Nonlinear dynamics of chemotherapeutic resistance

We use a three-component replicator dynamical system with healthy cells, sensitive cells, and resistant cells, with a prisoner’s dilemma payoff matrix from evolutionary game theory to understand the phenomenon of competitive release, which is the main mechanism by which tumors develop chemotherapeutic resistance. By comparing the phase portraits of the system without therapy compared to continuous therapy above a certain threshold, we show that chemotherapeutic resistance develops if there are pre-exisiting resistance cells in the population. We examine the basin boundaries of attraction associated with the chemo-sensitive population and the chemo-resistant population for increasing values of chemo-concentrations and show their spiral intertwined structure. We also examine the fitness landscapes both with and without continuous therapy and show that with therapy, the average fitness as well as the fitness functions of each of the subpopulations initially increases, but eventually decreases monotonically as the resistant subpopulation saturates the tumor.

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On the design of treatment schedules that avoid chemotherapeutic resistance

10.1101/325381 ◽

2018 ◽

Author(s):

Y. Ma ◽

P.K. Newton

Keyword(s):

Cell Population ◽

Evolutionary Game ◽

Maximum Tolerated Dose ◽

Payoff Matrix ◽

Theory Model ◽

Release Mechanism ◽

Trajectory Design ◽

Chemotherapeutic Resistance ◽

Competitive Release ◽

Resistant Cells

We introduce a method of designing treatment schedules for a model three-component replicator dynamical system that avoids chemotherapeutic resistance by controlling and managing the competitive release of resistant cells in the tumor. We use an evolutionary game theory model with prisoner’s dilemma payoff matrix that governs the competition among healthy cells, chemo-sensitive cells, and chemo-resistant cells and the goal is to control the evolution of chemo-resistance via the competitive release mechanism. The method is based on nonlinear trajectory design and energy transfer methods first introduced in the orbital mechanics literature for Hamiltonian systems. By using the structure of the trajectories defined by solutions of the replicator system for different constant chemotherapeutic concentrations (which produces a curvilinear coordinate system spanning the full region), we construct periodic (closed) orbits by switching the chemo-dose at carefully chosen times and appropriate levels to design schedules that are superior to both maximum tolerated dose (MTD) schedules and low-dose metronomic (LDM) schedules, both of which ultimately lead to fixation of either sensitive cells or resistant cells. By keeping the three sub-populations of cells in competition with each other, neither the sensitive cell population nor the resitant cell population are able to dominate as we balance the populations indefinitely (closed periodic orbits), thereby avoiding fixation of the cancer cell population and re-growth of a resistant tumor. The schedules we design have the feature that they maintain a higher average population fitness than either the MTD or the LDM schedules.PACS numbers: 87.23.Kg; 87.55.de; 87.19.Xj; 87.19.lr

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IsoMaTrix: a framework to visualize the isoclines of matrix games and quantify uncertainty in structured populations

Bioinformatics ◽

10.1093/bioinformatics/btaa1025 ◽

2020 ◽

Author(s):

Jeffrey West ◽

Yongqian Ma ◽

Artem Kaznatcheev ◽

Alexander R A Anderson

Keyword(s):

Spatial Configuration ◽

Evolutionary Game ◽

Payoff Matrix ◽

Structured Populations ◽

Continuous Treatment ◽

Supplementary Information ◽

Matrix Games ◽

Spatial Games ◽

Competitive Release ◽

Zero Growth

Abstract Evolutionary game theory describes frequency-dependent selection for fixed, heritable strategies in a population of competing individuals using a payoff matrix. We present a software package to aid in the construction, analysis, and visualization of three-strategy matrix games. The IsoMaTrix package computes the isoclines (lines of zero growth) of matrix games, and facilitates direct comparison of well-mixed dynamics to structured populations on a lattice grid. IsoMaTrix computes fixed points, phase flow, trajectories, (sub)velocities, and uncertainty quantification for stochastic effects in spatial matrix games. We describe a result obtained via IsoMaTrix’s spatial games functionality, which shows that the timing of competitive release in a cancer model (under continuous treatment) critically depends on the initial spatial configuration of the tumor. Availability The code is available at: https://github.com/mathonco/isomatrix. Supplementary information Supplementary data are available at Bioinformatics online.

