Prisoner's Dilemma Research Articles

Two-stage strategy update rule based on learning cost in weak prisoner's dilemma.

When players are dissatisfied with their actual payoffs, they will change the actuality by learning strategy of neighbors. The more effort players put in, the more likely they are to succeed in learning. Inspired by this, this paper proposes a two-stage strategy update rule based on learning cost. The players first decide whether to learn strategy according to the updating willingness. If the players imitate the strategy of neighbors, they need to pay the learning cost. Results show that for the well-mixed population, if the updating willingness is homogeneous and remains unchanged, reducing the updating willingness or increasing the learning cost can extend the life cycle of cooperators. If the updating willingness is heterogeneous and dynamically adjusted based on the difference between the actual payoff and the expected payoff, increasing aspiration value and learning cost promotes cooperation. For the structured population, if the updating willingness is homogeneous and remains unchanged, the moderate learning cost is beneficial for cooperators to resist the temptation of defection, and reducing updating willingness makes the system maintain cooperation within a larger parameter range. If the updating willingness is heterogeneous and dynamically adjusted, the larger learning cost and the appropriate aspiration value promote cooperation. This study highlights the complex dynamics of cooperation in paid strategy learning, contributing to the theory of cooperation in the evolutionary game.

Effects of two-person synchronized cycling exercise on interpersonal cooperation: A near-infrared spectroscopy hyperscanning study

ObjectiveAlthough psychological research indicating the synchronous activities can promote interpersonal cooperation, thus far there is no direct evidence that two-person synchronous exercise effectively enhances interpersonal cooperative behaviors in Physical exercise field. This suggests that, although synchronization phenomenon is widespread in sports and is considered a potential tool for enhancing teamwork, its specific effects and functioning mechanisms still need to be clarified by further scientific research. This study intends to use two-person synchronized cycling exercise to investigate the synchronized exercise effect on interpersonal cooperative behavior and its underlying neural mechanisms. MethodsEighty college students without regular exercise habits will be randomly assigned to the experimental group (10 male dyads and 10 female dyads) and the control group (10 male dyads and 10 female dyads). During the experiment, dyads in the experimental group performed a 30-minute synchronized cycling exercise with synchronized pedaling movements; dyads in the control group rested sedentary in the same environment for 30 minutes. Interpersonal cooperative behavior was assessed with the Prisoner's Dilemma task, and the interpersonal neural synchronization(INS) data were collected in the prefrontal cortex using near-infrared hyperscanning. ResultsThis study compared behavior and brain activity before and after synchronous exercise. Behavioral results revealed that, compared to pre-exercise, dyads in the post-exercise had higher average cooperation rates, higher cooperation efficiency and shorter cooperation response times. Compared to post-sedentary, dyads in the post-exercise had shorter cooperation response times and higher cooperation efficiency. Furthermore, brain data showed that,compared to pre-exercise, dyads in the post-exercise had stronger INS in the dorsolateral prefrontal cortex(DLPFC), whereas the dyads in the post-exercise had stronge INS in the DLPFC compared to post-sedentary. After controlling for dyads' anxiety and mood states, this study also found a marginally significant negative correlation between INS differences in the left DLPFC and cooperation response time differences. ConclusionsThis research confirms, from both behavioral and neuroscience perspectives, that one synchronization cycle can significantly enhance interpersonal cooperative behavior, and this positive effect is closely associated with increased INS in the left DLPFC. This study provides new insights into understanding how positive interactive exercises promote interpersonal cooperation through specific neural mechanisms.

Energy Protectionism: Tren Meningkatnya Kebijakan Proteksionisme Energi di Uni Eropa

This research discusses the impact of EU energy protectionism in the face of global challenges such as the Covid-19 pandemic and the energy crisis due to the Russia-Ukraine conflict. Those two major events reveal the risks of over-dependence on foreign suppliers and the lack of diversification in the EU supply chain. As a solution, the EU has implemented various policies, including RePowerE, Carbon Border Adjustment Mechanism (CBAM), and Green Deal Industrial Plan (GDIP), to reduce dependence on energy imports and increase domestic renewable energy production. Through the analysis of neoliberalism and Game Theory approaches, particularly the Prisoner's Dilemma concept, this article explores the implications of protectionist policies on international trade stability. The analysis shows that while protectionist policies can strengthen the EU's energy independence and domestic security, they also have the potential to trigger international trade tensions and protectionist retaliation from other countries.

