N-person Prisoner Research Articles

An Investigation of N-person Prisoners' Dilemmas

This paper is an attempt to systematically present the problem of various N-person Prisoners' Dilemma games and some of their possible solutions. 13 characteristics of the game are discussed. The role of payoff curves, personalities, and neighborhood is investigated. Experiments are performed with a new simulation tool for multi-agent Prisoners' Dilemma games. Investigations of realistic situations in which agents have various personalities show interesting new results. For the case of pavlovian agents the game has nontrivial but remarkably regular solutions. Examples of nonuniform distributions and mixed personalities are also presented. All solutions strongly depend on the choice of parameter values.

A game theory model of the Lombard effect in public spaces

The Lombard effect is the tendency for humans and other animals to raise their vocal intensity in the presence of background noise. As a result, the aggregate effect of many people talking in a public space can lead to multiple equilibria for speech intelligibility, as the incentive for an individual conversation is dependent on the actions of all the other speakers in the space. This system is modeled using game theory, in particular, an n-person Prisoner’s Dilemma model, otherwise known as the Unscrupulous Diner’s Dilemma. It is suggested that conscious knowledge of the dynamics of the system can affect the system's behavior up to a point, but that gradually the subconscious process of the Lombard Effect will cause the system to increase in background noise, only limited by the comfort of each speaker’s voice or an exogenous interrupting event.

Cooperation in the Multi-Agent System with Different Types of Interactions

This paper summarizes the list of our works that contain researches about optimality principles for the "n-person prisoner's dilemma" game. The classic model is considered through the new payoff function for each player that allows to consider it without restrictions for the number of players. The new characteristic function gives an opportunity to introduce the time-consistent subset of the core of the dynamic game. In accordance with this type of game we consider some specific properties of players' payoffs and construct the new way of their interactions. Using the network representation, the classic model is modified to the wider class of games that allows to specify players' influence to each other's payoff function. These investigations can be used for the description of cooperation in the other multi-agent systems.

An Effective Punishment for an n-Person Prisoner’s Dilemma on a Network

MSC: 91A06, 91A43 DOI: 10.21538/0134-4889-2021-27-3-256-262 The paper considers an $n$-person prisoner’s dilemma game. We present a modification of this model for the network interaction of players. A set of grim trigger strategies is a Nash equilibrium in the repeated $n$-person prisoner’s dilemma on a network, just as in the two-player game. However, even a slight deviation

Shapley value of n-person prisoner’s dilemma

n-Person prisoner’s dilemma is a Markovian sequence of static games that are realized randomly depending on players’ previous choices. The dynamic Shapley value is constructed in this case. The work is a continuation of the paper published earlier by Grinikh A. L. [1]. In this paper, we consider the new approach of dynamics of game which depends on the strategies of all players.

Cooperative n-person Prisoner's Dilemma on a Network

In the paper n-person prisoner's dilemma on the network is investigated. A cooperative game with the pairwise interaction of players is constructed. The model is a modification of the classic 2-person prisoner's dilemma problem in the game theory. Network interaction provide an ability to take into account the in uence only to the adjacent players from the whole set of players. The feature of the game is found that allows to make a decision about necessity of playing dominated strategy by a few players. This solution is based on the number of the adjacent players. The work is a continuation of the paper published earlier by Grinikh A.L. and Petrosyan L.A. in 2021.

Experimental Evidence on Cooperation, Political Affiliation, and Group Size

The main objective of this paper is to strengthen the knowledge about the relationship between cooperation and political affiliation. For this purpose, I carry out an incentivized N-person prisoner’s dilemma experiment. I find that left-wing voters cooperate more than right-wing voters in 3-person prisoner’s dilemmas. However, this difference in cooperation tapers off with group size due to a heterogeneous response to larger decision groups. While leftists cooperate less as the group size increases, I find no significant group size effect for rightists. These findings can partly be explained by differences in beliefs about the cooperativeness of others, but a substantial part remains unexplained.

Nash-2 Equilibrium: Selective Farsightedness Under Uncertain Response

This paper provides an extended analysis of an equilibrium concept for non-cooperative games with boundedly rational players: Nash-2 equilibrium. Players think one step ahead and account for all profitable responses of player-specific subsets of opponents because of both the cognitive limitations on predicting everyone’s reaction and the inability to make deeper and certain predictions. They cautiously reject improvements that might lead to worse profits after some reasonable response. For n-person games we introduce the notion of a reflection network consisting of direct competitors to express the idea of selective farsightedness. For almost every 2-person game with a complete reflection network, we prove the existence of a Nash-2 equilibrium. Nash-2 equilibrium sets are obtained in models of price and quantity competition, and in Tullock’s rent-seeking model with two players. It is shown that such farsighted behavior may provide strategic support for tacit collusion. The analyses of n-person Prisoner’s dilemma and oligopoly models with a star reflection structure demonstrate some possibilities of strategic collusion and a large variety of potentially stable outcomes.

