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

The Strength of Arcs and Edges in Interaction Networks: Elements of a Model-Based Approach

When analyzing interaction networks, it is common to interpret the amount of interaction between two nodes as the strength of their relationship. We argue that this interpretation may not be appropriate, since the interaction between a pair of nodes could potentially be explained only by characteristics of the nodes that compose the pair and, however, not by pair-specific features. In interaction networks, where edges or arcs are count-valued, the above scenario corresponds to a model of independence for the expected interaction in the network, and consequently we propose the notions of arc strength, and edge strength to be understood as departures from this model of independence. We discuss how our notion of arc/edge strength can be used as a guidance to study network structure, and in particular we develop a latent arc strength stochastic blockmodel for directed interaction networks. We illustrate our approach studying the interaction between the Kolkata users of the myGamma mobile network.Comment: 23 pages, 5 figures, 4 table

Random matrix analysis for gene interaction networks in cancer cells

Investigations of topological uniqueness of gene interaction networks in cancer cells are essential for understanding this disease. Based on the random matrix theory, we study the distribution of the nearest neighbor level spacings $P(s)$ of interaction matrices for gene networks in human cancer cells. The interaction matrices are computed using the Cancer Network Galaxy (TCNG) database, which is a repository of gene interactions inferred by a Bayesian network model. 256 NCBI GEO entries regarding gene expressions in human cancer cells have been selected for the Bayesian network calculations in TCNG. We observe the Wigner distribution of $P(s)$ when the gene networks are dense networks that have more than $\sim 38,000$ edges. In the opposite case, when the networks have smaller numbers of edges, the distribution $P(s)$ becomes the Poisson distribution. We investigate relevance of $P(s)$ both to the size of the networks and to edge frequencies that manifest reliance of the inferred gene interactions.Comment: 22 pages, 7 figure

A rewiring model of intratumoral interaction networks.

Intratumoral heterogeneity (ITH) has been regarded as a key cause of the failure and resistance of cancer therapy, but how it behaves and functions remains unclear. Advances in single-cell analysis have facilitated the collection of a massive amount of data about genetic and molecular states of individual cancer cells, providing a fuel to dissect the mechanistic organization of ITH at the molecular, metabolic and positional level. Taking advantage of these data, we propose a computational model to rewire up a topological network of cell-cell interdependences and interactions that operate within a tumor mass. The model is grounded on the premise of game theory that each interactive cell (player) strives to maximize its fitness by pursuing a rational self-interest strategy, war or peace, in a way that senses and alters other cells to respond properly. By integrating this idea with genome-wide association studies for intratumoral cells, the model is equipped with a capacity to visualize, annotate and quantify how somatic mutations mediate ITH and the network of intratumoral interactions. Taken together, the model provides a topological flow by which cancer cells within a tumor cooperate or compete with each other to downstream pathogenesis. This topological flow can be potentially used as a blueprint for genetically intervening the pattern and strength of cell-cell interactions towards cancer control