Prisoner's Dilemma Research Articles

Game Theory – The Repeated Prisoner's Dilemma Using the Example of the European Rail Market Leader

Game Theory – The Repeated Prisoner's Dilemma Using the Example of the European Rail Market Leader

An Introduction to Game Theory

Game theory is a branch of mathematics and economics that offers a unique lens through which to analyze strategic interactions among rational decision-makers. This paper provides a concise introduction to the fundamental concepts and applications of game theory. It explores the core components of games, including players, strategies, and payoffs, and distinguishes between normal form and extensive form games. Key classic games, such as the Prisoner's Dilemma and the Nash Equilibrium, are discussed to illustrate core principles. The paper also highlights the diverse applications of game theory in economics, political science, biology, and psychology, showcasing its versatility as a tool for understanding human behavior and decision-making in various fields. Whether you are a student new to the subject or a professional seeking a refresher, this introduction to game theory lays the foundation for a deeper appreciation of strategic thinking and its real-world implications.

Impact of Market Competition on Remanufacturing Investment

This article considers supply chain competition in which two symmetric manufacturers compete in both the new and remanufactured products markets. To engage in remanufacturing, the two competing manufacturers must appropriately determine their remanufacturing capability and design new products to facilitate their competition in remanufacturing. This inevitably changes the competing manufacturers’ cost structure in terms of both fixed and variable costs. The problem is formulated as a two-stage game. Therein, the competing manufacturers first determine whether to invest in remanufacturing, followed by determining the production quantities of new and remanufactured products if they decide to invest in remanufacturing. Our analytical results reveal that the equilibria associated with the three scenarios in which both manufacturers invest, neither manufacturer invests, and either manufacturer invests can be conditionally achieved, depending on the fixed cost incurred in developing remanufacturing capability and the difference between marginal costs associated with new and remanufactured products. Furthermore, it is found that despite the cost structure changes, remanufacturing investment can expand the two competing manufacturers’ market shares and outweigh the cannibalization effect between new and remanufactured products, resulting in higher profits. Nevertheless, the competing manufacturers may be trapped in a prisoner's dilemma when they both invest in remanufacturing operations. By comparing the environmental impact with and without remanufacturing investment, the result suggests that remanufacturing investment may not be environmental friendly, especially when the cost difference between new and remanufactured products is significant. Finally, the subsidy policy is proven to benefit manufacturers in gaining more profits and promoting the development of the remanufacturing industry, but may cause an unanticipated negative overall outcome on the environment.

‘I don’t want to play with you anymore’: dynamic partner judgements in moody reinforcement learners playing the prisoner’s dilemma

Abstract Emerging reinforcement learning algorithms that utilize human traits as part of their conceptual architecture have been demonstrated to encourage cooperation in social dilemmas when compared to their unaltered origins. In particular, the addition of a mood mechanism facilitates more cooperative behaviour in multi-agent iterated prisoner dilemma (IPD) games, for both static and dynamic network contexts. Mood-altered agents also exhibit humanlike behavioural trends when environmental aspects of the dilemma are altered, such as the structure of the payoff matrix used. It is possible that other environmental effects from both human and agent-based research will interact with moody structures in previously unstudied ways. As the literature on these interactions is currently small, we seek to expand on previous research by introducing two more environmental dimensions; voluntary interaction in dynamic networks, and stability of interaction through varied network restructuring. From an initial Erdos–Renyi random network, we manipulate the structure of a network IPD according to existing methodology in human-based research, to investigate possible replication of their findings. We also facilitated strategic selection of opponents through the introduction of two partner evaluation mechanisms and tested two selection thresholds for each. We found that even minimally strategic play termination in dynamic networks is enough to enhance cooperation above a static level, though the thresholds for these strategic decisions are critical to desired outcomes. More forgiving thresholds lead to better maintenance of cooperation between kinder strategies than stricter ones, despite overall cooperation levels being relatively low. Additionally, moody reinforcement learning combined with certain play termination decision strategies can mimic trends in human cooperation affected by structural changes to the IPD played on dynamic networks—as can kind and simplistic strategies such as Tit-For-Tat. Implications of this in comparison with human data is discussed, and suggestions for diversification of further testing are made.

Restructuring of neighborhood definition based on strategies will enhance the cooperation in a spatial prisoner's dilemma

Defectors often survive in spatial game theory, prompting researchers to devise models for cooperators' survival. However, most models overlook players' perspectives based on their strategies. This study introduces an agent-based model considering players' varied neighborhood conditions. In the first model, losing a competition alters the neighborhood definition, randomly adjusting the number of neighborhoods. In the second model, the number of neighborhoods changes based on the player's strategy after losing a competition. Compared to the other proposed model and a traditional spatial prisoner's dilemma model, the second model facilitates easier maintenance of cooperator density.

