Multiplayer Prisoner Research Articles

Pink-noise dynamics in an evolutionary game on a regular graph.

We consider a multiplayer prisoner's dilemma game on a square lattice and regular graphs based on the pairwise-Fermi update rule, and we obtain heatmaps of the fraction of cooperators and the correlation of neighboring pairs. In the heatmap, we find a mixed region where cooperators and defectors coexist, and the correlation between neighbors is significantly enhanced. Moreover, we observe pink-noise behavior in the mixed region, where the power spectrum can be fitted by a power-law function of frequency. We also find that the pink-noise behavior can be reproduced in a simple random-walk model. In particular, we propose a modified random-walk model which can reproduce not only the pink-noise behavior but also the deviation from it observed in a low-frequency region.

Mixing prisoner’s dilemma games on higher-order networks

The prisoner’s dilemma game is a paradigmatic example of a plight situation in which different individuals vie for maximal payoffs. And it has been shown that interaction networks that host such individuals have an immense impact on individual strategy choices. In this paper, we advance this subject by mixing the two-person prisoner’s dilemma and various multiplayer prisoner’s dilemma games and explore the role of 2-order simplicial complexes on the evolutionary dynamics. In the studied model, the fraction of multiplayer prisoner’s dilemma games on the network can be indirectly controlled by adjusting the ratio of 2-simplex complexes in the network. Through large-scale simulations, we show that by adjusting this ratio, the level of cooperation can be enhanced by a mechanism that is unique to higher-order networks. In particular, the strategic unity of the triangles in the network can foster the stability of cooperation and its spreading through enhanced network reciprocity. These results thus reveal benefits of higher-order interactions on cooperation that have thus far, on classical networks, been reserved only for games played in groups, such as the public goods game.

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

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

New memory-one strategies of the Iterated Prisoner’s Dilemma: a new framework to programmed human-AI interaction

With the rapid and continuing development of AI, the study of human-AI interaction is increasingly relevant. In this sense, we propose a reference framework to explore a model development in the context of social science to try to extract valuable information to the AI context. The model we choose was the Prisoner Dilemma using the Markov chain approach to study the evolution of memory-one strategies used in the Prisoner’s Dilemma in different agent-based simulation contexts using genetic algorithms programmed on the NetLogo environment. We developed the Multiplayer Prisoner’s Dilemma simulation from deterministic and probabilistic conditions, manipulating not only the probability of communication errors (noise) but also the probability of finding again the same agent. Our results suggest that the best strategies depend on the context of the game, following the rule: the lower the probability of finding the same agent again, the greater the chance of defect. Therefore, in environments with a low probability of interaction, the best strategies were the ‘Always Defect’ ones. But as the number of interactions increases, a different strategy emerges that is able to win Always Defect strategies, such as the Spiteful/grim. In addition, our results also highlight strategies that emerge in situations in which Spiteful/grim and Always Defect were banned. These are memory-one strategies with better performance than both TFT and PAVLOV under all conditions showing behaviors that are particularly deceiving but successful. The previously memory-one strategies for the Prisoner Dilemma represent a set of extensively tested strategies in contexts with different probability of encountering each other again and provide a framework for programming algorithms that interact with humans in PD-like trusted contexts.

IN THE MULTIPLAYER PRISONER'S DILEMMA, A PLAYER EMPLOYING A ZERO-DETERMINANT STRATEGY SECURES ADVANTAGEOUS OUTCOMES FOR THE ENTIRE GROUP.

When there is an interaction between the level of choice of an individual and a group, there is no favorite but to refer to the problem of a multi-member prisoner's dilemma game. Also in real life, there is a widespread need for cooperation or defection amongst a group of population in the matter of choice. The problem of multiplayer prisoner's dilemma is widely used in real life. We conducted this study to find out how people cooperate in a multiplayer interaction in the prisoner's dilemma game. In this study, we examine the interaction between an individual and a group of population and look for the Zero-Determinant strategies in the case of multiplayer prisoner's dilemma game.

Satisfaction and preferences in a legality social dilemma: Does corporate social responsibility impact consumers’ behaviour?

