Topologically robust zero-sum games and Pfaffian orientation: How network topology determines the long-time dynamics of the antisymmetric Lotka-Volterra equation

Geiger, Philipp; Knebel, Johannes; Frey, Erwin

doi:10.1103/physreve.98.062316

Cited by 13 publications

(11 citation statements)

References 101 publications

(317 reference statements)

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“…Knebel and co-authors [12,8] use the topology of the graph describing the interactions in each game to examine the "interplay between the network structure and the strengths of interaction links on global stability" and to classify coexistence networks, that is, those where all actions coexist for all strengths of the interactions. Again, a 3-action cycle seems to persist corresponding to the RSP cycle within the RSPLS game.…”

Section: Introductionmentioning

confidence: 99%

Stability of cycles in a game of Rock-Scissors-Paper-Lizard-Spock

Castro¹,

Garrido-da-Silva²,

Ferreira³

et al. 2021

Preprint

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We study a system of ordinary differential equations in R 5 that is used as a model both in population dynamics and in game theory, and is known to exhibit a heteroclinic network formed by three types of elementary heteroclinic cycles. We show the asymptotic stability of the network for parameter values in a range compatible with the two interpretations of the equations. We obtain estimates of the relative attractiveness of each one of the cycles by computing their stability indices. For the parameter values ensuring the asymptotic stability of the network we show that if one of the cycles has a weak form of attractiveness, then the other two are completely unstable. We also show the existence of an open region in parameter space where all three cycles are completely unstable and the network is asymptotically stable, giving rise to intricate dynamics that has been observed numerically by other authors.

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Section: Introductionmentioning

confidence: 99%

Stability of cycles in a game of Rock-Scissors-Paper-Lizard-Spock

Castro¹,

Garrido-da-Silva²,

Ferreira³

et al. 2021

Preprint

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“…Evolutionary stages that created Game theory are the ideas about the existence of mixed-strategy equilibria in two-person zero-sum games, followed by the rise of modern mathematical concepts (Geiger, Knebel, & Frey, 2018). In addition, the discovery of the law of development of organic nature by Darwin led to the biological application of the game theory.…”

Section: Game Theorymentioning

confidence: 99%

Strategy to Build a Transshipment Port as a Catalyst to Achieving Critical Mass for Sabah’s Economic Growth

Tom¹

2019

IBR

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Digital transformation has led to a new era of port development at an unprecedented pace. China represents a large percentage of total global trades, navigating the maritime silk-road to various global and regional ports. In Malaysia, the lack of concrete justifications for the issue of transhipment port strategy leads to a debatable framework. Hence, the aim of the paper is to critically discuss the strategy to build a transhipment port as a catalyst to achieving critical mass for economic growth in Sabah. The study draws heavily on existing literature on the theoretical evidence and the possible factors that shape strategy to build transshipment port in Sabah. Based on reviewed literature, various resultant strategies adopted to stand for their interest are discussed. In this way, this paper provides not only theoretical insights, but also strategically guides managers of organisations in Sabah, government, and businesses values towards building a transshipment port in Sabah to effectively retire cabotage policy to reduce cost, enhance port throughput, develop hinterland for critical mass, enhance ports-economic clusters connectivity, eliminate capacity bottleneck, unlock natural resources export potential, align port service towards regional port users’ needs and to give regional port powers a run for their money.

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“…Considerable work has been done studying the meanfield limit model [1,26,12,14,7] and stochastic extensions [5,19]. In the mean-field limit model it has been shown that a constant of motion exists and is a conserved quantity similar to energy or momentum in classical mechanics (though that analogy is not an exact interpretation) [1].…”

Section: Introductionmentioning

confidence: 99%

Period Estimation and Noise in a Neutrally Stable Stochastic Oscillator

Sanft¹,

Intoy²

2020

SPORA

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The periods of the orbits for the well-mixed cyclic three-species Lotka-Volterra model far away from the fixed point are studied. For finite system sizes, a discrete stochastic approach is employed and periods are found via wavelet analysis. As the system size is increased, a hierarchy of approximations ranging from Poisson noise to Gaussian noise to deterministic models are utilized. Based on the deterministic equations, a mathematical relationship between a conserved quantity of the model and the period of the population oscillations is found. Exploiting this property we then study the deterministic conserved quantity and period noise in finite size systems.

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Topologically robust zero-sum games and Pfaffian orientation: How network topology determines the long-time dynamics of the antisymmetric Lotka-Volterra equation

Cited by 13 publications

References 101 publications

Stability of cycles in a game of Rock-Scissors-Paper-Lizard-Spock

Stability of cycles in a game of Rock-Scissors-Paper-Lizard-Spock

Strategy to Build a Transshipment Port as a Catalyst to Achieving Critical Mass for Sabah’s Economic Growth

Period Estimation and Noise in a Neutrally Stable Stochastic Oscillator

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