Prisoner's science.

Decisions involving cooperation or competition are common in science. Here, we consider three situations frequently encountered in the biomedical sciences, namely, establishing priority, sharing reagents, and selecting a journal for publication, through the lens of the prisoner's dilemma. In each situation, cooperation is the best strategy for scientists and for science.

An incentive compatible ZD strategy-based data sharing model for federated learning: A perspective of iterated prisoner's dilemma

Federated learning has been increasingly adopted as an effective means to cope with the significant increase in the volume of training data needed for machine learning and address the privacy concerns in using these data. However, moral hazard may occur when individual data providers (IDPs) use smaller amounts or low-quality data to train their local models and submit these low-quality results (gradients) to free-ride on the benefits of the federated learning. Therefore, federated learning operators often face the dilemma of encouraging more IDPs to participate in data sharing and ensuring truthful contributions from IDPs to obtain high-quality global training results. This article proposes a spontaneous cooperative data-sharing model to address this dilemma. Through an iterated prisoner's dilemma model solved by the zero-determinant (ZD) strategy, we show that the optimal ZD strategies of all IDPs are to maximize their training efforts when participating in federated learning. According to the comparisons with other approaches through simulations, we demonstrate that either the two-IDP with binary strategies case or the multi-IDP with continuous strategies case could result in the optimal individual utility and social welfare. Therefore, the proposed spontaneous cooperative model effectively avoids the existing moral hazard problem in federated learning and provides a viable instrument for the federated learning operator to maximize the performance of the global model without the need to evaluate the quality of local gradients.

Cooperation, competition, and welfare in a matching market

We investigate the welfare effect of increasing competition in an anonymous two–sided matching market, where matched pairs play an infinitely repeated Prisoner's Dilemma. Higher matching efficiency is usually considered detrimental as it creates stronger incentives for defection. We point out, however, that a reduction in matching frictions also increases welfare because more agents find themselves in a cooperative relationship. We characterize the conditions for which increasing competition increases overall welfare. In particular, this is always the case when the incentives for defection are high.

Corporate profit tax, managerial delegation and multinational firm's transfer pricing

AbstractThis paper analyzes the transfer pricing decision of the multinational firm. There are differences in profit tax rates between home‐country and host‐country. The multinational firm determines the transfer price to its overseas affiliate and delegates the responsibility of deciding on the final sales to its affiliate manager. We find that: (1) The multinational firm will set a higher transfer price if its affiliate hires a manager. If the host‐country firm also hires a manager, the managerial delegation may lead to an asymmetry “prisoner's dilemma”. (2) When home‐country's tax rate is higher than that in the host‐country, multinational firm tends to set a lower transfer price relative to the marginal production cost. (3) When host‐country's tax rate is higher than that in the home‐country, an increase in the host‐country corporate tax rate decreases multinational firm's profit and the consumer surplus, while its impact on the host‐country firm's profit is non‐monotone; an increase in the home‐country tax rate decreases host‐country firm's profit, increases consumer surplus, but has a non‐monotone impact on multinational firm's profit.

The Outlook of Sino-US Relations Based on the Prisoner's Dilemma

The Prisoner's Dilemma represents a model in game theory which elucidates the choice between cooperation and betrayal faced by two self-interested individuals. Similarly, the US-China relationship confronts a comparable dilemma necessitating collaboration based on common interests, while also safeguarding own interests, such as security and trade. Nonetheless, the present US-China relationship is grappling with numerous challenges and obstacles, such as trade protectionism and regional tensions. As a result, the future of US-China relations is uncertain. This paper analyses the outlook of China-US relations through the lens of the Prisoner's Dilemma model. Based on the analysis, it is recommended that China and the United States enhance their strategic dialogue and cooperation to address global challenges effectively. They should also work together to establish a new type of international relationship as a community of destiny for all humanity. This could not be improved as it already adheres to the principles and lacks context.

Adaptations to infer fitness interdependence promote the evolution of cooperation.

The evolution of cooperation is a major question in the biological and behavioral sciences. While most theoretical studies model cooperation in the context of an isolated interaction (e.g., a Prisoner's Dilemma), humans live in heterogeneous social environments, characterized by large variations in fitness interdependence-the extent to which one's fitness is affected by others. Theoretical and experimental work indicates that humans can infer, and respond to, variations in interdependence. In a heterogeneous ancestral environment, these psychological mechanisms to infer fitness interdependence could have provided a selective advantage, allowing individuals to maximize their fitness by deciding when and with whom to cooperate. Yet, to date, the link between cognitive inference, variation in fitness interdependence, and cooperation remains unclear. Here we introduce a theoretical framework to study the evolution of inference and cooperation in heterogeneous social environments, where individuals experience interactions with varying levels of corresponding interests. Using a combination of evolutionary game theory and agent-based modeling, we model the evolution of adaptive agents, who incur a cost to infer interdependence, in populations of fixed-behavior agents who always cooperate or defect. Our results indicate that natural selection could promote the evolution of psychological mechanisms to infer fitness interdependence, provided that there is enough variation in fitness interdependence to offset the cost of inference. Under certain conditions, the fixation of adaptive agents results in higher levels of cooperation. This depends crucially on the type of inference performed and the features of the interdependence landscape.

