Learning and coordinating in a multilayer network

We introduce a two layer network model for social coordination incorporating two relevant ingredients: a) different networks of interaction to learn and to obtain a payoff , and b) decision making processes based both on social and strategic motivations. Two populations of agents are distributed in two layers with intralayer learning processes and playing interlayer a coordination game. We find that the skepticism about the wisdom of crowd and the local connectivity are the driving forces to accomplish full coordination of the two populations, while polarized coordinated layers are only possible for all-to-all interactions. Local interactions also allow for full coordination in the socially efficient Pareto-dominant strategy in spite of being the riskier one

Collaboration in Social Networks

The very notion of social network implies that linked individuals interact repeatedly with each other. This allows them not only to learn successful strategies and adapt to them, but also to condition their own behavior on the behavior of others, in a strategic forward looking manner. Game theory of repeated games shows that these circumstances are conducive to the emergence of collaboration in simple games of two players. We investigate the extension of this concept to the case where players are engaged in a local contribution game and show that rationality and credibility of threats identify a class of Nash equilibria -- that we call "collaborative equilibria" -- that have a precise interpretation in terms of sub-graphs of the social network. For large network games, the number of such equilibria is exponentially large in the number of players. When incentives to defect are small, equilibria are supported by local structures whereas when incentives exceed a threshold they acquire a non-local nature, which requires a "critical mass" of more than a given fraction of the players to collaborate. Therefore, when incentives are high, an individual deviation typically causes the collapse of collaboration across the whole system. At the same time, higher incentives to defect typically support equilibria with a higher density of collaborators. The resulting picture conforms with several results in sociology and in the experimental literature on game theory, such as the prevalence of collaboration in denser groups and in the structural hubs of sparse networks

Strategic Interaction and Networks

This paper brings a general network analysis to a wide class of economic games. A network, or interaction matrix, tells who directly interacts with whom. A major challenge is determining how network structure shapes overall outcomes. We have a striking result. Equilibrium conditions depend on a single number: the lowest eigenvalue of a network matrix. Combining tools from potential games, optimization, and spectral graph theory, we study games with linear best replies and characterize the Nash and stable equilibria for any graph and for any impact of players’ actions. When the graph is sufficiently absorptive (as measured by this eigenvalue), there is a unique equilibrium. When it is less absorptive, stable equilibria always involve extreme play where some agents take no actions at all. This paper is the first to show the importance of this measure to social and economic outcomes, and we relate it to different network link patterns.Networks, potential games, lowest eigenvalue, stable equilibria, asymmetric equilibria

Strategic Investment in Protection in Networked Systems

We study the incentives that agents have to invest in costly protection against cascading failures in networked systems. Applications include vaccination, computer security and airport security. Agents are connected through a network and can fail either intrinsically or as a result of the failure of a subset of their neighbors. We characterize the equilibrium based on an agent's failure probability and derive conditions under which equilibrium strategies are monotone in degree (i.e. in how connected an agent is on the network). We show that different kinds of applications (e.g. vaccination, malware, airport/EU security) lead to very different equilibrium patterns of investments in protection, with important welfare and risk implications. Our equilibrium concept is flexible enough to allow for comparative statics in terms of network properties and we show that it is also robust to the introduction of global externalities (e.g. price feedback, congestion).Comment: 32 pages, 3 figure

Learning the Structure and Parameters of Large-Population Graphical Games from Behavioral Data

We consider learning, from strictly behavioral data, the structure and parameters of linear influence games (LIGs), a class of parametric graphical games introduced by Irfan and Ortiz (2014). LIGs facilitate causal strategic inference (CSI): Making inferences from causal interventions on stable behavior in strategic settings. Applications include the identification of the most influential individuals in large (social) networks. Such tasks can also support policy-making analysis. Motivated by the computational work on LIGs, we cast the learning problem as maximum-likelihood estimation (MLE) of a generative model defined by pure-strategy Nash equilibria (PSNE). Our simple formulation uncovers the fundamental interplay between goodness-of-fit and model complexity: good models capture equilibrium behavior within the data while controlling the true number of equilibria, including those unobserved. We provide a generalization bound establishing the sample complexity for MLE in our framework. We propose several algorithms including convex loss minimization (CLM) and sigmoidal approximations. We prove that the number of exact PSNE in LIGs is small, with high probability; thus, CLM is sound. We illustrate our approach on synthetic data and real-world U.S. congressional voting records. We briefly discuss our learning framework's generality and potential applicability to general graphical games.Comment: Journal of Machine Learning Research. (accepted, pending publication.) Last conference version: submitted March 30, 2012 to UAI 2012. First conference version: entitled, Learning Influence Games, initially submitted on June 1, 2010 to NIPS 201

Emergence of social networks via direct and indirect reciprocity

Many models of social network formation implicitly assume that network properties are static in steady-state. In contrast, actual social networks are highly dynamic: allegiances and collaborations expire and may or may not be renewed at a later date. Moreover, empirical studies show that human social networks are dynamic at the individual level but static at the global level: individuals' degree rankings change considerably over time, whereas network-level metrics such as network diameter and clustering coefficient are relatively stable. There have been some attempts to explain these properties of empirical social networks using agent-based models in which agents play social dilemma games with their immediate neighbours, but can also manipulate their network connections to strategic advantage. However, such models cannot straightforwardly account for reciprocal behaviour based on reputation scores ("indirect reciprocity"), which is known to play an important role in many economic interactions. In order to account for indirect reciprocity, we model the network in a bottom-up fashion: the network emerges from the low-level interactions between agents. By so doing we are able to simultaneously account for the effect of both direct reciprocity (e.g. "tit-for-tat") as well as indirect reciprocity (helping strangers in order to increase one's reputation). This leads to a strategic equilibrium in the frequencies with which strategies are adopted in the population as a whole, but intermittent cycling over different strategies at the level of individual agents, which in turn gives rise to social networks which are dynamic at the individual level but stable at the network level

A Stochastic Model of Active Cyber Defense Dynamics

The concept of active cyber defense has been proposed for years. However, there are no mathematical models for characterizing the effectiveness of active cyber defense. In this paper, we fill the void by proposing a novel Markov process model that is native to the interaction between cyber attack and active cyber defense. Unfortunately, the native Markov process model cannot be tackled by the techniques we are aware of. We therefore simplify, via mean-field approximation, the Markov process model as a Dynamic System model that is amenable to analysis. This allows us to derive a set of valuable analytical results that characterize the effectiveness of four types of active cyber defense dynamics. Simulations show that the analytical results are inherent to the native Markov process model, and therefore justify the validity of the Dynamic System model. We also discuss the side-effect of the mean-field approximation and its implications