scholarly journals Evolutionary dynamics of multiple games

2018 ◽  
Author(s):  
Vandana R. Venkateswaran ◽  
Chaitanya S. Gokhale
Keyword(s):  
Game Theory ◽  
Population Dynamics ◽  
Social Behavior ◽  
Evolutionary Game Theory ◽  
Bacterial Population ◽  
Evolutionary Dynamics ◽  
Evolutionary Game ◽  
Fixation Probability ◽  
Replicator Equation ◽  
Multiple Games

AbstractEvolutionary game theory has been successful in describing phenomena from bacterial population dynamics to the evolution of social behavior. Interactions between individuals are usually captured by a single game. In reality, however, individuals take part in many interactions. Here, we include multiple games and analyze their individual and combined evolutionary dynamics. A typical assumption is that the evolutionary dynamics of individual behavior can be understood by constructing one big comprehensive interactions structure, a single big game. But if any one of the multiple games has more than two strategies, then the combined dynamics cannot be understood by looking only at individual games. Devising a method to study multiple games – where each game could have an arbitrary number of players and strategies – we provide a concise replicator equation, and analyze its resulting dynamics. Moreover, in the case of finite populations, we formulate and calculate a basic and useful property of stochasticity, fixation probability. Our results reveal that even when interactions become incredibly complex, their properties can be captured by relatively simple concepts of evolutionary game(s) theory.

scholarly journals Evolutionary game theory for physical and biological scientists. I. Training and validating population dynamics equations

2014 ◽  
Vol 4 (4) ◽  
pp. 20140037 ◽  
Author(s):  
David Liao ◽  
Thea D. Tlsty
Keyword(s):  
Game Theory ◽  
Population Dynamics ◽  
Evolutionary Game Theory ◽  
Evolutionary Dynamics ◽  
Evolutionary Game ◽  
Treatment Strategies ◽  
Analysis Method ◽  
Analysis Techniques ◽  
Game Theoretic ◽  
And Control

Failure to understand evolutionary dynamics has been hypothesized as limiting our ability to control biological systems. An increasing awareness of similarities between macroscopic ecosystems and cellular tissues has inspired optimism that game theory will provide insights into the progression and control of cancer. To realize this potential, the ability to compare game theoretic models and experimental measurements of population dynamics should be broadly disseminated. In this tutorial, we present an analysis method that can be used to train parameters in game theoretic dynamics equations, used to validate the resulting equations, and used to make predictions to challenge these equations and to design treatment strategies. The data analysis techniques in this tutorial are adapted from the analysis of reaction kinetics using the method of initial rates taught in undergraduate general chemistry courses. Reliance on computer programming is avoided to encourage the adoption of these methods as routine bench activities.

scholarly journals Evolutionary Game Theory: Darwinian Dynamics and the G Function Approach

Games ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 72
Author(s):  
Anuraag Bukkuri ◽  
Joel S. Brown
Keyword(s):  
Game Theory ◽  
Drug Resistance ◽  
Population Dynamics ◽  
Evolutionary Game Theory ◽  
Evolutionary Dynamics ◽  
Evolutionary Game ◽  
Function Model ◽  
Predator Prey ◽  
Evolutionary Stable Strategies ◽  
Over Time

Classical evolutionary game theory allows one to analyze the population dynamics of interacting individuals playing different strategies (broadly defined) in a population. To expand the scope of this framework to allow us to examine the evolution of these individuals’ strategies over time, we present the idea of a fitness-generating (G) function. Under this model, we can simultaneously consider population (ecological) and strategy (evolutionary) dynamics. In this paper, we briefly outline the differences between game theory and classical evolutionary game theory. We then introduce the G function framework, deriving the model from fundamental biological principles. We introduce the concept of a G-function species, explain the process of modeling with G functions, and define the conditions for evolutionary stable strategies (ESS). We conclude by presenting expository examples of G function model construction and simulations in the context of predator–prey dynamics and the evolution of drug resistance in cancer.