The cooperative evolution in the spatial prisoner's dilemma game with the local loyalty of two-strategy

The loyalty of individual strategies is an important factor affecting cooperative behavior in human society. Previous researches on the loyalty have mostly focused on the loyalty of individual to a single strategy, that is, the loyalty of individual to cooperative strategy. But from the perspective of defective strategy, individual holding defective strategy can also be seen as so-called loyalty to defective strategy.This paper presents a spatial prisoner's dilemma game model with the local loyalty of two-strategy, in which the loyalty to cooperative strategy and loyalty to defective strategy are considered simultaneously. To distinguish the loyalties of these two types of strategies, the loyalty value corresponding to defective strategy is represented as a negative number. A fitness of an individual is defined as weighted average of individual's payoff and power of average loyalty of local nearest neighbors. In strategy learning, if the loyalty of an individual and the loyalty of the target neighbor are different signs, a discount coefficient is added to the strategy transition probability function to reduce the probability.Numerical simulations show that considering individual loyalty to the two strategies can promote cooperative behavior in the system when the strength index of local loyalty in fitness function is positive, and there are optimal values for the weighting coefficient and the strength index of local loyalty, which can enable the system to reach full cooperators state. The discount coefficient to the fitness of neighbor can impact on the frequency of cooperators surviving and the proportion of surviving cooperators during phase transition.

Intra-port demand coordination and inter-port competition: Ports’ pricing strategies with congestion concerns

In practice, mix hub ports operate to satisfy both the hinterland demand and transshipment demand, which increases the processing workload, triggers the congestion concern, and hence weakens the port resilience. Note that the port capacity is limited, so decision-makers need to cautiously determine the service prices to coordinate exclusive hinterland demand with competing transshipment demand within the port capacity limit when competing with the other ports. This research formulates a mix hub port's key trade-offs in the pricing strategy choice, that is, whether to charge a uniform service price or two different service prices for the two kinds of demand. The finding of this study shows that the congestion concern (port resilience) plays a key role in determining ports' pricing strategies. And the intensified competition in transshipment demand induces the port to favor the uniform pricing strategy, especially when the hinterland demand potential is sufficiently large. Interestingly, the ports may be trapped in a Prisoner's Dilemma where the differentiated pricing strategy arises as the equilibrium, but they are actually better off under the uniform pricing strategy.

Research on the Iterated Prisoner Dilemma Based on Combinations of Two-side Strategies

The endless prisoner's dilemma game is described as a "primer" using the perspectives of the bilateral parties. Current research focuses on which player responds most effectively, which is a kind of self-protect behavior. Content analysis and mathematical justification were undertaken for the prisoners dilemma iteration to understand better how to improve the game in a partially competitive and cooperative collaborative setting. This aims to apply the two-side strategies to the real world, especially the political events in which the whole human outcome should be maximized. Participants, who were mostly chosen from game theory specialists from an experiment, provided the decision parameters and rules, in which they have to decide among certain personal strategy choices. The comparisons findings show that two-sided cooperation produces the best results. Still, two-sided inaction results in the poorest, and single cooperation and single noncooperation result from personal sacrifice and personal selfishness, which is a psychological phenomenon.

Government and Polluting Companies Game Strategies in the Context of Green Finance A Prisoners Dilemma Game Model

Promoting the development of green industries to facilitate the growth of green finance has become a consensus among various sectors of society. This article focuses on the game theory strategies between governments and polluting companies in the context of green finance. Taking the Prisoner's Dilemma game model as an example, we discuss if polluting companies, under different types of governments, would choose to allocate loans towards improving production and environmental projects. Furthermore, we analyze whether the preferences of the general public towards eco-friendly products would influence the game strategies of governments and polluting companies. Through solving the model, we find that when governments increase penalties for polluting projects, reduce the costs of environmental project research and development for polluting companies, enhance environmental awareness among the general public, and stimulate their preference for eco-friendly products, they can strengthen corporate social responsibility and promote green investments. Consequently, polluting companies are more likely to invest in environmental projects to gain greater returns.