Endogenous monitoring through voluntary reporting in an infinitely repeated prisoner's dilemma game: experimental evidence

AbstractExogenous reputational information is known to improve cooperation. This study experimentally investigates how people create such information by reporting their partner's action choices, and whether endogenous monitoring helps to sustain cooperation, in an indefinitely repeated prisoner's dilemma game with random matching. The experimental results show that most subjects report their opponents' action choices, thereby successfully cooperating when reporting does not involve costs. However, when reporting is costly, participants are strongly discouraged from doing so. Consequently, they fail to achieve strong cooperative norms when the reported information is conveyed privately only to their next‐round interaction partners. Costly reporting occurs only occasionally even when there is a public record whereby all future partners can check the reported information, but significantly more frequently relative to the condition in which it is sent to the next partner only. With public records, groups can foster cooperative norms aided by reported information that gradually accumulates and becomes more informative over time.

A study on omnichannel retailers' return strategies considering showroom and consumer preference behavior

AbstractTo address omnichannel retailers' return challenges, considering consumers' brand and channel preferences. Four subgame models for retailers' Experience‐in‐Store‐and‐Buy‐Online (ESBO) return strategies in a double oligopoly market are developed. Using an optimization model and inverse induction method, equilibrium strategies under different conditions are determined. Finally, simulation analyzes parameter sensitivity and equilibrium strategies. Findings show that when consumers' brand preference is low, the (Y,Y) subgame is the unique equilibrium solution, but profits do not significantly increase and are always lower than the (N,N) subgame, leading to a Prisoner's Dilemma. With a clear brand preference, both retailers always obtain the maximum profit under the (Y,Y) subgame. In markets with a high proportion of omnichannel consumers and a large number of high‐cost‐to‐store consumers, the party implementing the ESBO strategy benefits more in a fiercely competitive market, while the profit situation of the party not implementing the ESBO strategy is less optimistic.

Game-theoretic agent-based modelling of micro-level conflict: Evidence from the ISIS-Kurdish war.

This article delves into the dynamics of a dyadic political violence case study in Rojava, Northern Syria, focusing on the conflict between Kurdish rebels and ISIS from January 1, 2017, to December 31, 2019. We employ agent-based modelling and a formalisation of the conflict as an Iterated Prisoner's Dilemma game. The study provides a nuanced understanding of conflict dynamics in a highly volatile region, focusing on microdynamics of an intense dyadic strategic interaction between two near-equally- powered actors. The choice of using a model based on the Iterated Prisoner's Dilemma, though a classical approach, offers substantial insights due to its ability to model dyadic, equally-matched strategic interactions in conflict scenarios effectively. The investigation primarily reveals that shifts in territorial control are more critical than geographical or temporal factors in determining the conflict's course. Further, the study observes that the conflict is characterised by periods of predominantly one-sided violence. This pattern underscores that the distribution of attacks, and target choices are a more telling indicator of the conflict nature than specific behavioural patterns of the actors involved. Such a conclusion aligns with the strategic implications of the underlying model, which emphasises the outcome of interactions based on differing aggression levels. This research not only sheds light on the conflict in Rojava but also reaffirms the relevance of this type of game-theoretical approach in contemporary conflict analysis.

Empirically testing a relationship between cooperation and the prime numbers.

Theoretical models suggest a relationship between cooperation and the prime numbers. In environments where agents play multiple one-shot prisoner's dilemma games per generation, cooperators evolve to fixation more frequently when cooperating on a cyclical schedule with a prime-number period length. This finding parrots classic predator-prey models showing selection for prime-number prey life cycles. Here, I report an empirical test of the former models using previously published data concerning humans playing one-shot public goods games across multiple time points-i.e. an analogue to multiple one-shot prisoner's dilemma games. I find very modest evidence of cyclicality at prime-numbered time intervals, though results indicate rough agreement between theoretical predictions and observed rates of full cooperation across time points. Analyses of individual decisions find increased contributions to the public good at prime-number time points and separate placebo tests indicate a 4-in-1000 chance of spuriously estimating this effect. However, when exploratory analyses exclude low-value prime-numbered time points, the magnitude of the estimated effect decreases and the hypothesis of no effect cannot be rejected, implying that low-value, prime-number time points drive estimates, contrary to theoretical model predictions. These findings cast doubt on the hypothesis of increased cooperation at prime-number time points-at least among humans playing public goods games.

