Timing Uncertainty in Collective Risk Dilemmas Encourages Group Reciprocation and Polarization

Timing decisions as the next frontier for collective intelligence

The past decade has witnessed a growing interest in collective decision making, particularly the idea that groups can make more accurate decisions compared with individuals. However, nearly all research to date has focused on spatial decisions (e.g., food patches). Here, we highlight the equally important, but severely understudied, realm of temporal collective decision making (i.e., decisions about when to perform an action). We illustrate differences between temporal and spatial decisions, including the irreversibility of time, cost asymmetries, the speed-accuracy tradeoff, and game theoretic dynamics. Given these fundamental differences, temporal collective decision making likely requires different mechanisms to generate collective intelligence. Research focused on temporal decisions should lead to an expanded understanding of the adaptiveness and constraints of living in groups.

An outside individual option increases optimism and facilitates collaboration when groups form flexibly

Voluntary participation is a central yet understudied aspect of collaboration. Here, we model collaboration as people's voluntary choices between joining an uncertain public goods provisioning in groups and pursuing a less profitable but certain individual option. First, we find that voluntariness in collaboration increases the likelihood of group success via two pathways, both contributing to form more optimistic groups: pessimistic defectors are filtered out from groups, and some individuals update their beliefs to become cooperative. Second, we reconcile these findings with existing literature that highlights the detrimental effects of an individual option. We argue that the impact of an outside individual option on collaboration depends on the "externality" of loners - the influence that those leaving the group still exert on group endeavors. Theoretically and experimentally, we show that if collaboration allows for flexible group formation, the negative externality of loners remains limited, and the presence of an individual option robustly aids collaborative success.

Committing to the wrong artificial delegate in a collective-risk dilemma is better than directly committing mistakes

While autonomous artificial agents are assumed to perfectly execute the strategies they are programmed with, humans who design them may make mistakes. These mistakes may lead to a misalignment between the humans' intended goals and their agents' observed behavior, a problem of value alignment. Such an alignment problem may have particularly strong consequences when these autonomous systems are used in social contexts that involve some form of collective risk. By means of an evolutionary game theoretical model, we investigate whether errors in the configuration of artificial agents change the outcome of a collective-risk dilemma, in comparison to a scenario with no delegation. Delegation is here distinguished from no-delegation simply by the moment at which a mistake occurs: either when programming/choosing the agent (in case of delegation) or when executing the actions at each round of the game (in case of no-delegation). We find that, while errors decrease success rate, it is better to delegate and commit to a somewhat flawed strategy, perfectly executed by an autonomous agent, than to commit execution errors directly. Our model also shows that in the long-term, delegation strategies should be favored over no-delegation, if given the choice.

Success-driven opinion formation determines social tensions

Polarization is common in politics and public opinion. It is believed to be shaped by media as well as ideologies, and often incited by misinformation. However, little is known about the microscopic dynamics behind polarization and the resulting social tensions. By coupling opinion formation with the strategy selection in different social dilemmas, we reveal how success at an individual level transforms to global consensus or lack thereof. When defection carries with it the fear of punishment in the absence of greed, as in the stag-hunt game, opinion fragmentation is the smallest. Conversely, if defection promises a higher payoff and also evokes greed, like in the prisoner's dilemma and snowdrift game, consensus is more difficult to attain. Our research thus challenges the top-down narrative of social tensions, showing they might originate from fundamental principles at individual level, like the desire to prevail in pairwise evolutionary comparisons.

Santos F, Simoens P, Lenaerts T. The art of compensation: How hybrid teams solve collective-risk dilemmas

It is widely known how the human ability to cooperate has influenced the thriving of our species. However, as we move towards a hybrid human-machine future, it is still unclear how the introduction of artificial agents in our social interactions affect this cooperative capacity. In a one-shot collective risk dilemma, where enough members of a group must cooperate in order to avoid a collective disaster, we study the evolutionary dynamics of cooperation in a hybrid population. In our model, we consider a hybrid population composed of both adaptive and fixed behavior agents. The latter serve as proxies for the machine-like behavior of artificially intelligent agents who implement stochastic strategies previously learned offline. We observe that the adaptive individuals adjust their behavior in function of the presence of artificial agents in their groups to compensate their cooperative (or lack of thereof) efforts. We also find that risk plays a determinant role when assessing whether or not we should form hybrid teams to tackle a collective risk dilemma. When the risk of collective disaster is high, cooperation in the adaptive population falls dramatically in the presence of cooperative artificial agents. A story of compensation, rather than cooperation, where adaptive agents have to secure group success when the artificial agents are not cooperative enough, but will rather not cooperate if the others do so. On the contrary, when risk of collective disaster is low, success is highly improved while cooperation levels within the adaptive population remain the same. Artificial agents can improve the collective success of hybrid teams. However, their application requires a true risk assessment of the situation in order to actually benefit the adaptive population (i.e. the humans) in the long-term.

