Review: Game theory of public goods in one-shot social dilemmas without assortment

Journal of Theoretical Biology

2016

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Cancer cells produce growth factors that diffuse and sustain tumor proliferation, a form of cooperation among cancer cells that can be studied using mathematical models of public goods in the framework of evolutionary game theory. Cell populations, however, form heterogeneous networks that cannot be described by regular lattices or scale-free networks, the types of graphs generally used in the study of cooperation. To describe the dynamics of growth factor production in populations of cancer cells, I study public goods games on Voronoi networks, using a range of non-linear benefits that account for the known properties of growth factors, and different types of diffusion gradients. The results are surprisingly similar to those obtained on regular graphs and different from results on scale-free networks, revealing that network heterogeneity per se does not promote cooperation when public goods diffuse beyond one-step neighbours. The exact shape of the diffusion gradient is not crucial, however, whereas the type of non-linear benefit is an essential determinant of the dynamics. Public goods games on Voronoi networks can shed light on intra-tumor heterogeneity, the evolution of resistance to therapies that target growth factors, and new types of cell therapy.

Section: Public Goods In Evolutionary Game Theorymentioning

confidence: 99%

Section: Further Developments Of the Modelmentioning

confidence: 99%

Cooperation among cancer cells as public goods games on Voronoi networks

Journal of Theoretical Biology

2016

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“…In other words, because the products of glycolysis act as diffusible public goods, glycolysis should be modeled as a public goods game, rather than as a game with pairwise interactions; games with pairwise interactions, even when multiple interactions are allowed, do not generally have the same results as multi-player, collective action (public goods) games. An important difference is that, while in two-player nonlinear games the maximum benefit for the population is achieved when all players cooperate, in multi-player games the best outcome for the population is achieved at intermediate frequencies of cooperators (Archetti and Scheuring, 2012). This, as we will see, has important implications for the dynamics of potential therapies based on the modification of acidosis.…”

Section: Glycolysis As a Public Goods Gamementioning

confidence: 92%

Evolutionary dynamics of the Warburg effect: Glycolysis as a collective action problem among cancer cells

Journal of Theoretical Biology

2014

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The upregulation of glycolysis in tumors is common even when oxygen is not limiting. The adaptive value of this "Warburg effect" is unclear. Glycolysis is costly for a cell but the ensuing acidity is beneficial for the tumor. A collective action problem among cancer cells arises. Game theory shows that the acidity induced by glycolysis can explain the Warburg effect. a r t i c l e i n f o a b s t r a c tThe upregulation of glycolysis in cancer cells (the "Warburg effect") is common and has implications for prognosis and treatment. As it is energetically inefficient under adequate oxygen supply, its adaptive value for a tumor remains unclear. It has been suggested that the acidity produced by glycolysis is beneficial for cancer cells because it promotes proliferation against normal cells. Current models of this acid-mediated tumor invasion hypothesis, however, do not account for increased glycolysis under nonlimiting oxygen concentrations and therefore do not fully explain the Warburg effect. Here I show that the Warburg effect can be explained as a form of cooperation among cancer cells, in which the products of glycolysis act as a public good, even when oxygen supply is high enough to make glycolysis energetically inefficient. A multiplayer game with non-linear, non-monotonic payoff functions that models the benefits of the acidity induced by glycolysis reveals that clonal selection can stabilize glycolysis even when energetically costly, that is, under non-limiting oxygen concentration. Characterizing the evolutionary dynamics of glycolysis reveals cases in which anti-cancer therapies that rely on the modification of acidity can be effective.

“…While linear effects are more amenable to analytical study, it is known that most growth factors have a nonlinear, often sigmoid, effect on cell proliferation, and that nonlinear effects can lead to very different dynamics [25,26]. We decided, therefore, to analyse tumor-stroma interactions using a multiplayer public goods game with nonlinear benefits, sacrificing analytical tractability for the sake of realism.…”

Section: From Two-player Games To Collective Interactions With Nonlinmentioning

confidence: 99%

Game Theory of Tumor–Stroma Interactions in Multiple Myeloma: Effect of Nonlinear Benefits

Sartakhti

Manshaei

2018

Games

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Cancer cells and stromal cells often exchange growth factors with paracrine effects that promote cell growth: a form of cooperation that can be studied by evolutionary game theory. Previous models have assumed that interactions between cells are pairwise or that the benefit of a growth factor is a linear function of its concentration. Diffusible factors, however, affect multiple cells and generally have nonlinear effects, and these differences are known to have important consequences for evolutionary dynamics. Here, we study tumor-stroma paracrine signaling using a model with multiplayer collective interactions in which growth factors have nonlinear effects. We use multiple myeloma as an example, modelling interactions between malignant plasma cells, osteoblasts, and osteoclasts. Nonlinear benefits can lead to results not observed in linear models, including internal mixed stable equilibria and cyclical dynamics. Models with linear effects, therefore, do not lead to a meaningful characterization of the dynamics of tumor-stroma interactions. To understand the dynamics and the effect of therapies it is necessary to estimate the shape of the benefit functions experimentally and parametrize models based on these functions.