Dharshana Kasthurirathna

Evolutionary stable strategies in networked games: the influence of topology

Abstract Evolutionary game theory is used to model the evolution of competing strategies in a population of players. Evolutionary stability of a strategy is a dynamic equilibrium, in which any competing mutated strategy would be wiped out from a population. If a strategy is weak evolutionarily stable, the competing strategy may manage to survive within the network. Understanding the network-related factors that affect the evolutionary stability of a strategy would be critical in making accurate predictions about the behaviour of a strategy in a real-world strategic decision making environment. In this work, we evaluate the effect of network topology on the evolutionary stability of a strategy. We focus on two well-known strategies known as the Zero-determinant strategy and the Pavlov strategy. Zero-determinant strategies have been shown to be evolutionarily unstable in a well-mixed population of players. We identify that the Zero-determinant strategy may survive, and may even dominate in a population of players connected through a non-homogeneous network. We introduce the concept of ‘topological stability’ to denote this phenomenon. We argue that not only the network topology, but also the evolutionary process applied and the initial distribution of strategies are critical in determining the evolutionary stability of strategies. Further, we observe that topological stability could affect other well-known strategies as well, such as the general cooperator strategy and the cooperator strategy. Our observations suggest that the variation of evolutionary stability due to topological stability of strategies may be more prevalent in the social context of strategic evolution, in comparison to the biological context.

Optimisation of strategy placements for public good in complex networks

Game theory has long been used to model cognitive decision making in societies. While traditional game theoretic modelling has focussed on well-mixed populations, recent research has suggested that the topological structure of social networks play an important part in the dynamic behaviour of social systems. Any agent or person playing a game employs a strategy (pure or mixed) to optimise pay-off. Previous studies have analysed how selfish agents can optimise their payoffs by choosing particular strategies within a social network model. In this paper we ask the question that, if agents were to work towards the common goal of increasing the public good (that is, the total network utility), what strategies they should adapt within the context of a heterogeneous network. We consider a number of classical and recently demonstrated game theoretic strategies, including cooperation, defection, general cooperation, Pavlov, and zero-determinant strategies, and compare them pairwise. We use the Iterative Prisoners Dilemma game simulated on scale-free networks, and use a genetic-algorithmic approach to investigate what optimal placement patterns evolve in terms of strategy. In particular, we ask the question that, given a pair of strategies are present in a network, which strategy should be adopted by the hubs (highly connected people), for the overall betterment of society (high network utility). We find that cooperation as opposed to defection, Pavlov as opposed to general cooperator, general cooperator as opposed to zero-determinant, and pavlov as opposed to zero-determinant, strategies will be adopted by the hubs, for the overall increased utility of the network. The results are interesting, since given a scenario where certain individuals are only capable of implementing certain strategies, the results give a blueprint on where they should be placed in a complex network for the overall benefit of the society.

Emergence of scale-free characteristics in socio-ecological systems with bounded rationality.

Socio–ecological systems are increasingly modelled by games played on complex networks. While the concept of Nash equilibrium assumes perfect rationality, in reality players display heterogeneous bounded rationality. Here we present a topological model of bounded rationality in socio-ecological systems, using the rationality parameter of the Quantal Response Equilibrium. We argue that system rationality could be measured by the average Kullback–-Leibler divergence between Nash and Quantal Response Equilibria, and that the convergence towards Nash equilibria on average corresponds to increased system rationality. Using this model, we show that when a randomly connected socio-ecological system is topologically optimised to converge towards Nash equilibria, scale-free and small world features emerge. Therefore, optimising system rationality is an evolutionary reason for the emergence of scale-free and small-world features in socio-ecological systems. Further, we show that in games where multiple equilibria are possible, the correlation between the scale-freeness of the system and the fraction of links with multiple equilibria goes through a rapid transition when the average system rationality increases. Our results explain the influence of the topological structure of socio–ecological systems in shaping their collective cognitive behaviour, and provide an explanation for the prevalence of scale-free and small-world characteristics in such systems.

Modeling networked systems using the topologically distributed bounded rationality framework

In networked systems research, game theory is increasingly used to model a number of scenarios where distributed decision making takes place in a competitive environment. These scenarios include peer-to-peer network formation and routing, computer security level allocation, and TCP congestion control. It has been shown, however, that such modeling has met with limited success in capturing the real-world behavior of computing systems. One of the main reasons for this drawback is that, whereas classical game theory assumes perfect rationality of players, real world entities in such settings have limited information, and cognitive ability which hinders their decision making. Meanwhile, new bounded rationality models have been proposed in networked game theory which take into account the topology of the network. In this article, we demonstrate that game-theoretic modeling of computing systems would be much more accurate if a topologically distributed bounded rationality model is used. In particular, we consider (a) link formation on peer-to-peer overlay networks (b) assigning security levels to computers in computer networks (c) routing in peer-to-peer overlay networks, and show that in each of these scenarios, the accuracy of the modeling improves very significantly when topological models of bounded rationality are applied in the modeling process. Our results indicate that it is possible to use game theory to model competitive scenarios in networked systems in a way that closely reflects real world behavior, topology, and dynamics of such systems.

Evolution of coordination in scale-free and small world networks under information diffusion constraints

We study evolution of coordination in social systems by simulating a coordination game in an ensemble of scale-free and small-world networks and comparing the results. We give particular emphasis to the role information about the pay-offs of neighbours plays in nodes adapting strategies, by limiting this information up to various levels. We find that if nodes have no chance to evolutionarily adapt, then non-coordination is a better strategy, however when nodes adapt based on information of the neighbour payoffs, coordination quickly emerges as the better strategy. We find phase transitions in number of coordinators with respect to the relative pay-off of coordination, and these phase transitions are sharper in small-world networks. We also find that when pay-off information of neighbours is limited, small-world networks are able to better cope with this limitation than scale-free networks. We observe that provincial hubs are the quickest to evolutionarily adapt strategies, in both scale-free and small world networks. Our findings confirm that evolutionary tendencies of coordination heavily depend on network topology.