The United Nations Global Compact as a Facilitator of the Lockean Social Contract

The United Nations Global Compact (UNGC) has difficulties in attracting new voluntary members and inciting them to implement its ten principles. The present article analyzes this implementation deficit from the perspective of Lockean social contract theory and derives new strategies for reducing it. On this view, the UNGC presents itself as the attempt to realize a set of moral norms, typically enforced by an impartial minimal state, protecting its citizens from violations of their natural rights, negative externalities and discrimination by bribed officials. It will only succeed in facilitating the realization of those norms on a strictly voluntary basis, if it manages to overcome the underlying n-person prisoner’s dilemma. This requires the existence of a critical mass k < N of conditionally moral firms, which are willing to observe the UNGC principles and to resist the temptation to free ride on their observance by others, if it does not disadvantage them in comparison to their situation in a state of universal non-observance. Four contracting problems can impede the conclusion of this Lockean social contract. The UNGC has a slim chance of overcoming its implementation deficit on a non-coercive basis by cultivating four institutional capabilities assisting conditionally moral firms in surmounting those four problems of voluntary norm compliance.

Greed and fear in multiperson social dilemmas

We consider greed and fear in social dilemmas, represented by multiplayer games with two strategies, cooperation and defection. The dilemmas are defined by relevant axioms. The N-person Prisoner’s Dilemma, Public Goods, Tragedy of the Commons, Volunteer’s Dilemma, and Assurance Game, are included in the considered axiomatization. For two-player interactions the scheme leads to three types of social dilemmas, the PD (and the Weak PD), the Chicken and the Stag Hunt game. We define greed and fear for multiplayer social dilemmas, and observe that all the dilemmas have greed or fear build in.

A spatial agent-based model of a congestion game: evolutionary game theory in space

This paper develops a theoretical framework to analyze traffic congestion from a micro-behavioral foundation perspective. It extends the evolution of an n-person prisoner’s dilemma within actual geographical space, integrating an agent-based model with GIS, in conflicting spatial interactions that ultimately lead to the decline of cooperation. The spatial agent-based model captures the response strategies of autonomous individuals in a landscape that contextualizes both the natural and the built environment. The result suggests that the loss of context preservation could lead to the extinction of cooperation, the opposite of the earlier findings. This theoretical framework thus serves as a basis for the analysis of collective strategic decisions about the use of a common resource from a game theoretical perspective.

Egalitarian solutions to multiperson social dilemmas in populations

We consider a class of multiperson social dilemma games played in large populations. In particular, the popular games, such as for example the N-person Prisoner’s Dilemma, the Public Goods, the Tragedy of the Commons, the Volunteer’s Dilemma, and the Assurance game, are included in the proposed frame. The evolution of such populations is assumed to be governed by the replicator equations. We show that the egalitarian distribution of the social welfare generated in the multiperson social dilemma games fosters the long run cooperation in such populations.

Exit Option Can Make Cooperation Easier

In the modern society, mobility of players has increased dramatically. It is important to extend game theory to endogenize the set of players. In this paper, we extend the repeated n-person Prisoner's Dilemma by allowing some or all players to exit after each period and analyze how mobility affects endogenous cooperation in a fundamental sense: players voluntarily participate in the game and act non-myopically. We characterize the parameters (the allocation of exit options among players and the payoffs) under which eternal universal cooperation is sustained at a discount factor lower than the one for the ordinary repeated Prisoner's Dilemma. Factors that enhance endogenous long-term cooperation include payoff asymmetry in the Prisoner's Dilemma, multiple mobile players who have the exit option, and immobile players having low after-game payoffs. These are new insights which give policy implications on employment relationships and other voluntary partnership situations as well.

Group size effect on cooperation in one-shot social dilemmas

Social dilemmas are central to human society. Depletion of natural resources, climate protection, security of energy supply, and workplace collaborations are all examples of social dilemmas. Since cooperative behaviour in a social dilemma is individually costly, Nash equilibrium predicts that humans should not cooperate. Yet experimental studies show that people do cooperate even in anonymous one-shot interactions. In spite of the large number of participants in many modern social dilemmas, little is known about the effect of group size on cooperation. Does larger group size favour or prevent cooperation? We address this problem both experimentally and theoretically. Experimentally, we find that there is no general answer: it depends on the strategic situation. Specifically, we find that larger groups are more cooperative in the Public Goods game, but less cooperative in the N-person Prisoner's dilemma. Theoretically, we show that this behaviour is not consistent with either the Fehr & Schmidt model or (a one-parameter version of) the Charness & Rabin model, but it is consistent with the cooperative equilibrium model introduced by the second author.