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A Study of Taxi Service Mode Choice Based on Evolutionary Game Theory

Journal of Advanced Transportation ◽

10.1155/2019/8607942 ◽

2019 ◽

Vol 2019 ◽

pp. 1-17

Author(s):

Zhu Bai ◽

Mingxia Huang ◽

Shuai Bian ◽

Huandong Wu

Keyword(s):

Game Theory ◽

Evolutionary Game Theory ◽

Mode Choice ◽

Evolutionary Game ◽

Payoff Matrix ◽

Game Model ◽

Stable States ◽

Taxi Service ◽

Service Mode ◽

The Impact

The emergence of online car-hailing service provides an innovative approach to vehicle booking but has negatively influenced the taxi industry in China. This paper modeled taxi service mode choice based on evolutionary game theory (EGT). The modes included the dispatching and online car-hailing modes. We constructed an EGT framework, including determining the strategies and the payoff matrix. We introduced different behaviors, including taxi company management, driver operation, and passenger choice. This allowed us to model the impact of these behaviors on the evolving process of service mode choice. The results show that adjustments in taxi company, driver, and passenger behaviors impact the evolutionary path and convergence speed of our evolutionary game model. However, it also reveals that, regardless of adjustments, the stable states in the game model remain unchanged. The conclusion provides a basis for studying taxi system operation and management.

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An Analysis of Quality Liability Insurance for Prefabricated Components Using Evolutionary Game Theory

Canadian Journal of Civil Engineering ◽

10.1139/cjce-2020-0012 ◽

2021 ◽

Author(s):

Yan Liu ◽

Chenyao Lv ◽

Hong Xian Li ◽

Yan Li ◽

Zhen Lei ◽

...

Keyword(s):

Game Theory ◽

Evolutionary Game Theory ◽

Evolutionary Game ◽

Payoff Matrix ◽

Liability Insurance ◽

Insurance Companies ◽

Social Benefits ◽

Simulation Calculation ◽

The Government

Managing quality risks of prefabricated components is one of the challenges for prefabricated construction. The Quality Liability Insurance for Prefabricated Components (QLIPC) is an effective approach to transfer such risks; however, limited research has been conducted regarding the development of QLIPC. This study introduces an Evolutionary Game Theory (EGT)-based approach incorporating decisions from both the government and insurance companies. In the EGT model, a payoff matrix under disparate strategies is constructed, and the evolutionary stable strategies (ESS) are deduced. The simulation calculation is then carried out by MATLAB using sample virtual data to demonstrate the analysis. The results show that the government should act as the game promoter because the QLIPC can reduce governance cost and has significant social benefits. This research contributes a theoretical framework to analyze the QLIPC development using the EGT theory, and it could help the government to make long-term strategies for developing the QLIPC market.

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Exponential Families and Game Dynamics

Canadian Journal of Mathematics ◽

10.4153/cjm-1982-025-4 ◽

1982 ◽

Vol 34 (2) ◽

pp. 374-405 ◽

Cited By ~ 29

Author(s):

Ethan Akin

Keyword(s):

Game Theory ◽

Evolutionary Game ◽

Payoff Matrix ◽

Exponential Families ◽

Von Neumann ◽

Rational Player ◽

Large Populations ◽

Pure Strategies ◽

Classical Game ◽

Classical Game Theory

A symmetric game consists of a set of pure strategies indexed by {0, …, n} and a real payoff matrix (aij). When two players choose strategies i and j the payoffs are aij and aji to the i-player and j-player respectively. In classical game theory of Von Neumann and Morgenstern [16] the payoffs are measured in units of utility, i.e., desirability, or in units of some desirable good, e.g. money. The problem of game theory is that of a rational player who seeks to choose a strategy or mixture of strategies which will maximize his return. In evolutionary game theory of Maynard Smith and Price [13] we look at large populations of game players. Each player's opponents are selected randomly from the population, and no information about the opponent is available to the player. For each one the choice of strategy is a fixed inherited characteristic.