Emotion expression and cooperation under collective risks

The difficulties associated with solving Humanity's major global challenges have increasingly led world leaders and everyday citizens to publicly adopt strong emotional responses, with either mixed or unknown impacts on others' actions. Here, we present two experiments showing that non-verbal emotional expressions in group interactions play a critical role in determining how individuals behave when contributing to public goods entailing future and uncertain returns. Participants' investments were not only shaped by emotional expressions but also enhanced by anger when compared with joy. Our results suggest that global coordination may benefit from interaction in which emotion expressions can be paramount.

The evolution and social cost of herding mentality promote cooperation

Herding behavior has a social cost for individuals not following the herd, influencing human decision-making. This work proposes including a social cost derived from herding mentality into the payoffs of pairwise game interactions. We introduce a co-evolutionary asymmetric model with four individual strategies (cooperation vs. defection and herding vs. non-herding) to understand the co-emergence of herding behavior and cooperation. Computational experiments show how including herding costs promotes cooperation by increasing the parameter space under which cooperation persists. Results demonstrate a synergistic relationship between the emergence of cooperation and herding mentality: the highest cooperation is achieved when the herding mentality also achieves its highest level. Finally, we study different herding social costs and its relationship to cooperation and herding evolution. This study points to new social mechanisms, related to conformity-driven imitation behavior, that help to understand how and why cooperation prevails in human groups.

Evolution of conditional cooperation in collective-risk social dilemma with repeated group interactions

The evolution and long-term sustenance of cooperation has consistently piqued scholarly interest across the disciplines of evolutionary biology and social sciences. Previous theoretical and experimental studies on collective risk social dilemma games have revealed that the risk of collective failure will affect the evolution of cooperation. In the real world, individuals usually adjust their decisions based on environmental factors such as risk intensity and cooperation level. However, it is still not well understood how such conditional behaviours affect the evolution of cooperation in repeated group interactions scenario from a theoretical perspective. Here, we construct an evolutionary game model with repeated interactions, in which defectors decide whether to cooperate in subsequent rounds of the game based on whether the risk exceeds their tolerance threshold and whether the number of cooperators exceeds the collective goal in the early rounds of the game. We find that the introduction of conditional cooperation strategy can effectively promote the emergence of cooperation, especially when the risk is low. In addition, the risk threshold significantly affects the evolutionary outcomes, with a high risk promoting the emergence of cooperation. Importantly, when the risk of failure to reach collective goals exceeds a certain threshold, the timely transition from a defective strategy to a cooperative strategy by conditional cooperators is beneficial for maintaining high-level cooperation.

Coevolutionary dynamics via adaptive feedback in collective-risk social dilemma game

Human society and natural environment form a complex giant ecosystem, where human activities not only lead to the change in environmental states, but also react to them. By using collective-risk social dilemma game, some studies have already revealed that individual contributions and the risk of future losses are inextricably linked. These works, however, often use an idealistic assumption that the risk is constant and not affected by individual behaviors. Here, we develop a coevolutionary game approach that captures the coupled dynamics of cooperation and risk. In particular, the level of contributions in a population affects the state of risk, while the risk in turn influences individuals' behavioral decision-making. Importantly, we explore two representative feedback forms describing the possible effect of strategy on risk, namely, linear and exponential feedbacks. We find that cooperation can be maintained in the population by keeping at a certain fraction or forming an evolutionary oscillation with risk, independently of the feedback type. However, such evolutionary outcome depends on the initial state. Taken together, a two-way coupling between collective actions and risk is essential to avoid the tragedy of the commons. More importantly, a critical starting portion of cooperators and risk level is what we really need for guiding the evolution toward a desired direction.

