Triggers for cooperative behavior in the thermodynamic limit: A case study in Public goods game

Benjamin, Colin; Sarkar, Shubhayan

doi:10.1063/1.5085076

Cited by 14 publications

(6 citation statements)

References 9 publications

(39 reference statements)

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“…γ 0 ≈ 0.579 for r = 3, s = 0, p = 1 and t = 5 as shown in (9) and is independent of T . It should be however, noted that γ 0 does not mark a point of phase transition as neither the magnetization is discontinuous there, nor is it accompanied by any form of divergent susceptibility, as will be seen in Section VI.…”

Section: Cost Susceptibilitymentioning

confidence: 66%

“…where λ, λ ′ , µ, µ ′ are the transformations to payoffs. These transformations do not alter the Nash equilibrium of game (See appendix of [1,9] for a general proof). Choosing the transformations as…”

Section: B Thermodynamic Limit Of Social Dilemma Gamesmentioning

confidence: 99%

“…In order to map the 1D Ising model to the game as per recipe given in [9,10], it is important to note that in Ising model, we have to minimize energy to obtain the equilibrium, in game theory, in contrast, Nash equilibrium is obtained by maximizing the payoffs. Hence, to map these two models, we consider the negative of energy, i.e., " − E", where E is total energy in the Ising model.…”

Section: B Thermodynamic Limit Of Social Dilemma Gamesmentioning

confidence: 99%

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Thermodynamic susceptibility as a measure of cooperative behavior in social dilemmas

Benjamin,

Dash

2019

Preprint

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The emergence of cooperation in the thermodynamic limit of social dilemmas is an emerging field of research. While numerical approaches (using replicator dynamics) are dime a dozen, analytical approaches are rare. A particularly useful analytical approach is to utilize a mapping between the spin-1/2 Ising model in 1-D and the social dilemma game and calculate the magnetization, which is the net difference between the fraction of cooperators and defectors in a social dilemma. In this paper, we look at the susceptibility, which probes the net rate of change in the fraction of players adopting a certain strategy, for both classical and quantum social dilemmas. The reason being, in statistical mechanics problems, the thermodynamic susceptibility as compared to magnetization is a more sensitive probe for microscopic behavior, e.g., observing small changes in a population adopting a certain strategy. In this paper, we find the thermodynamic susceptibility for reward, sucker's payoff and temptation in classical Prisoner's Dilemma to be positive, implying that rate of change of players from defect to cooperate is greater than vice-versa, although the Nash Equilibrium for the two-player game is to defect. In classical Hawk-Dove game, the thermodynamic susceptibility for resource suggests that rate of switching of players to Hawk from Dove strategy is dominant. Entanglement in Quantum Prisoner's Dilemma (QPD) has a non-trivial role in determining the behavior of thermodynamic susceptibility. At maximal entanglement, we find that sucker's payoff and temptation increase the rate of players switching to defect. In the zero-temperature limit, we find that there are two second-order phase transitions in the game, marked by a divergence in the susceptibility. This behavior is similar to that seen in Type-II superconductors wherein also two second-order phase transitions are seen.

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Section: Cost Susceptibilitymentioning

confidence: 66%

Section: B Thermodynamic Limit Of Social Dilemma Gamesmentioning

confidence: 99%

Section: B Thermodynamic Limit Of Social Dilemma Gamesmentioning

confidence: 99%

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Thermodynamic susceptibility as a measure of cooperative behavior in social dilemmas

Benjamin,

Dash

2019

Preprint

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“…For example, an evolutionary extension of the game enables us to analyse the dynamics of players' behaviour 37 . If the relationships between players form a social network, local interactions of players influence the state of the whole market 37,53 . Results from evolutionary game theory and psychological experiments suggest that reputation and voluntary punishment promote altruistic behaviour in repeated games on social networks 38, [54][55][56][57][58] .…”