We investigate players’ preferences in a multiplayer prisoner's dilemma by comparing results from satisfaction-based and a choice-based approach by means of a laboratory experiment. The experimental design tests the effects of the legality rating frame on consumers’ choice between products from producers labeled by the legality rating and products by unlabeled producers. Both approaches provide strong evidence of preference heterogeneity, with players who cooperate above median being less affected in their choice by monetary payoffs vis-à-vis the public good component. The empirical findings support the hypothesis of our theoretical model that (part of the) players have, in addition to the standard self-interest component, an other-regarding preference argument that is further satisfied in the legality frame plus conformity design.A policy suggestion stemming from our experiment is based on the fact that corporate social responsibility legality frames and culture have a significant effect on an important portion of consumers. These consumers reveal that the often-declared willingness to pay for socially, environmentally and legally responsible features of products is confirmed by actual purchases of more expensive responsible products. Governments should therefore promote the creation of legality rating schemes with well-defined pre-established rules such as in the Italian case.

The Vote with the Wallet Game: Responsible Consumerism as a Multiplayer Prisoner’s Dilemma

Socially responsible consumers and investors are increasingly using their consumption and saving choices as a ‘vote with the wallet’ to award companies that are at vanguard in reconciling the creation of economic value with social and environmental sustainability. In our paper, we model the vote with the wallet as a multiplayer prisoner’s dilemma, outline equilibria and possible solutions to the related coordination failure problem in evolutionary games, apply our analysis to domains in which the vote with the wallet is empirically more relevant, and provide policy suggestions.

Groups and scores: the decline of cooperation.

Cooperation among unrelated individuals in social-dilemma-type situations is a key topic in social and biological sciences. It has been shown that, without suitable mechanisms, high levels of cooperation/contributions in repeated public goods games are not stable in the long run. Reputation, as a driver of indirect reciprocity, is often proposed as a mechanism that leads to cooperation. A simple and prominent reputation dynamic function through scoring: contributing behaviour increases one's score, non-contributing reduces it. Indeed, many experiments have established that scoring can sustain cooperation in two-player prisoner's dilemmas and donation games. However, these prior studies focused on pairwise interactions, with no experiment studying reputation mechanisms in more general group interactions. In this paper, we focus on groups and scores, proposing and testing several scoring rules that could apply to multi-player prisoners' dilemmas played in groups, which we test in a laboratory experiment. Results are unambiguously negative: we observe a steady decline of cooperation for every tested scoring mechanism. All scoring systems suffer from it in much the same way. We conclude that the positive results obtained by scoring in pairwise interactions do not apply to multi-player prisoner's dilemmas, and that alternative mechanisms are needed.

Quantum Entanglement and the Emergence of Collaboration in Social Media

In this paper, we devise a slightly modified version of the vote with the wallet game used by Becchetti et al. [L. Becchetti and F. Salustri, The vote with the wallet as a multiplayer prisoner’s dilemma, CEIS Tor Vergata Research Paper No. 359, Vol. 13, Issue 10, Centre for Economic and International Studies, Rome, Italy (2015); L. Becchetti, V. Pelligra and F. Salustri, Testing for heterogeneity of preferences in randomized experiments: A satisfaction-based approach applied to multiple prisoner dilemmas, Appl. Econ. Lett. 24(10) (2017) 722–726] for the use of social media, where the player decides whether to responsibly share social knowledge or not. We follow the point of view of Bennet and Bennet [D. Bennet and A. Bennet, Social learning from the inside out: The creation and sharing of knowledge from the mind/brain perspective, in Social Knowledge: Using Social Media to Know What You Know, eds. J. P. Girard and J. L. Girard (IGI Global, 2011), pp. 1–23] according to which another social settings may emerge through the so-called “process of collaborative entanglement.” In this environment, members of a community interact continuously with strong emotional feelings to combine the sources of knowledge and the beneficiaries of that knowledge and move toward a common direction. The application of the model to the quantum game theory substantially confirms that the cooperative strategy becomes the optimal one depending on the frequency of interactions and people’s cultural, geographical and social reachability and traceability.