Interdependent Self-Organizing Mechanisms for Cooperative Survival

Cooperative survival "games" are situations in which, during a sequence of catastrophic events, no one survives unless everyone survives. Such situations can be further exacerbated by uncertainty over the timing and scale of the recurring catastrophes, while the resource management required for survival may depend on several interdependent subgames of resource extraction, distribution, and investment with conflicting priorities and preferences between survivors. In social systems, self-organization has been a critical feature of sustainability and survival; therefore, in this article we use the lens of artificial societies to investigate the effectiveness of socially constructed self-organization for cooperative survival games. We imagine a cooperative survival scenario with four parameters: scale, that is, n in an n-player game; uncertainty, with regard to the occurrence and magnitude of each catastrophe; complexity, concerning the number of subgames to be simultaneously "solved"; and opportunity, with respect to the number of self-organizing mechanisms available to the players. We design and implement a multiagent system for a situation composed of three entangled subgames-a stag hunt game, a common-pool resource management problem, and a collective risk dilemma-and specify algorithms for three self-organizing mechanisms for governance, trading, and forecasting. A series of experiments shows, as perhaps expected, a threshold for a critical mass of survivors and also that increasing dimensions of uncertainty and complexity require increasing opportunity for self-organization. Perhaps less expected are the ways in which self-organizing mechanisms may interact in pernicious but also self-reinforcing ways, highlighting the need for some reflection as a process in collective self-governance for cooperative survival.

Delegation to artificial agents fosters prosocial behaviors in the collective risk dilemma

Home assistant chat-bots, self-driving cars, drones or automated negotiation systems are some of the several examples of autonomous (artificial) agents that have pervaded our society. These agents enable the automation of multiple tasks, saving time and (human) effort. However, their presence in social settings raises the need for a better understanding of their effect on social interactions and how they may be used to enhance cooperation towards the public good, instead of hindering it. To this end, we present an experimental study of human delegation to autonomous agents and hybrid human-agent interactions centered on a non-linear public goods dilemma with uncertain returns in which participants face a collective risk. Our aim is to understand experimentally whether the presence of autonomous agents has a positive or negative impact on social behaviour, equality and cooperation in such a dilemma. Our results show that cooperation and group success increases when participants delegate their actions to an artificial agent that plays on their behalf. Yet, this positive effect is less pronounced when humans interact in hybrid human-agent groups, where we mostly observe that humans in successful hybrid groups make higher contributions earlier in the game. Also, we show that participants wrongly believe that artificial agents will contribute less to the collective effort. In general, our results suggest that delegation to autonomous agents has the potential to work as commitment devices, which prevent both the temptation to deviate to an alternate (less collectively good) course of action, as well as limiting responses based on betrayal aversion.

Inferring strategies from observations in long iterated Prisoner's dilemma experiments

While many theoretical studies have revealed the strategies that could lead to and maintain cooperation in the Iterated Prisoner’s dilemma, less is known about what human participants actually do in this game and how strategies change when being confronted with anonymous partners in each round. Previous attempts used short experiments, made different assumptions of possible strategies, and led to very different conclusions. We present here two long treatments that differ in the partner matching strategy used, i.e. fixed or shuffled partners. Here we use unsupervised methods to cluster the players based on their actions and then Hidden Markov Model to infer what the memory-one strategies are in each cluster. Analysis of the inferred strategies reveals that fixed partner interaction leads to behavioral self-organization. Shuffled partners generate subgroups of memory-one strategies that remain entangled, apparently blocking the self-selection process that leads to fully cooperating participants in the fixed partner treatment. Analyzing the latter in more detail shows that AllC, AllD, TFT- and WSLS-like behavior can be observed. This study also reveals that long treatments are needed as experiments with less than 25 rounds capture mostly the learning phase participants go through in these kinds of experiments.

Modeling the effects of environmental and perceptual uncertainty using deterministic reinforcement learning dynamics with partial observability

Assessing the systemic effects of uncertainty that arises from agents' partial observation of the true states of the world is critical for understanding a wide range of scenarios, from navigation and foraging behavior to the provision of renewable resources and public infrastructures. Yet previous modeling work on agent learning and decision-making either lacks a systematic way to describe this source of uncertainty or puts the focus on obtaining optimal policies using complex models of the world that would impose an unrealistically high cognitive demand on real agents. In this work we aim to efficiently describe the emergent behavior of biologically plausible and parsimonious learning agents faced with partially observable worlds. Therefore we derive and present deterministic reinforcement learning dynamics where the agents observe the true state of the environment only partially. We showcase the broad applicability of our dynamics across different classes of partially observable agent-environment systems. We find that partial observability creates unintuitive benefits in several specific contexts, pointing the way to further research on a general understanding of such effects. For instance, partially observant agents can learn better outcomes faster, in a more stable way, and even overcome social dilemmas. Furthermore, our method allows the application of dynamical systems theory to partially observable multiagent leaning. In this regard we find the emergence of catastrophic limit cycles, a critical slowing down of the learning processes between reward regimes, and the separation of the learning dynamics into fast and slow directions, all caused by partial observability. Therefore, the presented dynamics have the potential to become a formal, yet practical, lightweight and robust tool for researchers in biology, social science, and machine learning to systematically investigate the effects of interacting partially observant agents.