The influence of environment-based reputation on cooperation in spatial prisoner's dilemma game

Research has shown that reputation mechanism can be effective in facilitating the generation and maintenance of cooperation in social dilemmas. In the traditional reputation mechanism, the amount of change in reputation is fixed. However, in real life, people's impression scores of a player are often influenced by the environment in which he lives. In other words, we prefer to celebrate the cooperative heroes who are surrounded by defectors and spurn the defectors who are hidden among the many cooperators. Thus, this paper proposes an environment-based reputation model, in which the increment of a player's reputation will be influenced by the local and global environment. The results of the research indicate that the greater the intensity of the environmental influence, the more it promotes the evolution of cooperation. It is worth noting that the local and global environmental focus shows peculiarities. Focusing on the global environment can improve the fraction of cooperators at low defection temptations while focusing on the local environment will facilitate cooperators’ survival at higher defection temptations.

Coupling injunctive social norms with evolutionary games

Human behaviors are strongly influenced by social norms. This work couples injunctive social norms with evolutionary games. Injunctive norms refer to behaviors which individuals should conform to and thereby entail social pressure to adhere to a particular action. Here we investigate impact of such social norms on both pairwise and multi-player games. It is shown that injunctive norms can enforce the system to either extreme, meaning that they give rise to the possibility of bi-stability (two stable equilibrium states) in evolutionary games. We derive the condition for such bi-stability in the mean-field limit. While investigating pairwise games with social norms, we observe that —besides other possibilities—Prisoner's dilemma (PD), snow-drift (SD), and Trivial (TR) games may experience the bi-stability like the stag-hunt (SH) game. Interestingly, SD game with social norms exhibits four possible asymptotic outcomes: all-cooperation (AllC), all-defection (AllD), either AllC or AllD (bi-stable), and coexistence. However, its multi-player variant does not manifest a unique coexistence equilibrium. Moreover, it demonstrates another bi-stable equilibrium, comprising either coexistence or AllC, besides other outcomes observed in the two-player case. Conversely, PD and its multi-player variant, i.e., public goods game with injunctive norms show identical evolutionary outcomes (AllD or bi-stable).

A product innovation game with managerial delegation

AbstractThis research introduces sales delegation in a product innovation game by considering Cournot and Bertrand duopolies. The article first revisits the existing results with profit‐maximising firms, showing that a prisoner's dilemma with undifferentiated products cannot occur in a Bertrand rivalry setting. Then, by considering the separation between ownership and control, the work shows, when managers are delegated to choose only over quantity or price in the product market, that sales delegation (1) increases (resp. reduces) the likelihood to innovate (not to innovate) under Cournot competition, and (2) increases the likelihood to innovate under Bertrand competition compared to the profit‐maximising setting. Unlike this, if managers are delegated to choose over quantity or price in the product market and product innovation is in the decision‐making stage, sales delegation reduces the likelihood of innovation in both Cournot and Bertrand rivalry settings. Overall, results pinpoint the importance of the managerial delegation in affecting investments in product innovation compared to the profit‐maximising model.

Using Team Discussions to Understand Behavior in Indefinitely Repeated Prisoner’s Dilemma Games

We compare behavior of two person teams with individuals in indefinitely repeated prisoner dilemma games with perfect monitoring. Team discussions are used to understand the rationale underlying these choices and how these choices come about. There are three main findings: (i) Teams learned to cooperate faster than individuals, and cooperation was more stable for teams. (ii) Strategies identified from team dialogues differ from those identified by the Strategy Frequency Estimation Method. This reflects the improvisational nature of teams’ decision making. (iii) Increasing cooperation was primarily driven by teams unilaterally cooperating in the hope of inducing their opponent to cooperate. (JEL C72, C73, C92)

Information accuracy of migration and imitation influences the evolution of cooperation in spatial prisoner's dilemma

Migration is ubiquitous in both biological worlds and human societies for seeking more suitable environments or greater benefits. Intensive studies have revealed that it may provide an effective mechanism to promote cooperation in the context of spatial prisoner' dilemma. As an attempt to give a more generic analysis on how migration influences the evolution of cooperation, we in this work propose a dynamic model that takes into account the agents' different tendencies on migration and imitation. More importantly, we introduce two information accuracy parameters that respectively affect the agents' decisions on the migration destination and on their imitation in the current neighborhood. The simulation results show that the higher accuracy of the information on imitation and migration contributes to a higher cooperation level. In particular, the imitation-oriented mode is more conducive to cooperation when the imitation information accuracy is high. Likewise, the migration-oriented mode is more conducive to cooperation with higher accuracy of the migration information. When imitation and migration information accuracies are both high, cooperation is effectively maintained in two different ways: the imitation-dominant pattern and the migration-dominant pattern, while the scenario in which the imitation tendency is close to the migration tendency has an inhibitory effect on cooperation. Finally, we analyse the robustness of the results under different population densities.