![Strategy selection in finite and infinite populations, depending on the information parameter m. The left column shows the outcome of a simulation of the replicator equation for 1000 randomly chosen initial populations. If only punishment is available to sway opportunistic behaviour, then cooperative outcomes become more likely if m exceeds roughly 1/3 (in which case [O C , P] becomes fixed). As soon as rewards are also allowed, punishment-enforced cooperation becomes predominant as soon as m. g/2b ¼ 1/4. Additionally, for smaller values of m, the population may tend to cycle between the strategies [O C , R], [O C , N], [O D , N] and [O D , R], represented by the orange line in the lower left graph. The right column shows the stationary distribution of strategies in a finite population. Again, without rewards a considerably higher information level m is necessary to promote punishment-enforced cooperation (either [O C , P] or [O D , P]; note that both opportunist strategies become indistinguishable in the limit case of complete information). In finite populations, rewarding strategies act merely as a catalyst for the emergence of punishment; even for small m, the outcomes [O C , R] (resp. [O D , R]) never prevail. Parameter values: b ¼ 4, c ¼ 1, b ¼ g ¼ 2. For finite populations, the population size is M ¼ 100 and the selection strength s ¼ 1/10.](https://www.researchgate.net/profile/Christian-Hilbe/publication/43073025/figure/fig1/AS:601735101956101@1520476236203/Strategy-selection-in-finite-and-infinite-populations-depending-on-the-information_Q320.jpg)
![Average number of mutations needed until a population of [O D , N] players is successfully invaded. Adding the possibility of rewards reduces the waiting time considerably (for m ¼ 0% it takes 500 mutations with rewards and almost 500 000 mutations without). As the information level increases, this catalytic effect of rewarding disappears. Parameter values: population size M ¼ 100, selection strength s ¼ 1/10; b ¼ 4, c ¼ 1, b ¼ g ¼ 2. Squares, P and N only; circles, P, N, R.](https://www.researchgate.net/profile/Christian-Hilbe/publication/43073025/figure/fig2/AS:601735101956102@1520476236237/Average-number-of-mutations-needed-until-a-population-of-O-D-N-players-is_Q320.jpg)
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Incentives and Opportunism: From the Carrot to the Stick
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Cooperation in public good games is greatly promoted by positive and negative incentives. In this paper, we use evolutionary game dynamics to study the evolution of opportunism (the readiness to be swayed by incentives) and the evolution of trust (the propensity to cooperate in the absence of information on the co-players). If both positive and negative incentives are available, evolution leads to a population where defectors are punished and players cooperate, except when they can get away with defection. Rewarding behaviour does not become fixed, but can play an essential role in catalysing the emergence of cooperation, especially if the information level is low.
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... Rewards cannot be misused for retaliation or spite, nor do they bear the risk of reducing overall welfare 19 . Existing models predict that rewards can promote cooperation and that they are particularly effective in populations with only a few cooperators (such that rewarding those cooperators is relatively cheap [21][22][23][24] ). These conclusions, however, are (again) based on biased strategy sets 53 . ...
... Importantly, however, the way how individuals reward others can become publicly known with some probability. In particular, similar to earlier models [21][22][23][24] , people may learn that a given group member tends to reward socially (or anti-socially). Such knowledge allows individuals to react opportunistically. ...
... The recipient can either never reward the donor (NR), reward donors who cooperate (social rewarding, SR), reward donors who defect (anti-social rewarding, AR), or reward unconditionally (UR). The last two options are absent in earlier two-player models of cooperation and rewarding 21,22 . This earlier work asks whether social rewards can promote the evolution of cooperation. ...
