Game Interactions and Dynamics on Networked Populations

Madeo, Dario; Mocenni, Chiara

doi:10.1109/tac.2014.2384755

Cited by 63 publications

(54 citation statements)

References 37 publications

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“…Hussein [56] investigated a similar problem for generic network social behaviors, while Pantoja and Quijano [57] investigate a distributed optimization problem on a network with the replicator. We note that recent work by Madeo and Mocenni [58] has developed a general replicator dynamic on graph structures, extending previous results [52,53]. A result most closely related to this paper is found in [59], which studies convergence of best-response strategies on graphs.…”

Section: Introductionsupporting

confidence: 80%

Consensus and Information Cascades in Game-Theoretic Imitation Dynamics with Static and Dynamic Network Topologies

Griffin¹,

Rajtmajer²,

Squicciarini³

et al. 2019

SIAM J. Appl. Dyn. Syst.

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We construct a model of strategic imitation in an arbitrary network of players who interact through an additive game. Assuming a discrete time update, we show a condition under which the resulting difference equations converge to consensus. Two conjectures on general convergence are also discussed. We then consider the case where players not only may choose their strategies, but also affect their local topology. We show that for prisoner's dilemma, the graph structure converges to a set of disconnected cliques and strategic consensus occurs in each clique. Several examples from various matrix games are provided. A variation of the model is then used to create a simple model for the spreading of trends, or information cascades in (e.g., social) networks. We provide theoretical and empirical results on the trend-spreading model.3. Finally, we show how these dynamics can be adapted to model trends in (social) networks and study the qualitative properties of trends theoretically and empirically. This is a significant extension of work [62] in which we present the basic game-theoretic model for weighted imitation and consider its evolution on static graphs, without showing a condition on strategic consensus or studying either topological changes or trends. Consensus in a changing network topology is considered in [12] and is related to this work in so far as we also analyze the case of an agent-controlled changing network topology. A changing topology is also considered in [63], but the authors consider a specific opinion formation game consistent with the DeGroot model rather than a general matrix game.The model considered in this paper is distinct from the unifying model in [1] because:1. the coupling strength in the evolution equation is defined by a game payoff, rather than by an increasing (or non-negative) influence function φ, and 2. the agents' state is the strategy played, rather than a physical location, opinion or velocity.The coupling function we investigate may not be monotonic as a function of any metric on the strategy space over which our dynamics operate. This difference leads to a distinct set of consensus criteria than those given in [1]. As a result, our model cannot be subsumed by the unifying model in [1].

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Section: Introductionsupporting

confidence: 80%

Consensus and Information Cascades in Game-Theoretic Imitation Dynamics with Static and Dynamic Network Topologies

Griffin¹,

Rajtmajer²,

Squicciarini³

et al. 2019

SIAM J. Appl. Dyn. Syst.

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show abstract

“…In the modeling and analysis of the evolution of appraisal and influence networks, we also build an insightful connection between our model and the well-known replicator dynamics studied in evolutionary game theory; see the textbook [28], some control applications [6,21], and the recent contributions [3,19].…”

Section: Literature Reviewmentioning

confidence: 99%

Dynamic models of appraisal networks explaining collective learning

Mei

Friedkin

Lewis

et al. 2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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This paper proposes models of learning process in teams of individuals who collectively execute a sequence of tasks and whose actions are determined by individual skill levels and networks of interpersonal appraisals and influence. The closely-related proposed models have increasing complexity, starting with a centralized manager-based assignment and learning model, and finishing with a social model of interpersonal appraisal, assignments, learning, and influences. We show how rational optimal behavior arises along the task sequence for each model, and discuss conditions of suboptimality. Our models are grounded in replicator dynamics from evolutionary games, influence networks from mathematical sociology, and transactive memory systems from organization science.

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“…In this subsection, the steady states of a microbial colony for different micro-environmental conditions are investigated without consideration of spatial pattern. These equilibrium points are calculated from the EGT-based replicator dynamics [11,22] of cooperators and defectors. The replicator equation [11] for x and y with x + y = 1 can be written aṡ…”

Section: Population Dynamics In Biofilms: a Replicator Systemmentioning

confidence: 99%

“…as these are directly calculated from the dynamics in (25), and we consider (0, 1) as it is a boundary value of the infinite set of equilibrium states. A notable difference between the dynamics in (4) and (25) is that the incorporation of the level of assortment induces a unique point of coexistence [11,22] between the competing strains.…”

Section: Analysis Of Replicator Dynam-ics With Spatial Patternmentioning

confidence: 99%

Stability Analysis of Population Dynamics Model in Microbial Biofilms with Non-participating Strains

Banerjee

Ranjan

Layek

2016

Proceedings of the 7th ACM International Conference on Bioinformatics, Computational Biology, and Health Informatics

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The existence of phenotypic heterogeneity in single-species bacterial biofilms is well-established in the published literature. However, the modeling of population dynamics in biofilms from the viewpoint of social interactions, i.e. interplay between heterotypic strains, and the analysis of this kind using control theory are not addressed significantly. Therefore, in this paper, we theoretically analyze the population dynamics model in microbial biofilms with non-participating strains (coexisting with public goods producers and non-producers) in the context of evolutionary game theory and nonlinear dynamics. Our analysis of the replicator dynamics model is twofold: first without the inclusion of spatial pattern, and second with the consideration of degree of assortment. In the first case, Lyapunov stability analysis of the stable equilibrium point of the proposed replicator system determines (1, 0) ('full dominance of cooperators') as a global asymptotic stable equilibrium whenever the return exceeds the metabolic cost of cooperation. Hence, the global asymptotic stable nature of (1, 0) in the context of nonconsideration of spatial pattern helps to justify mathematically the adversity in the eradication of "cooperative enterprise" that is an infectious biofilm. In the second case, we found non-existence of global asymptotic stability in the system, and it unveils two additional phenomena -bistability and coexistence. In this context, two inequality conditions are derived for the 'full dominance of cooperators' and coexistence. Therefore, the inclusion of spatial pattern in biofilms with non-competing strains intends conditional dominance of pathogenic (with respect to the hosts) public goods producers which can be an effective strategy towards the control of an infectious biofilm with the drug-dependent regulation of degree of segregation. Furthermore, the simulation results of the proposed dynamics for both the discussed scenario confirm the results of the analysis of equilibrium points. The proposed stability analysis not only demonstrate a mathematical framework to analyze the population dynamics in biofilms but also gives a clue to control an infectious biofilm, where phenotypic and spatial heterogeneity exist.

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Game Interactions and Dynamics on Networked Populations

Cited by 63 publications

References 37 publications

Consensus and Information Cascades in Game-Theoretic Imitation Dynamics with Static and Dynamic Network Topologies

Consensus and Information Cascades in Game-Theoretic Imitation Dynamics with Static and Dynamic Network Topologies

Dynamic models of appraisal networks explaining collective learning

Stability Analysis of Population Dynamics Model in Microbial Biofilms with Non-participating Strains

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