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Explore Knowledge-Sharing Strategy and Evolutionary Mechanism for Integrated Project Team Based on Evolutionary Game Model

Advances in Civil Engineering ◽

10.1155/2019/4365358 ◽

2019 ◽

Vol 2019 ◽

pp. 1-23

Author(s):

Yanchao Du ◽

Hengyu Zhou ◽

Yongbo Yuan ◽

Xiaoxue Liu

Keyword(s):

Knowledge Sharing ◽

Evolutionary Game ◽

Payoff Matrix ◽

Evolutionary Mechanism ◽

Interaction Behavior ◽

Sharing Strategy ◽

Overall Performance ◽

Integrated Project ◽

Cost Efficient ◽

Knowledge Absorption

Integrated Project Delivery (IPD) has become increasingly popular in the architecture, engineering, and construction industries. However, the current practice status by the construction industry fails to deliver the desired results. In that backdrop, how to promote cooperation within and improve the overall performance of integrated project team has received wide attention. Herein, knowledge-sharing plays a critical role in cooperation and overall performance. However, to the best of our knowledge, the research on knowledge-sharing strategy interaction and evolutionary mechanism is rare. To make up for the deficiency of the studies existing, a novel model is proposed by taking advantage of evolutionary game theory, to capture the interaction behavior of knowledge-sharing and explore its evolutionary mechanism. Six parameters of knowledge stock, knowledge-sharing degree, heterogeneous knowledge proportion, synergy effect, knowledge absorption coefficient, and knowledge-sharing cost efficient that are critical to knowledge-sharing are extracted and defined. The payoff matrix is constructed by analyzing the benefits and costs of knowledge-sharing. Then, a replicator dynamic system is established based on payoff matrix, to determine the evolutionary tendency of knowledge-sharing behavior. Finally, numerical simulations are conducted to explore the influences of all parameters on the knowledge-sharing strategy. The findings in this research reveal that strategy interaction behavior is significantly influenced by proportion of strategy of choosing to share knowledge in both game players. The authors also find that strategy interaction behavior has a strong negative correlation with knowledge-sharing cost efficient, but has a positive correlation with knowledge stock, heterogeneous knowledge proportion, degree of knowledge-sharing, knowledge absorption coefficient, and synergetic effect coefficient. This research can provide the evolutionary mechanism and broaden our understanding of relationship between project performance and knowledge-sharing and can offer valuable guidance on improving cooperation and performance of project teams.

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The Trilateral Evolutionary Game of Agri-Food Quality in Farmer-Supermarket Direct Purchase: A Simulation Approach

Complexity ◽

10.1155/2018/5185497 ◽

2018 ◽

Vol 2018 ◽

pp. 1-11 ◽

Cited By ~ 8

Author(s):

Xin Su ◽

Haolong Liu ◽

Shunqi Hou

Keyword(s):

Quality Assurance ◽

Food Quality ◽

Evolutionary Game ◽

Quality Standards ◽

Payoff Matrix ◽

Legal Rights ◽

Evolutionary System ◽

Key Factors ◽

Stable States ◽

High Quality

The prevalence of opportunistic behaviors in agri-food production and circulation results in frequent quality accidents in emerging economies. Numerous researches have discussed effective countermeasures to this problem, but few of them focus on the effectiveness and stability of quality assurance systems. Owing to the bounded rationality and information asymmetry, the dynamic quality game among producers, marketers, and consumers has significant characteristics of complexity. This paper aims at discussing the farmer-supermarket direct purchase’s contributions to ensure the agri-food quality and analyzing the effectiveness, stability, and key factors of this new industrial organization. Based on the evolutionary game theory, we establish the trilateral-game payoff matrix, build up the replicator dynamic equations, and discuss possible evolutionary stable states. The simulation results show that the evolutionary system converges to desired stability faster, when the high-quality agri-food’s market premium increases and the penalty for violating quality standards increases. Furthermore, when farmers share more high-quality agri-food’s market premiums and marketers compensate more for violating the quality standards than before, the evolutionary system also converges to desired stability faster. Therefore, the quality information tracing technology, farmers and marketers’ fair distribution of profits and risks, and consumers’ capabilities to safeguard their legal rights are the three key factors to maintain the effectiveness and stability of quality assurance systems.