People routinely cooperate with each other, even when cooperation is costly. To further encourage such pro-social behaviors, recipients often respond by providing additional incentives, for example by offering rewards. Although such incentives facilitate cooperation, the question remains how these incentivizing behaviors themselves evolve, and whether they would always be used responsibly. Herein, we consider a simple model to systematically study the co-evolution of cooperation and different rewarding policies. In our model, both social and antisocial behaviors can be rewarded, but individuals gain a reputation for how they reward others. By characterizing the game’s equilibria and by simulating evolutionary learning processes, we find that reputation effects systematically favor cooperation and social rewarding. While our baseline model applies to pairwise interactions in well-mixed populations, we obtain similar conclusions under assortment, or when individuals interact in larger groups. According to our model, rewards are most effective when they sway others to cooperate. This view is consistent with empirical observations suggesting that people reward others to ultimately benefit themselves. Rewards can motivate people to cooperate, but the evolution of rewarding behavior is itself poorly understood. Here, a game-theoretic analysis shows that reputation effects facilitate the simultaneous evolution of cooperation and social rewarding policies.
... Several theoretical models studied how to combine institutional reward and punishment for enhancing the emergence and stability of cooperation [2,6,1,10,27]. However, little attention has been given to addressing the cost optimisation of providing incentives. ...
... Note that, as discussed above, this mixed incentive, also known as the 'carrot and stick' approach, has been shown efficient for promoting cooperation in both pairwise and multi-player interactions [24,10,27,6]. However, these works have not studied cost optimisation and have not shown whether this approach is actually more cost-efficient and by how much. ...
In this paper, we rigorously study the problem of cost optimisation of hybrid institutional incentives (combination of reward and punishment) for maximising the level (or guaranteeing at least a certain level) of cooperative behaviour in a well-mixed, finite population of self-regarding individuals where players interact via cooperation dilemmas (Donation Game or Public Goods Game). We show that a mixed incentive scheme can offer a more cost-efficient approach for providing incentives while ensuring the same level or standard of cooperation in the long-run. We establish the asymptotic behaviour (namely weak selection, strong selection, and infinite-population limits). We prove the existence of a phase transition, obtaining the critical threshold of the strength of selection at which the monotonicity of the cost function changes and providing an algorithm for finding the optimal value of the individual incentive cost. Our analytical results are illustrated with numerical investigations. Overall, our analysis provides novel theoretical insights into the design of cost-efficient institutional incentive mechanisms for promoting the evolution of cooperation in stochastic systems.
... This field aims to describe which mechanisms promote cooperative behaviours, and in which social and ecological environments cooperation is most likely to spread. Among the mechanisms that facilitate cooperation are kin selection [8,9] and group selection [10,11], direct [12][13][14] and indirect reciprocity [15,16], network structure [17][18][19], and reward and punishment [20][21][22][23]. ...
One landmark application of evolutionary game theory is the study of social dilemmas. This literature explores why people cooperate even when there are strong incentives to defect. Much of this literature, however, assumes
that interactions are symmetric. Individuals are assumed to have the same
strategic options and the same potential pay-offs. Yet many interesting questions
arise once individuals are allowed to differ. Here, we study asymmetry
in simple coordination games. In our set-up, human participants need to
decide how much of their endowment to contribute to a public good. If a
group’s collective contribution reaches a pre-defined threshold, all group
members receive a reward. To account for possible asymmetries, individuals
either differ in their endowments or their productivities. According to a
theoretical equilibrium analysis, such games tend to have many possible solutions.
In equilibrium, group members may contribute the same amount,
different amounts or nothing at all. According to our behavioural experiment,
however, humans favour the equilibrium in which everyone
contributes the same proportion of their endowment. We use these experimental
results to highlight the non-trivial effects of inequality on
cooperation, and we discuss to which extent models of evolutionary game
theory can account for these effects.
This article is part of the theme issue ‘Half a century of evolutionary
games: a synthesis of theory, application and future directions’.
... Our definition of institutions, however, does not allow for rules that are enforced via promised rewards, because this turns rule compliance into a simple economic transaction. Hilbe and Sigmund (2010) use evolutionary game theory to show that societies evolve towards using punishment rather than rewards to enforce compliance, although rewards might be superior in a low-cooperation environment. 4 Below, we explain that the one subtype of institutions for which Schotter's definition appears appropriate to us are self-enforcing institutions. ...
... This establishes a dilemma between individual and collective interests when players are motivated to defect and consume more than they would individually. A similar dilemma occurs at a larger scale when countries use the same natural resources, like the oceans or the atmosphere [1][2][3][4]. ...