Evolution of cooperation in the regional environmental governance with institutional reward

The public goods game is extended with the assumption that increasing participation leads to increasing reward to promote cooperation in the regional environmental governance. This model constitutes a generalisation of the N-person prisoners' dilemma, and we study the infinite population case. The replicator dynamics reveals the existence of regimes in which two internal fixed points appear simultaneously, which is similar with that of N-person stag hunt evolutionary game. It is shown that the one at the lower frequency of cooperators is unstable, determining the threshold for cooperative collective action, while the one at the higher frequency is stable, determining the final frequency of cooperators in the population. Moreover, larger scale groups make the cooperation more difficult.

Dangerous drivers foster social dilemma structures hidden behind a traffic flow with lane changes

Motivated by the fact that there are quite a few ill-mannered drivers who disregard traffic rules concerning lane-changing and maximum speed, we investigated an interesting question: whether or not social dilemma structures can be formed from a frequent dangerous lane-changing attitude in a typical traffic flow without any explicit bottlenecks. In our model system, two classes of driver-agents coexist: C agents (cooperative strategy) always keep to traffic regulations with respect to lane-changing and speed, while D agents (defective strategy) disregard them to move ahead. In relatively high-density flows, such as the metastable and high-density phases, we found structures that correspond to either n-person Prisoner's Dilemma (n-PD) games or to quasi-PD games. In these situations, existing ill-mannered drivers create heavy traffic jams that reduce social efficiency.

Social dilemma structures hidden behind traffic flow with lane changes

.Aiming to merge traffic flow analysis with evolutionary game theory, we investigated the question of whether such structures can be formed from frequent lane changes in usual traffic flow without any explicit bottlenecks. In our model system, two classes of driver-agents coexist: C-agents (cooperative strategy) always remain in the lane they are initially assigned, whereas D-agents (defective strategy) try to change lanes to move ahead. In relatively high-density flows, such as the metastable and high-density phases, we found structures that correspond to either n-person prisoner dilemma (n-PD) games or quasi-PD games. In these situations, lane changes by D-agents create heavy traffic jams that reduce social efficiency.

Which Cooperative Strategies are Evolutionarily Stable?

In repeated games, reciprocity helps to sustain group cooperation. Using the Markovian strategy as a touchstone, we explore the evolution of cooperation in the infinitely repeated and noisy n-person Prisoner's Dilemma. With some modified game settings, we show that a class of cooperative strategies based on reciprocity may be evolutionarily stable. When a cooperative strategy satisfies some properties in our study, that strategy becomes evolutionarily stable if it outperforms the mutant permanent defector. We also argue that evolutionary stability in a noisy n-person setting implies the Markov perfect equilibrium.

Asymmetries in Altruistic Behavior during Violent Intergroup Conflict

Recent theoretical and experimental investigations of altruistic behavior in intergroup conflict in humans frequently make use of the assumption that warfare can be modeled as a symmetrical n-person prisoner's dilemma, abstracting away the strategic differences between attack and defense. In contrast, some empirical studies on intergroup conflict in hunter-gatherer societies and chimpanzees indicate that fitness relevant risks and potential benefits of attacks and defenses might have differed substantially under ancestral conditions. Drawing on these studies, it is hypothesized that the success of defenses was much more important for individual and kin survival and that a disposition to act altruistically during intergroup conflict is thus more likely to evolve for the strategic situation of defense. It is then investigated empirically if such asymmetries in the occurrence of altruistic behavior during intergroup conflict can be found. Analyzing detailed historical case data from 20th century wars, this study finds that altruistic behavior towards members of the in-group indeed seems to occur more frequently when soldiers are defending themselves and their comrades against enemy attacks. It is proposed that this asymmetry reflects adaptive behavioral responses to the materially different strategic character of attacks and defenses under ancestral conditions. If true, this would call for a refinement of theories of the evolutionary interaction of intergroup conflict and altruism.

Cooperation in small groups: the effect of group size

We study the effect of group size on cooperation in voluntary contribution mechanism games. As in previous experiments, we study four- and eight-person groups in high and low marginal per capita return (MPCR) conditions. We find a positive effect of group size in the low MPCR condition, as in previous experiments. However, in the high MPCR condition we observe a negative group size effect. We extend the design to investigate two- and three-person groups in the high MPCR condition, and find that cooperation is highest of all in two-person groups. The findings in the high MPCR condition are consistent with those from n-person prisoner’s dilemma and oligopoly experiments that suggest it is more difficult to sustain cooperation in larger groups. The findings from the low MPCR condition suggest that this effect can be overridden. In particular, when cooperation is low other factors, such as considerations of the social benefits of contributing (which increase with group size), may dominate any negative group size effect.