scholarly journals Modelling population dynamics in a unicellular social organism community using a minimal model and evolutionary game theory

Open Biology ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. 200206
Author(s):  
Ravindra Garde ◽  
Jan Ewald ◽  
Ákos T. Kovács ◽  
Stefan Schuster
Keyword(s):  
Game Theory ◽  
Population Dynamics ◽  
Evolutionary Game Theory ◽  
Evolutionary Game ◽  
Minimal Models ◽  
Unicellular Organisms ◽  
Cyclic Dynamics ◽  
High Level ◽  
Complex Phenomena ◽  
Social Organism

Most unicellular organisms live in communities and express different phenotypes. Many efforts have been made to study the population dynamics of such complex communities of cells, coexisting as well-coordinated units. Minimal models based on ordinary differential equations are powerful tools that can help us understand complex phenomena. They represent an appropriate compromise between complexity and tractability; they allow a profound and comprehensive analysis, which is still easy to understand. Evolutionary game theory is another powerful tool that can help us understand the costs and benefits of the decision a particular cell of a unicellular social organism takes when faced with the challenges of the biotic and abiotic environment. This work is a binocular view at the population dynamics of such a community through the objectives of minimal modelling and evolutionary game theory. We test the behaviour of the community of a unicellular social organism at three levels of antibiotic stress. Even in the absence of the antibiotic, spikes in the fraction of resistant cells can be observed indicating the importance of bet hedging. At moderate level of antibiotic stress, we witness cyclic dynamics reminiscent of the renowned rock–paper–scissors game. At a very high level, the resistant type of strategy is the most favourable.

scholarly journals Fisheries management as a Stackelberg Evolutionary Game: Finding an evolutionarily enlightened strategy

PLoS ONE ◽  
2021 ◽  
Vol 16 (1) ◽  
pp. e0245255
Author(s):  
Monica Salvioli ◽  
Johan Dubbeldam ◽  
Kateřina Staňková ◽  
Joel S. Brown
Keyword(s):  
Game Theory ◽  
Fisheries Management ◽  
Evolutionary Game Theory ◽  
Evolutionary Dynamics ◽  
Evolutionary Game ◽  
Fish Population ◽  
Stackelberg Equilibrium ◽  
Negative Effects ◽  
Evolutionary Changes ◽  
Body Sizes

Fish populations subject to heavy exploitation are expected to evolve over time smaller average body sizes. We introduce Stackelberg evolutionary game theory to show how fisheries management should be adjusted to mitigate the potential negative effects of such evolutionary changes. We present the game of a fisheries manager versus a fish population, where the former adjusts the harvesting rate and the net size to maximize profit, while the latter responds by evolving the size at maturation to maximize the fitness. We analyze three strategies: i) ecologically enlightened (leading to a Nash equilibrium in game-theoretic terms); ii) evolutionarily enlightened (leading to a Stackelberg equilibrium) and iii) domestication (leading to team optimum) and the corresponding outcomes for both the fisheries manager and the fish. Domestication results in the largest size for the fish and the highest profit for the manager. With the Nash approach the manager tends to adopt a high harvesting rate and a small net size that eventually leads to smaller fish. With the Stackelberg approach the manager selects a bigger net size and scales back the harvesting rate, which lead to a bigger fish size and a higher profit. Overall, our results encourage managers to take the fish evolutionary dynamics into account. Moreover, we advocate for the use of Stackelberg evolutionary game theory as a tool for providing insights into the eco-evolutionary consequences of exploiting evolving resources.

scholarly journals Which games are growing bacterial populations playing?