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.
... In past decades, a substantial body of theoretical and experimental investigations have illuminated various solutions including norms and incentive mechanisms that can be used to promote the evolution of cooperation [18][19][20][21][22][23][24][25][26][27][28][29]. A frequently discussed incentive mechanism is punishment, with which some cooperators pay extra cost to punish selfish individuals [30][31][32][33][34][35][36]. As a special form of punishment, social exclusion has been introduced. ...
Explaining the emergence and maintenance of cooperation among selfish individuals from an evolutionary perspective remains a grand challenge in biology, economy, and social sciences. Social exclusion is believed to be an answer to this conundrum. However, previously related studies often assume one-shot interactions and ignore how free-riding is identified, which seem to be too idealistic. In this work, we consider repeated interactions where excluders need to pay a monitoring cost to identify free-riders for exclusion and free-riders cannot participate in the following possible game interactions once they are identified and excluded by excluders in the repeated interaction process. We reveal that the introduction of such exclusion can prevent the breakdown of cooperation in repeated group interactions. In particular, we demonstrate that an evolutionary oscillation among cooperators, defectors, and excluders can appear in infinitely large populations when early exclusion is implemented. In addition, we find that the population spends most of the time in states where cooperators dominate for early exclusion when stochastic mutation-selection is considered in finite populations. Our results highlight that early exclusion is successful in solving the mentioned enigma of cooperation in repeated group interactions.
Notwithstanding the voluminous studies of accountability, little is known about its internal mechanism and its controversial relationship with blame avoidance. Based on the ‘accountability cube’ model, this study identifies four essential components of accountability: monitoring intensity, discussion quality, reward-based consequences, and punishment-based consequences. It explores the impacts of the four elements and their diverse configurations on bureaucrats’ blame avoidance. Drawing on survey data from Chinese civil servants, this study suggests that sanction-based accountability comprising stringent monitoring and punishment may trigger blame avoidance. Trust-based accountability, which includes high discussion quality and potential rewarding consequences, is more beneficial in containing blame avoidance.
This document represents Deliverable 2.1 “Overview of regulatory and incentive instruments for biodiversity management on farms” within WP2 „Identifying incentives to promote biodiversity and ecosystem services in agricultural landscapes“ of the EU Horizon 2020 project SHOWCASE. It reports the outcomes of WP2 Task 2.1 “Evaluating regulatory and incentive instruments for biodiversity management on farms”.
In the 1st and 2nd chapter, the report gives a short introduction of the deliverable’s objectives, the tasks addressed, the report’s outline and the main focus of the literature review.
Chapter 3 gives an overview of the main laws governing biodiversity protection in the European Union. The main elements of the Birds and Habitats directives are presented, alongside other biodiversity laws and policies, with a focus on the obligations and requirements they set on agriculture in order to protect European native wildlife. Chapter 3 also covers the features of the EU’s Common Agricultural Policy that operate as a regulatory baseline for all beneficiaries of farm subsidies, i.e., cross-compliance and greening requirements under the current CAP and the new conditionality in the CAP 2023-2027.
Chapter 4 gives an overview of economic and non-economic approaches potentially promoting farmers’ pro-biodiversity behaviour. Whereas economically oriented approaches imply positive or negative monetary flows – compensation payments or rewards vs. penalties – to motivate farmers to implement biodiversity-friendly management practices or to prevent them from harming biodiversity, partnerships and networks steer farmers’ behaviour through agreeing on a common goal and working towards it by sharing resources, skills and risk. With regards to the agricultural focus of SHOWCASE, Chapter 4 looks in more detail at the incentives provided by the Common Agricultural Policy (CAP) of the European Union. This covers both the current and future CAP, with an overview of how the novel eco-schemes can provide new incentives for farmers to adopt biodiversity friendly practices.
