This lecture focuses on mathematical descriptions of strategic situations in which payoffs to agents depend on the behavior of the other agents (applied to the analysis of conflict, cooperation, and corruption).
Often we are interested in finding and characterizing pattern which appear over time. This lecture introduces formal tools to design, model, and analyze evolving socio-technological systems in which information, data sensing, and decision-making mechanisms strongly couple two or more systems. Formal techniques include frequency-domain and time-domain methods.
Preview this course - (2 preview lessons)
This lecture focuses on strategic interaction that take place on networks. Part 1 overviews structural properties of empirical networks. Part 2 introduces a mathematical framework and notions of equilibria for thinking about strategic interaction between multiple players. Part 3 focuses on applications of game theory, including modeling network traffic, link analysis and web search and voting processes.
Hybrid systems are often necessary when the simplifications introduced by continuous models mask effects that are worthy of attention. This lecture introduces fundamental concepts and tools for the study of dynamical systems that combine both continuous and discrete entities (differential equations and discrete events).
This lecture presents formal methods to quantify the dynamics of corruption through modeling basic features of the structure and function of complex networks. It overviews the statistical way of thinking about social and technological networks.
A perspective on how these courses relate to each other
Modern technology provides the capacity to collect and analyze growing sets of data on both the behavior and structure of socio-technological systems. Information networks offers the potential to uncover and illustrate hidden relationships between data, revealing patterns that non-graphical statistical method cannot.
Moreover, formal models of networks serve as a substrate for agent-based simulations which capture structural properties that resemble real-world patterns (e.g., community components, contact patterns, and urban street configurations). Agent-based models use tools from Game theory to explicitly represent dynamic processes at the local level, supplemented with ideas from mechanism design and behavioral law and economics (to capture bounded rationality and strategic behavior). Such models are useful to explain how individuals who repeatedly interact with one another tend to gravitate towards particular macro behavior (e.g, how far into the past do agents have to be able to remember each other’s previous actions for aggregate patterns to emerge?).
If macro patterns emerge, models of coupled differential equations (or difference equations) may capture aggregated behavioral outcomes (i.e., when the law of large numbers and the central limit theorem is applicable to independent and identically distributed observations). Feedback systems focuses on mean-field approximations to describe such collective behavior. Aggregated equation-based representations may be too general and thus misleading. Done right, however, operating on “average rules” may allows us to mathematically analyze the emerging properties generated by agent-based models, while ignoring irrelevant micro-level processes.
As equation-based models include larger number of equations, different sets of equations may drive the system as it evolves. Hybrid systems offers a unifying framework to analyze such systems as a whole, allowing for more flexibility in modeling dynamic phenomena.