2015 ◽  
Vol 12 (108) ◽  
pp. 20150121 ◽  
Author(s):  
Xiang-Yi Li ◽  
Cleo Pietschke ◽  
Sebastian Fraune ◽  
Philipp M. Altrock ◽  
Thomas C. G. Bosch ◽  
...  
Keyword(s):  
Game Theory ◽  
Population Dynamics ◽  
Microbial Communities ◽  
Evolutionary Game Theory ◽  
Community Dynamics ◽  
Growth Parameters ◽  
Evolutionary Game ◽  
Frequency Dependent

Microbial communities display complex population dynamics, both in frequency and absolute density. Evolutionary game theory provides a natural approach to analyse and model this complexity by studying the detailed interactions among players, including competition and conflict, cooperation and coexistence. Classic evolutionary game theory models typically assume constant population size, which often does not hold for microbial populations. Here, we explicitly take into account population growth with frequency-dependent growth parameters, as observed in our experimental system. We study the in vitro population dynamics of the two commensal bacteria ( Curvibacter sp. (AEP1.3) and Duganella sp. (C1.2)) that synergistically protect the metazoan host Hydra vulgaris (AEP) from fungal infection. The frequency-dependent, nonlinear growth rates observed in our experiments indicate that the interactions among bacteria in co-culture are beyond the simple case of direct competition or, equivalently, pairwise games. This is in agreement with the synergistic effect of anti-fungal activity observed in vivo . Our analysis provides new insight into the minimal degree of complexity needed to appropriately understand and predict coexistence or extinction events in this kind of microbial community dynamics. Our approach extends the understanding of microbial communities and points to novel experiments.

Evolutionary Games and Local Dynamics

2015 ◽  
Vol 17 (02) ◽  
pp. 1540016 ◽  
Author(s):  
Philippe Uyttendaele ◽  
Frank Thuijsman
Keyword(s):  
Game Theory ◽  
Population Dynamics ◽  
Evolutionary Game Theory ◽  
Evolutionary Game ◽  
Evolutionary Games ◽  
Global Dynamics ◽  
Local Interactions ◽  
Local Dynamics

In this paper, we examine several options for modeling local interactions within the framework of evolutionary game theory. Several examples show that there is a major difference between population dynamics using local dynamics versus global dynamics. Moreover, different modeling choices may lead to very diverse results.

scholarly journals The contribution of evolutionary game theory to understanding and treating cancer

2020 ◽  
Author(s):  
Benjamin Wölfl ◽  
Hedy te Rietmole ◽  
Monica Salvioli ◽  
Frank Thuijsman ◽  
Joel S. Brown ◽  
...  
Keyword(s):  
Game Theory ◽  
Cancer Progression ◽  
Evolutionary Game Theory ◽  
Cancer Biology ◽  
Evolutionary Dynamics ◽  
Evolutionary Game ◽  
Great Promise ◽  
Full Potential ◽  
Theory Approach ◽  
Game Theoretic

AbstractEvolutionary game theory mathematically conceptualizes and analyzes biological interactions where one’s fitness not only depends on one’s own traits, but also on the traits of others. Typically, the individuals are not overtly rational and do not select, but rather, inherit their traits. Cancer can be framed as such an evolutionary game, as it is composed of cells of heterogeneous types undergoing frequency-dependent selection. In this article, we first summarize existing works where evolutionary game theory has been employed in modeling cancer and improving its treatment. Some of these game-theoretic models suggest how one could anticipate and steer cancer’s eco-evolutionary dynamics into states more desirable for the patient via evolutionary therapies. Such therapies offer great promise for increasing patient survival and decreasing drug toxicity, as demonstrated by some recent studies and clinical trials. We discuss clinical relevance of the existing game-theoretic models of cancer and its treatment, and opportunities for future applications. We discuss the developments in cancer biology that are needed to better utilize the full potential of game-theoretic models. Ultimately, we demonstrate that viewing tumors with an evolutionary game theory approach has medically useful implications that can inform and create a lockstep between empirical findings, and mathematical modeling. We suggest that cancer progression is an evolutionary game and needs to be viewed as such.

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