Chapter 5 looks into how the combination of regulatory frameworks and incentives operate in practice for farmers in the EU. To this end, grey literature and European Commission publications related to farming for biodiversity have been reviewed. A specific focus is set on biodiversity-friendly farming in Natura 2000 sites, as central exemplary areas of continuous and long-lasting efforts in biodiversity conservation. This is followed by revising some of the main conclusions from very recent grey literature assessing the successes and failures of the CAP in relation to biodiversity.
Chapter 6 provides an overview of approaches that have already been implemented to incentivize farmers’ pro-biodiversity behaviour. Based on grey literature, various types of approaches – i. e. focusing on plot or farm level, land tenure or the entire value chain, building on organic farming or including market-based, value-based or measure-based mechanisms – were identified within the EBA countries, further EU member states and selected western countries outside the EU. In sum, 62 examples of pro-biodiversity schemes were included in the further analysis representing highly divergent incentivizing mechanisms and the most important agricultural systems of the EBAs as well as in consequence serving as an information platform for further EBA scheme design activities.
Based on the preceding chapters and their focus on result-based approaches, Chapter 7 casts a critical eye on their suitability with regards to various regulatory, policy, social and administrative contexts also considering potential national differences. On the international level, WTO requirements such as Green Box rules are a limiting factor with regards to result- based payment modalities and thus scheme design. On the national and regional level, issues to be considered include long-term availability of funding, guaranteeing additionality if requested, stakeholders’ and decision-makers’ attitudes towards agri-environment-climate measures in general as well as towards result-oriented approaches specifically, availability of suitable indicators and IT-systems, access to extension services and profound know-how of
farmers and public authorities regarding the interlinkages between biodiversity and farming practices. On individual level, farmers’ trust in involved institutions and their willingness to participate are additionally discussed as highly relevant factors affecting the suitability of result- based approaches.
In Chapter 8 a structured overview on factors influencing farmers’ willingness to promote biodiversity by implementing voluntary biodiversity measures is presented. Based on the review of scientific literature, the chapter describes several determinants which have been identified along three scales, i.e. 1) society, community and landscape, 2) farm scale, and 3) farmers’ intrinsic factors. The main influencing factors at the first scale range from the design of policies, to economic aspects, to socio-cultural norms. The second scale encompasses relevant farm characteristics, such as farm type and size to field conditions. For the farmers’ intrinsic factors age, education, experience, and self-identity play an important role. However, it is important to make a distinction between farmers’ willingness to participate in schemes and their actual behaviour, because the latter is determined by their ability to do so.
Chapter 9 closes the Deliverable by giving an outlook on the further use of the results for scientific analyses within SHOWCASE, supporting mainly the work of designing interventions in WP1 and of developing surveys and model designs in WP2, as well as providing a basis for communication and policy recommendation material for WP4.
Recent studies show that different update rules are invariant regarding the evolutionary outcomes for a well-mixed population or homogeneous network. In this paper, we investigate how the Q-learning algorithm, one of the reinforcement learning methods, affects the evolutionary outcomes in square lattice. Especially, we consider the mixed strategy update rule, among which some agents adopt Q-learning method to update their strategies, the proportion of these agents (these agents are denoted as Artificial Intelligence (AI)) is controlled by a simple parameter ρ. The rest of other agents, the proportion is denoted by 1 − ρ, adopt the Fermi function to update their strategies. Through extensive numerical simulations, we found that the mixed strategy-update rule can facilitate cooperation compared with the pure Fermi-function-based update rule. Besides, if the proportion of AI is moderate, cooperators among the whole population exhibit conditional behavior and moody conditional behavior. However, if the whole population adopts the pure Fermi-function-based strategy update rule or the pure Q-learning-based strategy update rule, then cooperators among the whole population exhibit the hump-shaped conditional behavior. Our results provide a new insight to understand the evolution of cooperation from AI's view.