On the influence of topological characteristics on robustness of complex networks

Abstract In this paper, we explore the relationship between the topological characteristics of a complex network and its robustness to sustained targeted attacks. Using synthesised scale-free, small-world and random networks, we look at a number of network measures, including assortativity, modularity, average path length, clustering coefficient, rich club profiles and scale-free exponent (where applicable) of a network, and how each of these influence the robustness of a network under targeted attacks. We use an established robustness coefficient to measure topological robustness, and consider sustained targeted attacks by order of node degree. With respect to scale-free networks, we show that assortativity, modularity and average path length have a positive correlation with network robustness, whereas clustering coefficient has a negative correlation. We did not find any correlation between scale-free exponent and robustness, or rich-club profiles and robustness. The robustness of small-world networks on the other hand, show substantial positive correlations with assortativity, modularity, clustering coefficient and average path length. In comparison, the robustness of Erdos-Renyi random networks did not have any significant correlation with any of the network properties considered. A significant observation is that high clustering decreases topological robustness in scale-free networks, yet it increases topological robustness in small-world networks. Our results highlight the importance of topological characteristics in influencing network robustness, and illustrate design strategies network designers can use to increase the robustness of scale-free and small-world networks under sustained targeted attacks.

Cyclic Preferential Attachment in Complex Networks

Abstract Preferential Attachment (PA), which was originally proposed in the Barabasi-Albert (BA) Model, has been widely ac- cepted as a network growth model which returns in scale-free networks. Preferential attachment in the BA model operates on the assumption that a node which has more links has a better likelihood to create new links. In this work, we expand the PA mechanism by treating it as a cyclic mechanism which is linked to both direct and indirect neighbours of a node. The assumption behind this extension is that the preference of nodes is influenced by their indirect neighbours as well. We show that traditional PA can be absorbed as a special case of this new growth model, which we name ‘cyclic preferential attachment’ (CPA). We also discuss the properties of simulated networks that were generated based on CPA. Finally, we compare and contrast the CPA based networks with the traditional PA based networks and several real-world networks of similar sizes and link-to-node ratios, and show that CPA offers more flexibility in modeling real world networks.

Network robustness and topological characteristics in scale-free networks

In this paper, we explore the relationship between the topological characteristics of a complex network and its robustness to sustained targeted attacks. Using synthesized scale-free networks, we look at a number of network measures, including rich club profiles, scale-free exponent, modularity, assortativity, average path length and clustering coefficient of a network, and how each of these influence the robustness of a scale-free network under targeted attacks. We consider sustained targeted attacks by order of node degree. We show that assortativity and average path length have a positive correlation with network robustness, whereas clustering coefficient has a negative correlation. We did not find any correlation between the modularity and robustness, scale-free exponent and robustness, or rich-club profiles and robustness. Our results highlight the importance of topological characteristics in influencing network robustness, and illustrate design strategies network designers can use to increase the robustness of scale-free networks under sustained targeted attacks.

The performance of page rank algorithm under degree preserving perturbations

Page rank is a ranking algorithm based on a random surfer model which is used in Google search engine and many other domains. Because of its initial success in Google search engine, page rank has become the de-facto choice when it comes to ranking nodes in a network structure. Despite the ubiquitous utility of the algorithm, little is known about the effect of topology on the performance of the page rank algorithm. Hence this paper discusses the performance of page rank algorithm under different topological conditions. We use scale-free networks and random networks along with a custom search engine we implemented in order to experimentally prove that the performance of page rank algorithm is deteriorated when the random network is perturbed. In contrast, scale-free topology is proven to be resilient against degree preserving perturbations which aids the page rank algorithm to deliver consistent results across multiple networks that are perturbed to varying proportions. Not only does the top ranking results emerge as stable nodes, but the overall performance of the algorithm is proven to be remarkably resilient which deepens our understanding about the risks in applying page rank algorithm without an initial analysis on the underlying network structure. The results conclusively suggests that while page rank algorithm can be applied to scale-free networks with relatively low risk, applying page rank algorithm to other topologies can be risky as well as misleading. Therefore, the success of the page rank algorithm in real world in search engines such as Google is at least partly due to the fact that the world wide web is a scale-free network. Since the world wide web is constantly evolving, we postulate that if the topological structure of the world wide web changes significantly so that it loses its scale-free nature to some extent, the page rank algorithm will not be as effective.

Optimising influence in social networks using bounded rationality models

Influence models enable the modelling of the spread of ideas, opinions and behaviours in social networks. Bounded rationality in social networks suggests that players make non-optimum decisions due to the limitations of access to information. Based on the premise that adopting a state or an idea can be regarded as being ‘rational’, we propose an influence model based on the heterogeneous bounded rationality of players in a social network. We employ the quantal response equilibrium model to incorporate the bounded rationality in the context of social influence. We hypothesise that bounded rationality of following a seed or adopting the strategy of a seed is negatively proportional to the distance from that node, and it follows that closeness centrality is the appropriate measure to place influencers in a social network. We argue that this model can be used in scenarios where there are multiple types of influencers and varying pay-offs of adopting a state. We compare different seed placement mechanisms to compare and contrast the optimum method to minimise the existing social influence in a network when there are multiple and conflicting seeds. We ascertain that placing of opposing seeds according to a measure derived from a combination of the betweenness centrality values from the seeds, and the closeness centrality of the network provide the maximum negative influence. Further, we extend this model to a strategic decision-making scenario where each seed operates a strategy in a strategic game.