Interrelations between stochastic equations for systems with pair interactions

Helbing, Dirk

doi:10.1016/0378-4371(92)90195-v

Cited by 71 publications

(94 citation statements)

References 60 publications

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“…The replicator dynamics [25] is the traditional approach for wellmixed populations (populations with no structure where individuals play with each other). For evolutionary models, finite populations and discrete time, the equivalent classic approach is the use of the proportional imitation rule [26,27]. The update of strategies is performed as follows.…”

Section: A Description Of the Modelmentioning

confidence: 99%

Evolution of cooperation under social pressure in multiplex networks

Pereda

2016

Phys. Rev. E

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In this work, we aim to contribute to the understanding of the human pro-social behavior by studying the influence that a particular form of social pressure "being watched" has on the evolution of cooperative behavior. We study how cooperation emerge in multiplex complex topologies by analyzing a particular bidirectionallycoupled dynamics on top of a two-layers multiplex network (duplex). The coupled dynamics appears between the Prisoner's Dilemma game in a network, and a threshold cascade model in the other. The threshold model is intended to abstract the behavior of a network of vigilant nodes, that impose pressure of being observed altering hence the temptation to defect of the dilemma. Cooperation or defection in the game also affects the state of a node of being vigilant. We analyze these processes on different duplex networks structures and assess the influence of the topology, average degree and correlated multiplexity, on the outcome of cooperation. Interestingly, we find that the social pressure of vigilance may impact cooperation positively or negatively, depending on the duplex structure, specifically the degree correlations between layers is determinant. Our results give further quantitative insights in the promotion of cooperation under social pressure.

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Section: A Description Of the Modelmentioning

confidence: 99%

Evolution of cooperation under social pressure in multiplex networks

Pereda

2016

Phys. Rev. E

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“…The denominator takes this form in order to ensure that P ij r1. This update rule is also known as ''replicator rule'', since in the thermodynamical limit it results in the replicator equation, as shown by Helbing (1992) and Schlag (1998). Again, this rule is a common choice in research on evolutionary games.…”

Section: Modelmentioning

confidence: 99%

The spatial Ultimatum game revisited

Iranzo

Román

Sánchez

2011

Journal of Theoretical Biology

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a b s t r a c tWe revisit the issue of the emergence of fair behavior in the framework of the spatial Ultimatum game, adding many important results and insights to the pioneering work by The spatial Ultimatum game. Proc. R. Soc. London B 267, 2177], who showed in a specific example that on a two dimensional setup evolution may lead to strategies with some degree of fairness. Within this spatial framework, we carry out a thorough simulation study and show that the emergence of altruism is a very generic phenomenon whose details depend on the dynamics considered. A very frequent feature is the spontaneous emergence and fixation of quasiempathetic individuals, whose offers are very close to their acceptance thresholds. We present analytical arguments that allow an understanding of our results and give insights on the manner in which local effects in evolution may lead to such non rational or apparently maladaptive behaviors.

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“…The third is based on the fixed point solution to a Fokker-Planck equation (FPE) phrased in terms of stochastic partial differential equations applied to entire populations of incentivised agents [26]. The interest in this model comes from the fact that it is based on a very large number of individuals interacting with each other stochastically over time, very much like an idealised economy, see for example the body of work by Traulsen et al in finite populations [26][27][28] and Helbing [29][30][31]. The FPE is an important stochastic partial differential equation that has been used extensively in the social and natural sciences [32].…”

Section: −1 Xmentioning

confidence: 99%

“…In this sense the strategic space can be thought of as smoothly connected. A key aspect of the QRE though is that there are a number of important macroscopic properties of the QRE surface, notably the appearance of unavoidable tipping points and the dangerous erosion of equilibrium islands (also described in the next section) that are lost if we were to use Equation (29) as an approximation to a non-homogeneous population for which the QRE of Equations (22)- (23) are the equilibrium solutions. Some of these properties have only recently been explored [10] and so the following section introduces some of these so far unexplored properties as a function of the underlying system parameters.…”

Section: The Qre and The Non-linear Effects Of Group Interactionsmentioning

confidence: 99%

Strategic Islands in Economic Games: Isolating Economies From Better Outcomes

Harré

Bossomaier

2014

Entropy

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Many of the issues we face as a society are made more problematic by the rapidly changing context in which important decisions are made. For example buying a petrol powered car is most advantageous when there are many petrol pumps providing cheap petrol whereas buying an electric car is most advantageous when there are many electrical recharge points or high capacity batteries available. Such collective decision-making is often studied using economic game theory where the focus is on how individuals might reach an agreement regarding the supply and demand for the different energy types. But even if the two parties find a mutually agreeable strategy, as technology and costs change over time, for example through cheaper and more efficient batteries and a more accurate pricing of the total cost of oil consumption, so too do the incentives for the choices buyers and sellers make, the result of which can be the stranding of an industry or even a whole economy on an island of inefficient outcomes. In this article we consider the issue of how changes in the underlying incentives can move us from an optimal economy to a sub-optimal economy while at the same time making it impossible to collectively navigate our way to a better strategy without forcing us to pass through a socially undesirable "tipping point". We show that different perturbations to underlying incentives results in the creation or destruction of "strategic islands" isolated by disruptive transitions between strategies. The significant result in this work is the illustration that an economy that remains strategically stationary can over time become stranded in a suboptimal outcome from which there is no easy way to put the economy on a path to better outcomes without going through an economic tipping point.

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Interrelations between stochastic equations for systems with pair interactions

Cited by 71 publications

References 60 publications

Evolution of cooperation under social pressure in multiplex networks

Evolution of cooperation under social pressure in multiplex networks

The spatial Ultimatum game revisited

Strategic Islands in Economic Games: Isolating Economies From Better Outcomes

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