Explaining the emergence and maintenance of cooperation among selfish individuals from an evolutionary perspective remains a grand challenge in biology, economy and social sciences. Social exclusion is believed to be an answer to this conundrum. However, previously related studies often assume one-shot interactions and ignore how free-riding is identified, which seem to be too idealistic. In this work, we consider repeated interactions where excluders need to pay a monitoring cost to identify free-riders for exclusion and free-riders cannot participate in the following possible game interactions once they are identified and excluded by excluders in the repeated interaction process. We reveal that the introduction of such exclusion can prevent the breakdown of cooperation in repeated group interactions. In particular, we demonstrate that an evolutionary oscillation among cooperators, defectors and excluders can appear in infinitely large populations when early exclusion is implemented. In addition, we find that the population spends most of the time in states where cooperators dominate for early exclusion when stochastic mutation-selection is considered in finite populations. Our results highlight that early exclusion is successful in solving the mentioned enigma of cooperation in repeated group interactions.
The evolution of human cooperation remains a puzzle because cooperation persists even in conditions that rule out mainstream explanations. We present a novel solution that links two recent theories. First, Johnson & Kruger (2004) suggested that ancestral cooperation was promoted because norm violations were deterred by the threat of supernatural punishment. However, this only works if individuals attribute negative life events (or a prospective afterlife) as intentionally caused by supernatural agents. A complementary cognitive mechanism is therefore required. Recently, Bering and Shackelford (2004) suggested precisely this. The evolution of “theory of mind” and, specifically, the “intentionality system” (a cognitive system devoted to making inferences about the epistemic contents and intentions of other minds), strongly favoured: (1) the selection of human psychological traits for monitoring and controlling the flow of social information within groups; and (2) attributions of life events to supernatural agency. We argue that natural selection favoured such attributions because, in a cognitively sophisticated social environment, a fear of supernatural punishment steered individuals away from costly social transgressions resulting from unrestrained, evolutionarily ancestral, selfish interest (acts which would rapidly become known to others, and thereby incur an increased probability and severity of punishment by group members). As long as the net costs of selfish actions from real-world punishment by group members exceeded the net costs of lost opportunities from self-imposed norm abiding, then god-fearing individuals would outcompete non-believers.
Models indicate that opportunities for reputation formation can play an important role in sustaining cooperation and prosocial behavior. Results from experimental economic games support this conclusion, as manipulating reputational opportunities affects prosocial behavior. Noting that some prosocial behavior remains even in anonymous noniterated games, some investigators argue that humans possess a propensity for prosociality independent of reputation management. However, decision-making processes often employ both explicit propositional knowledge and intuitive or affective judgments elicited by tacit cues. Manipulating game parameters alters explicit information employed in overt strategizing but leaves intact cues that may affect intuitive judgments relevant to reputation formation. To explore how subtle cues of observability impact prosocial behavior, we conducted five dictator games, manipulating both auditory cues of the presence of others (via the use of sound-deadening earmuffs) and visual cues (via the presentation of stylized eyespots). Although earmuffs appeared to reduce generosity, this effect was not significant. However, as predicted, eyespots substantially increased generosity, despite no differences in actual anonymity; when using a computer displaying eyespots, almost twice as many participants gave money to their partners compared with the controls. Investigations of prosocial behavior must consider both overt information about game parameters and subtle cues influencing intuitive judgments.
How does cooperation emerge among selfish individuals? When do people share resources, punish those they consider unfair, and engage in joint enterprises? These questions fascinate philosophers, biologists, and economists alike, for the "invisible hand" that should turn selfish efforts into public benefit is not always at work.The Calculus of Selfishnesslooks at social dilemmas where cooperative motivations are subverted and self-interest becomes self-defeating. Karl Sigmund, a pioneer in evolutionary game theory, uses simple and well-known game theory models to examine the foundations of collective action and the effects of reciprocity and reputation.Focusing on some of the best-known social and economic experiments, including games such as the Prisoner's Dilemma, Trust, Ultimatum, Snowdrift, and Public Good, Sigmund explores the conditions leading to cooperative strategies. His approach is based on evolutionary game dynamics, applied to deterministic and probabilistic models of economic interactions.Exploring basic strategic interactions among individuals guided by self-interest and caught in social traps,The Calculus of Selfishnessanalyzes to what extent one key facet of human nature--selfishness--can lead to cooperation.