The impact of redistribution mechanisms in the vote with the wallet game: experimental results

We use the vote-with-the-wallet game to model socially or environmentally responsible consumption, an increasingly relevant but still under-researched phenomenon. Based on a theoretical model outlining game equilibria and the parametric interval of the related multiplayer prisoners’ dilemma we evaluate with a controlled lab experiment players’ behaviour in the game and test the effects of an ex post redistribution mechanism between defectors and cooperators. Our findings document that the redistribution mechanism interrupts cooperation decay and stabilizes the share of cooperators at a level significantly higher, even though inferior to the Nash equilibrium.

Gender differences in socially responsible consumption. An experimental investigation

ABSTRACTWe report on a simple experimental study designed to investigate the different gender attitudes towards socially responsible consumption. We use the Vote-with-the-Wallet Game, (VWG), a version of a repeated multiplayer prisoner’s dilemma that mimics the characteristics of the choice between a conventional and a socially responsible product. More precisely we test the effect of three factors: two different frames and an ex-post redistribution mechanism that transfers resources from purely self-interested consumers to responsible ones. We find that women remain significantly more cooperative (choosing more often the responsible good) when the redistribution mechanism is interrupted and are significantly less satisfied about the behaviour of the other players in that treatment.

Relativistic and noise effects on multiplayer Prisoners’ dilemma with entangling initial states

Three-players Prisoners’ dilemma (Alice, Bob and Colin) is studied in the presence of a single collective environment effect as a noise. The environmental effect is coupled with final states by a particular form of Kraus operators $$K_0$$ and $$K_1$$ through amplitude damping channel. We introduce the decoherence parameter $$0\le p\le 1$$ to the corresponding noise matrices, in order to controling the rate of environment influence on payoff of each players. Also, we consider the Unruh effect on the payoff of player, who is located at a noninertial frame. We suppose that two players (Bob and Colin) are in Rindler region I from Minkowski space-time, and move with same uniform acceleration ( $$r_b=r_c$$ ) and frequency mode. The game is begun with the classical strategies cooperation (C) and defection (D) accessible to each player. Furthermore, the players are allowed to access the quantum strategic space (Q and M). The quantum entanglement is coupled with initial classical states by the parameter $$\gamma \in [0,\pi /2]$$ . Using entangled initial states by exerting an unitary operator $$\hat{J}$$ as entangling gate, the quantum game (competition between Prisoners, as a three-qubit system) is started by choosing the strategies from classical or quantum strategic space. Arbitrarily chosen strategy by each player can lead to achieving profiles, which can be considered as Nash equilibrium or Pareto optimal. It is shown that in the presence of noise effect, choosing quantum strategy Q results in a winning payoff against the classical strategy D and, for example, the strategy profile (Q, D, C) is Pareto optimal. We find that the unfair miracle move of Eisert from quantum strategic space is an effective strategy for accelerated players in decoherence mode ( $$p=1$$ ) of the game.

The Impact of Cash Mobs in the Vote with the Wallet Game: Experimental Results

We simulate in a randomised lab experiment the effect of Cash Mobs on consumers’ behaviour in an original variant of the multiplayer Prisoner’s dilemma called Vote-with-the-wallet Game (VWG). The effect is modelled in a sequential game with/without an environmental frame in which a subset of players (cash-mobbers) is given the opportunity to reveal publicly (in aggregate without disclosing individual identities) their cooperation decision. We find that the treatment has a positive gross effect, that is, the share of cooperators is significantly higher in treated sessions and this is mainly due to the higher share of cooperators among cash-mobbers. Our results suggest that cash mobs-like mechanisms can help to solve social dilemmas with entirely private solutions (not based on punishment but on positive action) without costs for government budgets.

Reinforcement learning accounts for moody conditional cooperation behavior: experimental results

In social dilemma games, human participants often show conditional cooperation (CC) behavior or its variant called moody conditional cooperation (MCC), with which they basically tend to cooperate when many other peers have previously cooperated. Recent computational studies showed that CC and MCC behavioral patterns could be explained by reinforcement learning. In the present study, we use a repeated multiplayer prisoner’s dilemma game and the repeated public goods game played by human participants to examine whether MCC is observed across different types of game and the possibility that reinforcement learning explains observed behavior. We observed MCC behavior in both games, but the MCC that we observed was different from that observed in the past experiments. In the present study, whether or not a focal participant cooperated previously affected the overall level of cooperation, instead of changing the tendency of cooperation in response to cooperation of other participants in the previous time step. We found that, across different conditions, reinforcement learning models were approximately as accurate as a MCC model in describing the experimental results. Consistent with the previous computational studies, the present results suggest that reinforcement learning may be a major proximate mechanism governing MCC behavior.