Adoption of Zero-Determinant Strategy in Multiplayer Prisoner's Dilemma

Adoption of Zero-Determinant Strategy in Multiplayer Prisoner's Dilemma

Exploring cyclic dominance in rock-paper-scissor strategies within the Optional Prisoner's Dilemma: A quantitative analysis with environmental feedback

This research investigation delves into the concept of cyclic dominance and its interplay with environmental feedback within the framework of the Optional Prisoner's Dilemma (OPD) game. A quantitative model has been meticulously constructed to encompass both the OPD and Rock-Paper-Scissors (RPS) games, wherein the outcomes are contingent upon environmental feedback. The intricate relationship between player populations and their surrounding environment is elucidated through the utilization of replicator dynamics. The empirical findings of this study shed light on the existence of distinct equilibria contingent upon the prevailing environmental circumstances. Under scenarios characterized by resource depletion, an equilibrium state emerges wherein only solitary individuals (referred to as "loners") persist. Conversely, under conditions of resource replenishment, an equilibrium is established where various strategic approaches coexist in equal proportions, akin to the dynamics of the Rock-Paper-Scissors game. Notably, cyclic dominance manifests itself during periods characterized by intermediate environmental conditions. Several pivotal factors have been identified as determinants of these dynamic phenomena, including the rate of environmental replenishment, the strength of the dilemma presented, the payoff for loners, and the reward for a draw. It has been empirically demonstrated that the presence of extreme values in the replenishment rate, irrespective of whether exceptionally high or exceptionally low, serves as an impediment to the emergence of cyclic dominance. This model underscores the substantial influence of environmental feedback on social dilemmas, particularly in the context of the OPD game, ultimately leading to the emergence of competitive cyclic dominance games reminiscent of the Rock-Paper-Scissors game. In doing so, it elucidates the intricate interplay between evolutionary game incentives and the dynamics of the surrounding environment.

The Importance of Being Consistent: Attribution of Mental States in Strategic Human-Robot Interactions.

This article investigates the attribution of mental state (AMS) to an anthropomorphic robot by humans in a strategic interaction. We conducted an experiment in which human subjects are paired with either a human or an anthropomorphic robot to play an iterated Prisoner's Dilemma game, and we tested whether AMS is dependent on the robot "consistency," that is, the correspondence between the robot's verbal reaction and its behavior after a nonoptimal social outcome of the game is obtained. We find that human partners are attributed a higher mental state level than robotic partners, regardless of the partner's consistency between words and actions. Conversely, the level of AMS assigned to the robot is significantly higher when the robot is consistent in its words and actions. This finding is robust to the inclusion of psychological factors such as risk attitude and trust, and it holds regardless of subjects' initial beliefs about the adaptability of the robot. Finally, we find that when the robot apologizes for its behavior and defects in the following stage, the epistemic component of the AMS significantly increases.

Pricing and Capacity Allocation in Opaque Selling

To solve the supply and demand mismatch problem, intermediaries have emerged as an opaque channel for service providers to dispose of leftover capacity. This paper focuses on pricing and capacity allocation in opaque selling. We develop a Stackelberg game model, where two capacity-constrained service providers first decide the capacity allocated to an intermediary who then determines the opaque price based on its capacity. We examine the conditions under which the service providers should cooperate with the intermediary, and find that the opaque price and capacity allocation decisions are affected by product type, service providers’ capacity, and commission rate. Moreover, we find that the service providers may fall into the prisoner's dilemma when distributing through the intermediary. It indicates that although opaque selling can bring service providers more profit, it may not help them achieve the optimal profit. In view of this, we propose an alliance policy to eliminate the prisoners’ dilemma and examine when the service providers should ally. Results show that this policy can improve the profits of the service providers and the whole supply chain if the commission rate is adequately low. Our findings suggest that opaque selling can be less beneficial than previously shown and demonstrate the importance of an alliance policy.

The role of payoff parameters for cooperation in the one-shot Prisoner's Dilemma

The Prisoner's Dilemma is arguably the most important model of social dilemmas, but our knowledge about how its material payoff structure affects cooperation is incomplete. We investigate the effect of variation in material payoffs on cooperation in one-shot Prisoner's Dilemma games. We report results from three experiments (N = 1,993): in a preliminary experiment, we vary the payoffs over a large range. In our first main experiment (Study 1), we present a novel design that varies payoffs orthogonally in a within-subjects design. Our second main experiment, Study 2, investigates the orthogonal variation of payoffs in a between-subjects design. In a complementary analysis we also study the closely related payoff indices of normalized loss and gain, and the K-index. A robust finding of our experiments is that cooperation increases with the gains of mutual cooperation over mutual defection.