Section: Discussionmentioning

confidence: 99%

Social Dilemmas in Nature-Based Tourism Depend on Social Value Orientations

Honjo

Kubo

2020

Sci Rep

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nature-based tourism (nBt) is vulnerable to a rapid increase in visitors because natural resources are often open access. Market failure caused by over-exploitation of natural resources is an example of social dilemmas in common-pool resource systems. Game theory, which describes people's decision making under conflicts, has been applied to the analysis of social dilemmas in NBT. However, previous studies use non-cooperative games assuming individualistic players and discuss the emergence of social dilemmas only in a limited situation. Here, we demonstrate, by developing a two-player non-cooperative game of wildlife viewing, that the traditional game-theoretic approach fails to find social dilemmas. By analysing the competition between tour operators (players) with different social value orientations (SVOs), we found that concentration of tours becomes a Pareto-inefficient Nash equilibrium (PINE) when both players are competitive. Whether the wildlife-viewing market is a Prisoner's dilemma depends on players' SVOs. Furthermore, we found that fair punishment on competitive players promotes rather than suppresses the emergence of pine. our results suggest that the diversity of SVos is an essential factor in understanding social dilemmas in nBt. Tourism demand has been rapidly increasing in recent years. According to the World Travel and Tourism Council 1 , travel and tourism contributed USD 8,272 billion (at 2017 constant prices and exchange rates) to world GDP in 2017. The amount is expected to reach USD 12,450 billion in 2028. Meanwhile, many tourism destinations face a rapid increase in visitors with the associated problems: degraded tourist experiences, damage to nature, and threats to culture and heritage 2. Nature-based tourism (NBT) is vulnerable to overcrowding because natural resources are often open access. On an analogy with the tragedy of the commons 3,4 , we can imagine the tourism dilemma as follows: (1) Self-interested tourism firms increase tour supply to maximise their benefits. (2) Over-exploitation of natural resources happens, undermining the basis of NBT. (3) The economic value of NBT decreases, and the payoff allocation to tourism firms becomes inefficient. The tourism dilemma is an example of social dilemmas in common-pool resource systems 5-7. Game theory, which describes people's decision making under conflicts, is a useful tool to analyse social dilemmas in common-pool resource systems 8. There are many game-theoretic studies in the fields of fisheries, water resource management, and climate change 9-11. Game theory is not widely applied to NBT, but several studies discuss tourism dilemmas based on non-cooperative games. For example, Sobhee and co-workers 12 use the Prisoner's dilemma to represent the conflict between fishers and water-sport operators in a marine park. Blanco and co-workers 13 propose a strategic-form game structurally different from the Prisoner's dilemma, pointing out that many tourism firms voluntarily engage in resource conservation. In another paper 14 , they demonstr...

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“…Then it is possible to improve both pay-offs of L and F. 7: What can be said about the situation with many followers and more than one leader [16]? This interesting problem should be studied in future possibly via tools of statistical mechanics that were recently applied to game theory [67][68][69].…”

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confidence: 99%

Leadership scenarios in prisoner’s dilemma game

Babajanyan

Melkikh

Allahverdyan

2020

Physica A: Statistical Mechanics and its Applications

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The prisoner's dilemma game is the most known contribution of game theory into social sciences. Here we describe new implications of this game for transactional and transformative leadership. While the autocratic (Stackelberg's) leadership is inefficient for this game, we discuss a Paretooptimal scenario, where the leader L commits to react probabilistically to pure strategies of the follower F, which is free to make the first move. Offering F to resolve the dilemma, L is able to get a larger average pay-off. The exploitation can be stabilized via repeated interaction of L and F, and turns to be more stable than the egalitarian regime, where the pay-offs of L and F are equal. The total (summary) pay-off of the exploiting regime is never larger than in the egalitarian case. We discuss applications of this solution to a soft method of fighting corruption and to modeling the Machiavellian leadership. Whenever the defection benefit is large, the optimal strategies of F are mixed, while the summary pay-off is maximal. One mechanism for sustaining this solution is that L recognizes intentions of F.

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Triggers for cooperative behavior in the thermodynamic limit: A case study in Public goods game

Cited by 14 publications

References 9 publications

Thermodynamic susceptibility as a measure of cooperative behavior in social dilemmas

Thermodynamic susceptibility as a measure of cooperative behavior in social dilemmas

Social Dilemmas in Nature-Based Tourism Depend on Social Value Orientations

Leadership scenarios in prisoner’s dilemma game

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