The Evolution of Cooperation at the Level of Individuals.- Evolutionary Foundations of Cooperation and Group Cohesion.- How to Evolve Cooperation.- Beyond Enlightened Self-Interest: Social Norms, Other-Regarding Preferences, and Cooperative Behavior.- Evolution, Cooperation, and Repeated Games.- Public Good Games with Incentives: The Role of Reputation.- Groups and Networks: Their Role in the Evolution of Cooperation.- Cooperation and Group Formation.- Evolution and Construction of Moral Systems.- Games, Groups, Norms, and Societies.- Evolutionary Theory and Cooperation in Everyday Life.- The Error of God: Error Management Theory, Religion, and the Evolution of Cooperation.- Moral Motivation.- Explaining Religion: Notes Toward a Research Agenda.- Cooperation and Problems of the Commons.- Building Trust to Solve Commons Dilemmas: Taking Small Steps to Test an Evolving Theory of Collective Action.- How Democracy Resolves Conflict in Difficult Games.- Two Strategic Issues in Apologizing.- Neither Self-interest Nor Self-sacrifice: The Fraternal Morality of Market Relationships.
Much uncertainty surrounds the detailed mechanisms whereby the human immunodeficiency virus (HIV) causes the acquired immunodeficiency syndrome (AIDS) after a long and variable asymptomatic period. The virus impairs immune responses by infecting and/or killing one of the most important cell populations of the immune system, the CD4 cells. HIV mutates so rapidly that many different variants arise (and coexist) during an individual infection. This article reviews mathematical models that outline the potential importance of this variability as a major factor for the development of AIDS. The essential idea is that the virus evades immune pressure by the continuous production of new mutants resistant to current immunological attacks (= antigenic variation). This results in the accumulation of antigenic diversity during the asymptotic period of the infection. The existence of an antigenic diversity threshold is derived from the interaction between the virus population and the immune cells: CD4 cells mount immune responses, some of which are directed against specific HIV variants, but each virus strain can induce killing of all CD4 cells regardless of their specificity. Therefore increasing HIV diversity enables the virus population to escape from control by the immune system. In this context the observed variability is responsible for the fact that the virus establishes a persistant infection without being cleared by the immune response and induces AIDS after a long and variable incubation period. HIV infections are evolutionary processes on the time scale of a few years. The mathematical models are based on ordinary differential equations. Virus mutation is described by a stochastic process.
Many studies show that people act cooperatively and are willing to punish free riders (i.e., people who are less cooperative than others). However, nonpunishers benefit when free riders are punished, making punishment a group-beneficial act. Presented here are four studies investigating whether punishers gain social benefits from punishing. Undergraduate participants played public goods games (PGGs) (cooperative group games involving money) in which there were free riders, and in which they were given the opportunity to impose monetary penalties on free riders. Participants rated punishers as being more trustworthy, group focused, and worthy of respect than nonpunishers. In dyadic trust games following PGGs, punishers did not receive monetary benefits from punishing free riders in a single-round PGG, but did benefit monetarily from punishing free riders in iterated PGGs. Punishment that was not directed at free riders brought no monetary benefits, suggesting that people distinguish between justified and unjustified punishment and only respond to punishment with enhanced trust when the punishment is justified.
Every form of behaviour is shaped by trial and error. Such stepwise adaptation can occur through individual learning or through natural selection, the basis of evolution. Since the work of Maynard Smith and others, it has been realised how game theory can model this process. Evolutionary game theory replaces the static solutions of classical game theory by a dynamical approach centred not on the concept of rational players but on the population dynamics of behavioural programmes. In this book the authors investigate the nonlinear dynamics of the self-regulation of social and economic behaviour, and of the closely related interactions between species in ecological communities. Replicator equations describe how successful strategies spread and thereby create new conditions which can alter the basis of their success, i.e. to enable us to understand the strategic and genetic foundations of the endless chronicle of invasions and extinctions which punctuate evolution. In short, evolutionary game theory describes when to escalate a conflict, how to elicit cooperation, why to expect a balance of the sexes, and how to understand natural selection in mathematical terms.