The Big M Game

This article discusses "extreme" Prisoner's Dilemma games, and questions Nash equilibrium as a solution concept in such situations. A slight reformulation of the concept is suggested, securing that a more reasonable solution is chosen. A SMALL WARNING TO THE READER: This article is special, not everything is true. That is, there are fictional parts. The reader is left for deciding what is fictional and what is science. Perhaps we could categorize the paper as a quiz where the objective is to rule out fictional parts from the content which at least is meant to be scientific.

Memory–based adaptive interaction willingness enhances cooperation in spatial prisoner's dilemma

As an important part of the evolution of cooperation, interaction diversity has attracted extensive attention. Traditional studies mainly focus exclusively on either time or space, and the comprehensive impact of these two dimensions on the evolution of cooperation deserves further exploration. In this paper, the interaction willingness is abstracted as the network weight, and an adaptive mechanism for interaction willingness based on the delay effect is proposed by combining the network weight and accumulated payoff. Specifically, individuals adjust their willingness to participate in the game with a delay, considering the change in accumulated payoffs within a certain period, rather than the change in immediate payoffs. The degree of delay is reflected in the length of individuals' memory of historical payoffs. Simulation results deviate from the intuition that more information facilitates cooperation, and in certain modes of interaction willingness adjustment, the correlation between cooperation level and memory–length is non–monotonic. Long–memory is conducive to promoting cooperation under the condition of a relatively large range adjustment of interaction willingness. Conversely, with a narrow adjustment range of interaction willingness, cooperation can be effectively established with short–memory. These results hold substantial implications for both theory and practice, as slight adjustment often corresponds to low loss and high operability. In addition, the underlying mechanism is furthermore explored, revealing that the ‘isolation zones’ composed of individuals with low interaction willingness play an important role in promoting cooperation.

Socio‐economic strategy for settlement of refugees amidst crisis: The case of Pak‐Afghan

AbstractToday, global concerns are at their peak due to the fast‐growing number of refugees. The world faces the dilemma of the refugee crisis, which needs to be addressed by the United Nations (U.N.) sustainable development goals (SDGs). Pakistan hosts about 1.4 million registered refugees in camps and urban areas. The majority consist of Afghans who departed due to severe poverty, conflict, and security concerns. These refugees bring socio‐economic distress to the host country. In order to comprehend the whole crisis, this study primarily focuses on three areas: the unstable political and security situation in the country of origin, the refugee concerns and their implications. This research is unique throughout the literature as it applies the interpretive structural modelling (ISM) tool to view the refugee crisis holistically. Results from ISM show that the ‘Political situation of Afghanistan’ is the most influential factor with very high driving power. Afterward, 10 resulting factors were opted from the ISM model, which demonstrate the implications on the host country. The relative importance index (RII) approach was used to rank the resultant factors. Ranking from RII depicts a significantly different impact of refugees while residing in urban areas. Using the Prisoner's dilemma of cooperative game theory (GT), this study concludes by recommending refugees to get registered and the host country to settle them in the local population. The use of cooperative GT with the nexus of ISM and RII is also exceptional and will be helpful for researchers and policymakers to resolve any conflict.

Mixed strategy approach destabilizes cooperation in finite populations with clustering coefficient.

Evolutionary game theory, encompassing discrete, continuous, and mixed strategies, is pivotal for understanding cooperation dynamics. Discrete strategies involve deterministic actions with a fixed probability of one, whereas continuous strategies employ intermediate probabilities to convey the extent of cooperation and emphasize expected payoffs. Mixed strategies, though akin to continuous ones, calculate immediate payoffs based on the action chosen at a given moment within intermediate probabilities. Although previous research has highlighted the distinct impacts of these strategic approaches on fostering cooperation, the reasons behind the differing levels of cooperation among these approaches have remained somewhat unclear. This study explores how these strategic approaches influence cooperation in the context of the prisoner's dilemma game, particularly in networked populations with varying clustering coefficients. Our research goes beyond existing studies by revealing that the differences in cooperation levels between these strategic approaches are not confined to finite populations; they also depend on the clustering coefficients of these populations. In populations with nonzero clustering coefficients, we observed varying degrees of stable cooperation for each strategic approach across multiple simulations, with mixed strategies showing the most variability, followed by continuous and discrete strategies. However, this variability in cooperation evolution decreased in populations with a clustering coefficient of zero, narrowing the differences in cooperation levels among the strategies. These findings suggest that in more realistic settings, the robustness of cooperation systems may be compromised, as the evolution of cooperation through mixed and continuous strategies introduces a degree of unpredictability.

