step further, understanding the role of heterogeneity by investigating the effects of quenched disorder in the critical properties of random games. We observe that payoff fluctuations induce a very slow dynamic, making the cooperation decay behave as power laws with varying exponents, instead of the usual exponential decay after the critical point, showing the emergence of a Griffiths phase. We also find a symmetric Griffiths phase near the defector's extinction point when fluctuations are present, indicating that Griffiths phases may be frequent in evolutionary game dynamics and play a role in the coexistence of different strategies.

Evolution of honesty in higher-order social networks

Sender-receiver games are simple models of information transmission that provide a formalism to study the evolution of honest signaling and deception between a sender and a receiver. In many practical scenarios, lies often affect groups of receivers, which inevitably entangles the payoffs of individuals to the payoffs of other agents in their group, and this makes the formalism of pairwise sender-receiver games inapt for where it might be useful the most. We therefore introduce group interactions among receivers and study how their interconnectedness in higher-order social networks affects the evolution of lying. We observe a number of counterintuitive results that are rooted in the complexity of the underlying evolutionary dynamics, which has thus far remained hidden in the realm of pairwise interactions. We find conditions for honesty to persist even when there is a temptation to lie, and we observe the prevalence of moral strategy profiles even when lies favor the receiver at a cost to the sender. We confirm the robustness of our results by further performing simulations on hypergraphs created from real-world data using the SocioPatterns database. Altogether, our results provide persuasive evidence that moral behavior may evolve on higher-order social networks, at least as long as individuals interact in groups that are small compared to the size of the network.

Stimuli strategy and learning dynamics promote the wisdom of crowds

ABSTRACT

Collective wisdom is the ability of a group to perform more effectively than any individual alone. Through an evolutionary game-theoretic model of collective prediction, we investigate the role that reinforcement learning stimulus may play the role in enhancing collective voting accuracy. And collective voting bias can be dismissed through self-reinforcing global cooperative learning. Numeric simulations suggest that the provided method can increase collective voting accuracy. We conclude that real-world systems might seek reward-based incentive mechanism as an alternative to surmount group decision error.

Facial threat affects trust more strongly than facial attractiveness in women than it does in men

Trust is essential in initiating social relationships. Due to the differential evolution of sex hormones as well as the fitness burdens of producing offspring, evaluations of a potential mating partner's trustworthiness likely differ across sexes. Here, we explore unknown sex-specific effects of facial attractiveness and threat on trusting other-sex individuals. Ninety-three participants (singles; 46 women) attracted by the other sex performed an incentivized trust game. They had to decide whether to trust individuals of the other sex represented by a priori-created face stimuli gradually varying in the intensities of both attractiveness and threat. Male and female participants trusted attractive and unthreatening-looking individuals more often. However, whereas male participants' trust behavior was affected equally by attractiveness and threat, female participants' trust behavior was more strongly affected by threat than by attractiveness. This indicates that a partner's high facial attractiveness might compensate for high facial threat in male but not female participants. Our findings suggest that men and women prioritize attractiveness and threat differentially, with women paying relatively more attention to threat cues inversely signaling parental investment than to attractiveness cues signaling reproductive fitness. This difference might be attributable to an evolutionary, biologically sex-specific decision regarding parental investment and reproduction behavior.

Human infants can override possessive tendencies to share valued items with others

Possessiveness toward objects and sharing are competing tendencies that influence dyadic and group interactions within the primate lineage. A distinctive form of sharing in adult Homo sapiens involves active giving of high-valued possessions to others, without an immediate reciprocal benefit. In two Experiments with 19-month-old human infants (N = 96), we found that despite measurable possessive behavior toward their own personal objects (favorite toy, bottle), infants spontaneously gave these items to a begging stranger. Moreover, human infants exhibited this behavior across different types of objects that are relevant to theory (personal objects, sweet food, and common objects)-showing flexible generalizability not evidenced in non-human primates. We combined these data with a previous dataset, yielding a large sample of infants (N = 192), and identified sociocultural factors that may calibrate young infants' sharing of objects with others. The current findings show a proclivity that is rare or absent in our closest living relatives-the capacity to override possessive behavior toward personally valued objects by sharing those same desired objects with others.

Mathematical foundations of moral preferences

One-shot anonymous unselfishness in economic games is commonly explained by social preferences, which assume that people care about the monetary pay-offs of others. However, during the last 10 years, research has shown that different types of unselfish behaviour, including cooperation, altruism, truth-telling, altruistic punishment and trustworthiness are in fact better explained by preferences for following one's own personal norms-internal standards about what is right or wrong in a given situation. Beyond better organizing various forms of unselfish behaviour, this moral preference hypothesis has recently also been used to increase charitable donations, simply by means of interventions that make the morality of an action salient. Here we review experimental and theoretical work dedicated to this rapidly growing field of research, and in doing so we outline mathematical foundations for moral preferences that can be used in future models to better understand selfless human actions and to adjust policies accordingly. These foundations can also be used by artificial intelligence to better navigate the complex landscape of human morality.

An epidemiological model with voluntary quarantine strategies governed by evolutionary game dynamics

During pandemic events, strategies such as social distancing can be fundamental to reduce simultaneous infections and mitigate the disease spreading, which is very relevant to the risk of a healthcare system collapse. Although these strategies can be recommended, or even imposed, their actual implementation may depend on the population perception of the risks associated with a potential infection. The current COVID-19 crisis, for instance, is showing that some individuals are much more prone than others to remain isolated. To better understand these dynamics, we propose an epidemiological SIR model that uses evolutionary game theory for combining in a single process social strategies, individual risk perception, and viral spreading. In particular, we consider a disease spreading through a population, whose agents can choose between self-isolation and a lifestyle careless of any epidemic risk. The strategy adoption is individual and depends on the perceived disease risk compared to the quarantine cost. The game payoff governs the strategy adoption, while the epidemic process governs the agent's health state. At the same time, the infection rate depends on the agent's strategy while the perceived disease risk depends on the fraction of infected agents. Our results show recurrent infection waves, which are usually seen in previous historic epidemic scenarios with voluntary quarantine. In particular, such waves re-occur as the population reduces disease awareness. Notably, the risk perception is found to be fundamental for controlling the magnitude of the infection peak, while the final infection size is mainly dictated by the infection rates. Low awareness leads to a single and strong infection peak, while a greater disease risk leads to shorter, although more frequent, peaks. The proposed model spontaneously captures relevant aspects of a pandemic event, highlighting the fundamental role of social strategies.

Oscillatory dynamics in the dilemma of social distancing

Social distancing as one of the main non-pharmaceutical interventions can help slow down the spread of diseases, like in the COVID-19 pandemic. Effective social distancing, unless enforced as drastic lockdowns and mandatory cordon sanitaire, requires consistent strict collective adherence. However, it remains unknown what the determinants for the resultant compliance of social distancing and their impact on disease mitigation are. Here, we incorporate into the epidemiological process with an evolutionary game theory model that governs the evolution of social distancing behaviour. In our model, we assume an individual acts in their best interest and their decisions are driven by adaptive social learning of the real-time risk of infection in comparison with the cost of social distancing. We find interesting oscillatory dynamics of social distancing accompanied with waves of infection. Moreover, the oscillatory dynamics are dampened with a non-trivial dependence on model parameters governing decision-makings and gradually cease when the cumulative infections exceed the herd immunity. Compared to the scenario without social distancing, we quantify the degree to which social distancing mitigates the epidemic and its dependence on individuals’ responsiveness and rationality in their behaviour changes. Our work offers new insights into leveraging human behaviour in support of pandemic response.