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Game Analysis of the Multiagent Evolution of Existing Building Green Retrofitting from the Perspective of Green Credit

Discrete Dynamics in Nature and Society ◽

10.1155/2021/5560671 ◽

2021 ◽

Vol 2021 ◽

pp. 1-19

Author(s):

Liwen Chen ◽

Mengjia Zhang ◽

Shiwen Zhao

Keyword(s):

Large Scale ◽

Simulation Analysis ◽

Evolutionary Game ◽

Payoff Matrix ◽

Strategic Choices ◽

Existing Building ◽

The Sustainable Development ◽

Factors Affecting ◽

Service Companies ◽

The Government

Existing building green retrofitting can reduce building energy consumption and greenhouse gas emissions, which is conducive to the sustainable development of the construction industry. The financing dilemma of the existing building green retrofitting hinders the large-scale development of green retrofitting in China. This paper establishes the perceived payoff matrix and evolutionary game model of the government, Energy Service Companies (ESCOs), banks, and owners. Through simulation analysis, the primary factors affecting the choice of game strategy and the stable strategy under different conditions are discussed. The results show that the strategic choices of the government, ESCOs, banks, and owners influence each other in the two game models. Government regulations will have an impact on the strategic choices of ESCOs, banks, and owners. The owners’ strategy choice is closely related to the perceived benefits and costs of retrofitting. Based on the results, corresponding suggestions are proposed to provide theoretical support for the development of the existing building green retrofitting market.

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Multi-Player Evolutionary Game of Network Attack and Defense Based on System Dynamics

Mathematics ◽

10.3390/math9233014 ◽

2021 ◽

Vol 9 (23) ◽

pp. 3014

Author(s):

Pengxi Yang ◽

Fei Gao ◽

Hua Zhang

Keyword(s):

Evolutionary Game ◽

Stable State ◽

Payoff Matrix ◽

Game Model ◽

Network Attack ◽

Evolutionary Stable Strategies ◽

Player Game ◽

Attack And Defense ◽

Mathematical Derivation

We formalize the adversarial process between defender and attackers as a game and study the non-cooperative evolutionary game mechanism under bounded rationality. We analyze the long-term dynamic process between the attacking and defending parties using the evolutionary stable strategies derived from the evolutionary game model. First, we construct a multi-player evolutionary game model consisting of a defender and multiple attackers, formally describe the strategies, and construct a three-player game payoff matrix. Then, we propose two punishment schemes, i.e., static and dynamic ones. Moreover, through the combination of mathematical derivation with simulation, we obtain the evolutionary stable strategies of each player. Different from previous work, in this paper, we consider the influence of strategies among different attackers. The simulation shows that (1) in the static punishment scheme, increasing the penalty can quickly control the occurrence of network attacks in the short term; (2) in the dynamic punishment scheme, the game can be stabilized effectively, and the stable state and equilibrium values are not affected by the change of the initial values.

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Alternate Models of Replicator Dynamics

Volume 7B: 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control ◽

10.1115/detc2013-12046 ◽

2013 ◽

Author(s):

Elizabeth N. Wesson ◽

Richard H. Rand

Keyword(s):

Evolutionary Dynamics ◽

Total Population ◽

Replicator Dynamics ◽

Standard Form ◽

Exponential Model ◽

Payoff Matrix ◽

Replicator Equation ◽

Game Theoretic ◽

Average Fitness ◽

Strategy I

Models of evolutionary dynamics are often approached via the replicator equation, which in its standard form is given by x.i=xifix-ϕ,i = 1,…, n, where xi is the frequency, or relative abundance, of strategy i, fi is its fitness, and ϕ=∑i=1nxifi is the average fitness. A game-theoretic aspect is introduced to the model via the payoff matrix A, where Ai,j is the expected payoff of i vs. j, by taking fi(x) = (A·x)i. This model is based on the exponential model of population growth, ẋi = xifi, with ϕ introduced in order both to hold the total population constant and to model competition between strategies. We analyze the dynamics of analogous models for the replicator equation of the form x.i=gxifi-ϕ, for selected growth functions g.

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