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Register a new userCooperative success in epithelial public goods games
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Cancer cells obtain mutations which rely on the production of diffusible growth factors to confer a fitness benefit. These mutations can be considered cooperative, and studied as public goods games within the framework of evolutionary game theory. The population structure, benefit function and update rule all influence the evolutionary success of cooperators. We model the evolution of cooperation in epithelial cells using the Voronoi tessellation model. Unlike traditional evolutionary graph theory, this allows us to implement global updating, for which birth and death events are spatially decoupled. We compare, for a sigmoid benefit function, the conditions for cooperation to be favoured and/or beneficial for well mixed and structured populations. We find that when population structure is combined with global updating, cooperation is more successful than if there were local updating or the population were well-mixed. Interestingly, the qualitative behaviour for the well-mixed population and the Voronoi tessellation model is remarkably similar, but the latter case requires significantly lower incentives to ensure cooperation.
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Public goods games in undirected networks are generally known to have pure Nash equilibria, which are easy to find. In contrast, we prove that, in directed networks, a broad range of public goods games have intractable equilibrium problems: The existence of pure Nash equilibria is NP-hard to decide, and mixed Nash equilibria are PPAD-hard to find. We define general utility public goods games, and prove a complexity dichotomy result for finding pure equilibria, and a PPAD-completeness proof for mixed Nash equilibria. Even in the divisible goods variant of the problem, where existence is easy to prove, finding the equilibrium is PPAD-complete. Finally, when the treewidth of the directed network is appropriately bounded, we prove that polynomial-time algorithms are possible.
Finding ways to overcome the temptation to exploit one another is still a challenge in behavioural sciences. In the framework of evolutionary game theory, punishing strategies are frequently used to promote cooperation in competitive environments. Here, we introduce altruistic punishers in the spatial public goods game. This strategy acts as a cooperator in the absence of defectors, otherwise it will punish all defectors in their vicinity while bearing a cost to do so. We observe three distinct behaviours in our model: i) in the absence of punishers, cooperators (who dont punish defectors) are driven to extinction by defectors for most parameter values; ii) clusters of punishers thrive by sharing the punishment costs when these are low iii) for higher punishment costs, punishers, when alone, are subject to exploitation but in the presence of cooperators can form a symbiotic spatial structure that benefits both. This last observation is our main finding since neither cooperation nor punishment alone can survive the defector strategy in this parameter region and the specificity of the symbiotic spatial configuration shows that lattice topology plays a central role in sustaining cooperation. Results were obtained by means of Monte Carlo simulations on a square lattice and subsequently confirmed by a pairwise comparison of different strategies payoffs in diverse group compositions, leading to a phase diagram of the possible states.
Bacterial quorum sensing is the communication that takes place between bacteria as they secrete certain molecules into the intercellular medium that later get absorbed by the secreting cells themselves and by others. Depending on cell density, this uptake has the potential to alter gene expression and thereby affect global properties of the community. We consider the case of multiple bacterial species coexisting, referring to each one of them as a genotype and adopting the usual denomination of the molecules they collectively secrete as public goods. A crucial problem in this setting is characterizing the coevolution of genotypes as some of them secrete public goods (and pay the associated metabolic costs) while others do not but may nevertheless benefit from the available public goods. We introduce a network model to describe genotype interaction and evolution when genotype fitness depends on the production and uptake of public goods. The model comprises a random graph to summarize the possible evolutionary pathways the genotypes may take as they interact genetically with one another, and a system of coupled differential equations to characterize the behavior of genotype abundance in time. We study some simple variations of the model analytically and more complex variations computationally. Our results point to a simple trade-off affecting the long-term survival of those genotypes that do produce public goods. This trade-off involves, on the producer side, the impact of producing and that of absorbing the public good. On the non-producer side, it involves the impact of absorbing the public good as well, now compounded by the molecular compatibility between the producer and the non-producer. Depending on how these factors turn out, producers may or may not survive.
Productive societies feature high levels of cooperation and strong connections between individuals. Public Goods Games (PGGs) are frequently used to study the development of social connections and cooperative behavior in model societies. In such games, contributions to the public good are made only by cooperators, while all players, including defectors, can reap public goods benefits. Classic results of game theory show that mutual defection, as opposed to cooperation, is the Nash Equilibrium of PGGs in well-mixed populations, where each player interacts with all others. In this paper, we explore the coevolutionary dynamics of a low information public goods game on a network without spatial constraints in which players adapt to their environment in order to increase individual payoffs. Players adapt by changing their strategies, either to cooperate or to defect, and by altering their social connections. We find that even if players do not know other players strategies and connectivity, cooperation can arise and persist despite large short-term fluctuations.
This paper considers incentives to provide goods that are partially excludable along social links. Individuals face a capacity constraint in that, conditional upon providing, they may nominate only a subset of neighbours as co-beneficiaries. Our model has two typically incompatible ingredients: (i) a graphical game (individuals decide how much of the good to provide), and (ii) graph formation (individuals decide which subset of neighbours to nominate as co-beneficiaries). For any capacity constraints and any graph, we show the existence of specialised pure strategy Nash equilibria - those in which some individuals (the Drivers, D) contribute while the remaining individuals (the Passengers, P) free ride. The proof is constructive and corresponds to showing, for a given capacity, the existence of a new kind of spanning bipartite subgraph, a DP-subgraph, with partite sets D and P. We consider how the number of Drivers in equilibrium changes as the capacity constraints are relaxed and show a weak monotonicity result. Finally, we introduce dynamics and show that only specialised equilibria are stable against individuals unilaterally changing their provision level.
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