Testing for heterogeneity of preferences in randomized experiments: a satisfaction-based approach applied to multiplayer prisoners’ dilemmas

ABSTRACTWe use experimental data from the ‘vote with the wallet’ multiplayer prisoner’s dilemma to investigate with a finite mixture approach the effect of a responsible purchase on players’ satisfaction. We find clear-cut evidence of heterogeneity of preferences with two groups of players that differ significantly in terms of effects of the responsible choice on satisfaction.

Testing for Heterogeneity of Preferences in Randomized Experiments: A Satisfaction-Based Approach Applied to Multiplayer Prisonerss Dilemmas

We use experimental data from the “vote with the wallet” multiplayer prisoner’s dilemma to investigate with a finite mixture approach the effect of a responsible purchase on players’ satisfaction. We find clear-cut evidence of heterogeneity of preferences with two groups of players that differ significantly in terms of effects of the responsible choice on satisfaction.

Happiness and Preferences in a Legality Social Dilemma: Comparing the Direct and Indirect Approach

We investigate players’ preferences in a multiplayer prisoner’s dilemma by comparing results from a direct (satisfaction based) and an indirect (choice based) approach. Both approaches provide strong evidence of preference heterogeneity, with players who cooperate above median being less affected in their choice by monetary payoffs vis-a-vis the public good component. The combination of a legality frame plus a conformity information design reduces further the relative preference (satisfaction) for the non-cooperative choice for such players. Our findings support the hypothesis that (part of the) players have, in addition to the standard self-interest component, an other-regarding preference argument that is further satisfied in the legality frame plus conformity design.

The Vote with the Wallet as a Multiplayer Prisoner's Dilemma

Socially responsible consumers and investors are increasingly using their consumption and saving choices as a “vote with the wallet” to award companies which are at vanguard in reconciling the creation of economic value with social and environmental sustainability. In our paper we model the vote with the wallet as a multiplayer prisoner’s dilemma, outline equilibria and possible solutions to the related coordination failure problem, apply our analysis to domains in which the vote with the wallet is empirically more relevant, and provide policy suggestions.

The Impact of Redistribution Mechanisms in the Vote with the Wallet Game: Experimental Results

We use the Vote-with-the-Wallet game (VWG) to model socially or environmentally responsible consumption, an increasingly relevant but still under-researched phenomenon. Based on a theoretical model outlining game equilibria and the parametric interval of the related multiplayer prisoners’ dilemma (PD) we evaluate with a controlled lab experiment players’ behavior in the game and test the effects of an ex post redistribution mechanism between defectors and cooperators. Our findings document that the redistribution mechanism interrupts cooperation decay and stabilizes the share of cooperators at a level significantly higher, even though inferior to the Nash equilibrium.

Benefits of memory for the evolution of tag-based cooperation in structured populations

We study the effects of working memory capacity and network rewiring probability on the evolution of cooperation in the standard and modified versions of an agent-based model of tag-mediated altruism. In our evolutionary model, computational agents populate a large complex network, engage into multiplayer Prisoner’s Dilemma-like interactions, and reproduce sexually. Agents carry discernible phenotypic traits subject to mutation, memorize their own experiences, and employ different strategies when interacting with different types of co-players. Choices made are selected from a pool of two conditional and two unconditional strategies, depending on the available memory contents and phenotypic similarity among interactors. For the dominating strategy in our standard model version, we found a strong dependence of cooperation on network structure and a weak one on memory, whereas in the modified version, the structural effect was weaker than that of memory. Most importantly, we found that the previously reported decline of cooperation in memory-based models, typically observed at a high memory capacity, is now prevented with the help of tags. This suggests that the evolutionary advantages of memory capacity limits may be far more complex than previously assumed. For much smaller systems, we observed a quasi-symmetric alternation of the two winning groups of strategists. This result provides an example of ingroup biased interactions that are characterized by bursts of intra-tag cooperation interspersed with periods of unconditional transient altruism. Such switches of strategies may represent a boosting mechanism necessary for the emergence and stability of global altruism in its early evolutionary stages.