Dynamical systems as a level of cognitive analysis of multi-agent learning: Algorithmic foundations of temporal-difference learning dynamics

A dynamical systems perspective on multi-agent learning, based on the link between evolutionary game theory and reinforcement learning, provides an improved, qualitative understanding of the emerging collective learning dynamics. However, confusion exists with respect to how this dynamical systems account of multi-agent learning should be interpreted. In this article, I propose to embed the dynamical systems description of multi-agent learning into different abstraction levels of cognitive analysis. The purpose of this work is to make the connections between these levels explicit in order to gain improved insight into multi-agent learning. I demonstrate the usefulness of this framework with the general and widespread class of temporal-difference reinforcement learning. I find that its deterministic dynamical systems description follows a minimum free-energy principle and unifies a boundedly rational account of game theory with decision-making under uncertainty. I then propose an on-line sample-batch temporal-difference algorithm which is characterized by the combination of applying a memory-batch and separated state-action value estimation. I find that this algorithm serves as a micro-foundation of the deterministic learning equations by showing that its learning trajectories approach the ones of the deterministic learning equations under large batch sizes. Ultimately, this framework of embedding a dynamical systems description into different abstraction levels gives guidance on how to unleash the full potential of the dynamical systems approach to multi-agent learning.

Cooperation dynamics under pandemic risks and heterogeneous economic interdependence

The spread of COVID-19 and ensuing containment measures have accentuated the profound interdependence among nations or regions. This has been particularly evident in tourism, one of the sectors most affected by uncoordinated mobility restrictions. The impact of this interdependence on the tendency to adopt less or more restrictive measures is hard to evaluate, more so if diversity in economic exposures to citizens' mobility are considered. Here, we address this problem by developing an analytical and computational game-theoretical model encompassing the conflicts arising from the need to control the economic effects of global risks, such as in the COVID-19 pandemic. The model includes the individual costs derived from severe restrictions imposed by governments, including the resulting economic interdependence among all the parties involved in the game. By using tourism-based data, the model is enriched with actual heterogeneous income losses, such that every player has a different economic cost when applying restrictions. We show that economic interdependence enhances cooperation because of the decline in the expected payoffs by free-riding parties (i.e., those neglecting the application of mobility restrictions). Furthermore, we show (analytically and through numerical simulations) that these cross-exposures can transform the nature of the cooperation dilemma each region or country faces, modifying the position of the fixed points and the size of the basins of attraction that characterize this class of games. Finally, our results suggest that heterogeneity among regions may be used to leverage the impact of intervention policies by ensuring an agreement among the most relevant initial set of cooperators.

Segregation and clustering of preferences erode socially beneficial coordination

Polarization on various issues has increased in many Western democracies over the last decades, leading to divergent beliefs, preferences, and behaviors within societies. We develop a model to investigate the effects of polarization on the likelihood that a society will coordinate on a welfare-improving action in a context in which collective benefits are acquired only if enough individuals take that action. We examine the impacts of different manifestations of polarization: heterogeneity of preferences, segregation of the social network, and the interaction between the two. In this context, heterogeneity captures differential perceived benefits from coordinating, which can lead to different intentions and sensitivity regarding the intentions of others. Segregation of the social network can create a bottleneck in information flows about others' preferences, as individuals may base their decisions only on their close neighbors. Additionally, heterogeneous preferences can be evenly distributed in the population or clustered in the local network, respectively reflecting or systematically departing from the views of the broader society. The model predicts that heterogeneity of preferences alone is innocuous and it can even be beneficial, while segregation can hamper coordination, mainly when local networks distort the distribution of valuations. We base these results on a multimethod approach including an online group experiment with 750 individuals. We randomize the range of valuations associated with different choice options and the information respondents have about others. The experimental results reinforce the idea that, even in a situation in which all could stand to gain from coordination, polarization can impede social progress.

