Towards a Theory of Large-Scale Human Interactions
Abstract
Most complex human interactions, ranging from adversarial behavior to transactions on economic and financial markets to determination of opinions and social influence in structured and unstructured groups, involve the simultaneous strategic actions of a very large number of actors influencing each other in diverse ways. The promise of social and economic networks was to provide the foundations of a formal analysis of such phenomena, but the unstructured nature of most networks has meant that beyond some simple small-scale setups, progress has been limited. Our goal in this project is to provide a more systematic study of strategic interactions over large networks . The heterogeneity in each agent s network effects, the intractability of analysis of general strategic interactions over networks and the large scale of the underlying game necessitate a new framework that uses advanced mathematical tools that go beyond traditional approaches (based on convex optimization and graph theory) for modeling and analysis of these network games. This project will bring tools from variational inequalities and graphon theory to forge the underpinnings of a new theory of large-scale human interactions. Specifically, in the first part of the project, we present a unifying variational inequality framework for the study of general network games with multidimensional and possibly constrained strategy sets. Our main objective is to uncover the role of the network in determining static and dynamic strategic behavior. In addition to characterization of equilibrium behavior in these settings, our work will enable analysis of learning dynamics with partial and asymmetric information. Our framework will also allow a systematic analysis of the effect of changes in cost and network structure on the resulting equilibrium. In the second part of the project, we propose a novel way to approximate games played over networks of large size, by using the graph limiting concept of graphon. To this end, we introduce a new class of infinite population games which we call "graphon games". A key point of our analysis will be to investigate the relation between the equilibria of such infinite population graphon games and of finite population sampled network games. Our end goal is to show that the setup of graphon games is a low dimensional and computationally tractable model of large networked systems that can be used both for analysis and control tasks. This setup will allow design of optimal control and intervention strategies that are robust to variations in network structure and size.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 14, 2019
- Source ID
- W911NF1810407
Entities
People
- Asuman Özdağlar
Organizations
- Army Contracting Command
- Massachusetts Institute of Technology
- United States Army