India Counterterrorism: India and Pakistan's Lack of Cooperation in Fighting Lashar e-Taiba after Mumbai Attacks 2008

Following the 2008 Mumbai Attacks, India refrained from engaging in counterterrorism cooperation with Pakistan, the origin country of Lashkar e-Taiba (LeT), marking a significant departure from previous approaches. This study investigates the factors influencing India's decision through the lens of the Prisoner's Dilemma Theory. By examining India's strategic calculations and contextualizing them within the security dilemma framework post-Mumbai terror, this research aims to elucidate the rationale behind India's non-cooperative stance. Results reveal a complex interplay of historical distrust, perceived security threats, and strategic considerations shaping India's decision-making, highlighting the implications for future counter-terrorism efforts and international relations strategies.

Private list sharing leads to cooperation and central hubs emergence in ABM

We introduce an agent based model framework to investigate how an alternative to classic image score and gossip can support the emergence of cooperation in a repeated prisoner dilemma game with agents employing mixed strategies. We debate the universality of image scores, arguing that they cannot be considered an objective property of the agents observed but rather a subjective property of each observer. From this assumption, we develop a private list mechanism for opponent selection and gossip sharing among the population of the simulation. The results show that the private list mechanism is able to foster the emergence of cooperation, and that for various levels of list usage different levels of cooperation correspond in the system. Finally, we observe interesting topological properties emerging, with networks characterised by one ‘super-hub’ connected to every other node, suggesting the emergence of centralized entities to support cooperation.

Belief Updating during Social Interactions: Neural Dynamics and Causal Role of Dorsomedial Prefrontal Cortex.

In competitive interactions, humans have to flexibly update their beliefs about another person's intentions in order to adjust their own choice strategy, such as when believing that the other may exploit their cooperativeness. Here we investigate both the neural dynamics and the causal neural substrate of belief updating processes in humans. We used an adapted prisoner's dilemma game in which participants explicitly predicted the coplayer's actions, which allowed us to quantify the prediction error between expected and actual behavior. First, in an EEG experiment, we found a stronger medial frontal negativity (MFN) for negative than positive prediction errors, suggesting that this medial frontal ERP component may encode unexpected defection of the coplayer. The MFN also predicted subsequent belief updating after negative prediction errors. In a second experiment, we used transcranial magnetic stimulation (TMS) to investigate whether the dorsomedial prefrontal cortex (dmPFC) causally implements belief updating after unexpected outcomes. Our results show that dmPFC TMS impaired belief updating and strategic behavioral adjustments after negative prediction errors. Taken together, our findings reveal the time course of the use of prediction errors in social decisions and suggest that the dmPFC plays a crucial role in updating mental representations of others' intentions.

Revisiting the bounded generalized reciprocity model: Ingroup favoritism and concerns about negative evaluation

The bounded generalized reciprocity (BGR) model, grounded in reputation management, predicts that the motivation underlying ingroup favoritism (favoring one's own group over other groups) is driven by avoiding a negative reputation within one's own group. This research conducted two economic games with minimal groups in which reputational concerns (partners' knowledge of participants' group membership) were manipulated. We aimed to verify the replicability of the experimental results in support of the BGR model. A study (N = 394) using a dictator game (in which participants unilaterally determined their partners' payoffs) indicated the following: (1) participants were more likely to behave cooperatively with ingroup partners than with outgroup partners, regardless of whether their partners knew the participants' group membership; and (2) individual differences in fear of negative evaluation by others were not associated with cooperation toward the ingroup. Similar results were found in another study (N = 429) using a prisoner's dilemma game (in which participants' payoffs were determined by their partners). However, while sharing knowledge about group membership facilitated cooperation with the outgroup in the dictator game, no such tendency was observed in the prisoner's dilemma game. These findings suggest that concerns about a bad reputation may not play a relatively important role in ingroup favoritism, and that generosity toward outgroup members is influenced by the presence or absence of interdependence (i.e., whether the partner's behavior affects the participant's payoffs). This research proposes a reconsideration of the motivations behind cooperation within or between groups.