30 research outputs found

    Evolutionary Network Games: Equilibria from Imitation and Best Response Dynamics

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    We consider games of strategic substitutes and complements on networks and introduce two evolutionary dynamics in order to refine their multiplicity of equilibria. Within mean field, we find that for the best-shot game, taken as a representative example of strategic substitutes, replicator-like dynamics does not lead to Nash equilibria, whereas it leads to a unique equilibrium for complements, represented by a coordination game. On the other hand, when the dynamics becomes more cognitively demanding, predictions are always Nash equilibria: for the best-shot game we find a reduced set of equilibria with a definite value of the fraction of contributors, whereas, for the coordination game, symmetric equilibria arise only for low or high initial fractions of cooperators. We further extend our study by considering complex topologies through heterogeneous mean field and show that the nature of the selected equilibria does not change for the best-shot game. However, for coordination games, we reveal an important difference: on infinitely large scale-free networks, cooperative equilibria arise for any value of the incentive to cooperate. Our analytical results are confirmed by numerical simulations and open the question of whether there can be dynamics that consistently leads to stringent equilibria refinements for both classes of games

    The Economics of Social Networks

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    The science of social networks is a central field of sociological study, a major application of random graph theory, and an emerging area of study by economists, statistical physicists and computer scientists. While these literatures are (slowly) becoming aware of each other, and on occasion drawing from one another, they are still largely distinct in their methods, interests, and goals. Here, my aim is to provide some perspective on the research from these literatures, with a focus on the formal modeling of social networks and the two major types of models: those based on random graphs and those based on game theoretic reasoning. I highlight some of the strengths, weaknesses, and potential synergies between these two network modeling approaches

    Contagions in Random Networks with Overlapping Communities

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    We consider a threshold epidemic model on a clustered random graph with overlapping communities. In other words, our epidemic model is such that an individual becomes infected as soon as the proportion of her infected neighbors exceeds the threshold q of the epidemic. In our random graph model, each individual can belong to several communities. The distributions for the community sizes and the number of communities an individual belongs to are arbitrary. We consider the case where the epidemic starts from a single individual, and we prove a phase transition (when the parameter q of the model varies) for the appearance of a cascade, i.e. when the epidemic can be propagated to an infinite part of the population. More precisely, we show that our epidemic is entirely described by a multi-type (and alternating) branching process, and then we apply Sevastyanov's theorem about the phase transition of multi-type Galton-Watson branching processes. In addition, we compute the entries of the matrix whose largest eigenvalue gives the phase transition.Comment: Minor modifications for the second version: added comments (end of Section 3.2, beginning of Section 5.3); moved remark (end of Section 3.1, beginning of Section 4.1); corrected typos; changed titl

    Nestedness in Networks: A Theoretical Model and Some Applications

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    We develop a dynamic network formation model that can explain the observed nestedness in real-world networks. Links are formed on the basis of agents’ centrality and have an exponentially distributed life time. We use stochastic stability to identify the networks to which the network formation process converges and find that they are nested split graphs. We completely determine the topological properties of the stochastically stable networks and show that they match features exhibited by real-world networks. Using four different network datasets, we empirically test our model and show that it fits well the observed networks.Nestedness, Bonacich centrality, network formation, nested split graphs

    Aggregate fluctuations and the network structure of intersectoral trade

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    This paper analyzes the flow of intermediate inputs across sectors by adopting a network perspective on sectoral interactions. I apply these tools to show how fluctuations in aggregate economic activity can be obtained from independent shocks to individual sectors. First, I characterize the network structure of input trade in the U.S. On the demand side, a typical sector relies on a small number of key inputs and sectors are homogeneous in this respect. However, in their role as input-suppliers sectors do differ: many specialized input suppliers coexist alongside general purpose sectors functioning as hubs to the economy. I then develop a model of intersectoral linkages that can reproduce these connectivity features. In a standard multisector setup, I use this model to provide analytical expressions linking aggregate volatility to the network structure of input trade. I show that the presence of sectoral hubs - by coupling production decisions across sectors - leads to fluctuations in aggregates.Aggregation; Business Cycles; Comovement; Input-Output; Multisector Growth Models; Networks; Technological Diversification.

    Dynamic Network Formation in Two-Sided Economies

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    We study the dynamic stability of networks in a two-sided economy of agents labelled men and women. Each agent desires relationships with the other type, but having multiple partners is costly. This cost-benefit trade-off results in each agent having a single-peaked utility function, the peak being greater for men than for women. We propose two stochastic Markov processes in which self-interested agents form and sever links over time, but may also take actions that do not increase their utility with small probability. In the first process, an agent who invests more time in a relationship signals commitment to his/her partner, whereas in the second, such an agent is perceived as having a weaker position. We prove that only egalitarian pairwise stable networks (in which all agents have the same number of partners) form in the long run under the first process, while under the second, only anti-egalitarian pairwise stable networks (in which all women are matched to a small number of men) arise. This latter outcome is also consistent with the presence of "herd externality" or "informational cascade", leading to a pattern of a one-sided thin market. Applying these results to communication shows that the diffusion of a given piece of information can widely vary across identical economies, and that information concentrates more in women than in men. The model sheds light on patterns of network formation in several two-sided markets, including employer-employee, dating, buyer-seller, and faculty-student relationships

    Dynamic Network Formation in Two-Sided Economies

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    We study the dynamic stability of networks in a two-sided economy of agents labelled men and women. Each agent desires relationships with the other type, but having multiple partners is costly. This cost-benefit trade-off results in each agent having a single-peaked utility function, the peak being greater for men than for women. We propose two stochastic Markov processes in which self-interested agents form and sever links over time, but may also take actions that do not increase their utility with small probability. In the first process, an agent who invests more time in a relationship signals commitment to his/her partner, whereas in the second, such an agent is perceived as having a weaker position. We prove that only egalitarian pairwise stable networks (in which all agents have the same number of partners) form in the long run under the first process, while under the second, only anti-egalitarian pairwise stable networks (in which all women are matched to a small number of men) arise. This latter outcome is also consistent with the presence of "herd externality" or "informational cascade", leading to a pattern of a one-sided thin market. Applying these results to communication shows that the diffusion of a given piece of information can widely vary across identical economies, and that information concentrates more in women than in men. The model sheds light on patterns of network formation in several two-sided markets, including employer-employee, dating, buyer-seller, and faculty-student relationships

    Networks and Learning in Game Theory.

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    This work concentrates on two topics, networks and game theory, and learning in games. The first part of this thesis looks at network games and the role of incomplete information in such games. It is assumed that players are located on a network and interact with their neighbors in the network. Players only have incomplete information on the network structure. The first part of this thesis studies how players' beliefs over the network they belong to affect game-theoretic outcomes, and develops a natural model for players' beliefs. The second part of this thesis focuses on learning in games. An intuitive learning model is introduced, and the predictions of this model are analyzed. Furthermore, learning in a class of congestion games is studied from different perspectives.
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