Cost efficiency of institutional incentives for promoting cooperation in finite populations

Institutions can provide incentives to enhance cooperation in a population where this behaviour is infrequent. This process is costly, and it is thus important to optimize the overall spending. This problem can be mathematically formulated as a multi-objective optimization problem where one wishes to minimize the cost of providing incentives while ensuring a minimum level of cooperation, sustained over time. Prior works that consider this question usually omit the stochastic effects that drive population dynamics. In this paper, we provide a rigorous analysis of this optimization problem, in a finite population and stochastic setting, studying both pairwise and multi-player cooperation dilemmas. We prove the regularity of the cost functions for providing incentives over time, characterize their asymptotic limits (infinite population size, weak selection and large selection) and show exactly when reward or punishment is more cost efficient. We show that these cost functions exhibit a phase transition phenomenon when the intensity of selection varies. By determining the critical threshold of this phase transition, we provide exact calculations for the optimal cost of the incentive, for any given intensity of selection. Numerical simulations are also provided to demonstrate analytical observations. Overall, our analysis provides for the first time a selection-dependent calculation of the optimal cost of institutional incentives (for both reward and punishment) that guarantees a minimum level of cooperation over time. It is of crucial importance for real-world applications of institutional incentives since the intensity of selection is often found to be non-extreme and specific for a given population.

Risk sensitivity and theory of mind in human coordination

What humans do when exposed to uncertainty, incomplete information, and a dynamic environment influenced by other agents remains an open scientific challenge with important implications in both science and engineering applications. In these contexts, humans handle social situations by employing elaborate cognitive mechanisms such as theory of mind and risk sensitivity. Here we resort to a novel theoretical model, showing that both mechanisms leverage coordinated behaviors among self-regarding individuals. Particularly, we resort to cumulative prospect theory and level-k recursions to show how biases towards optimism and the capacity of planning ahead significantly increase coordinated, cooperative action. These results suggest that the reason why humans are good at coordination may stem from the fact that we are cognitively biased to do so.

We propose a new computational model characterizing coordination among self-regarding individuals under theory of mind and risk sensitivity. Theory of mind enables decision-making based on the attribution of beliefs, knowledge, or goals to others, whereas different risk sensitivities allows one to assess the impact of different ways of valuing uncertain returns, as captured by descriptive theories from social-economic studies. Together they provide evidence that biases towards optimism, and the capacity for planning ahead, significantly increase coordinated, cooperative action.

Combination of institutional incentives for cooperative governance of risky commons

Finding appropriate incentives to enforce collaborative efforts for governing the commons in risky situations is a long-lasting challenge. Previous works have demonstrated that both punishing free-riders and rewarding cooperators could be potential tools to reach this goal. Despite weak theoretical foundations, policy makers frequently impose a punishment-reward combination. Here, we consider the emergence of positive and negative incentives and analyze their simultaneous impact on sustaining risky commons. Importantly, we consider institutions with fixed and flexible incentives. We find that a local sanctioning scheme with pure reward is the optimal incentive strategy. It can drive the entire population toward a highly cooperative state in a broad range of parameters, independently of the type of institutions. We show that our finding is also valid for flexible incentives in the global sanctioning scheme, although the local arrangement works more effectively.

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Pure reward in a local scheme is more effective both for fixed and flexible incentives

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It can drive the entire population toward a highly cooperative state

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Increasing the efficiency of the institution can induce the success of pure reward

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A local scheme promotes group success more effectively than a global scheme

Conditional cooperation in group contests

In this paper we show experimentally that conditional cooperation, a phenomenon described in the private provision of public goods, is also present in group contests, where participants' contributions to their group performance partially determines if they overcome a rival group. This environment allows us to identify new determinants of conditional cooperation. We observe conditional cooperation in successful groups and in groups where members contribute more than rivals (even if they lose), but it vanishes in those groups that lose the contest due to low group performance. A random-effect linear panel regression analysis with an extensive set of controls confirms the findings.

Signalling boosts the evolution of cooperation in repeated group interactions

Many biological and social systems show significant levels of collective action. Several cooperation mechanisms have been proposed, yet they have been mostly studied independently. Among these, direct reciprocity supports cooperation on the basis of repeated interactions among individuals. Signals and quorum dynamics may also drive cooperation. Here, we resort to an evolutionary game-theoretical model to jointly analyse these two mechanisms and study the conditions in which evolution selects for direct reciprocity, signalling, or their combination. We show that signalling alone leads to higher levels of cooperation than when combined with reciprocity, while offering additional robustness against errors. Specifically, successful strategies in the realm of direct reciprocity are often not selected in the presence of signalling, and memory of past interactions is only exploited opportunistically in the case of earlier coordination failure. Differently, signalling always evolves, even when costly. In the light of these results, it may be easier to understand why direct reciprocity has been observed only in a limited number of cases among non-humans, whereas signalling is widespread at all levels of complexity.