Complexity Theory, Game Theory, and Economics: The Barbados Lectures

This document collects the lecture notes from my mini-course "Complexity Theory, Game Theory, and Economics," taught at the Bellairs Research Institute of McGill University, Holetown, Barbados, February 19--23, 2017, as the 29th McGill Invitational Workshop on Computational Complexity. The goal of this mini-course is twofold: (i) to explain how complexity theory has helped illuminate several barriers in economics and game theory; and (ii) to illustrate how game-theoretic questions have led to new and interesting complexity theory, including recent several breakthroughs. It consists of two five-lecture sequences: the Solar Lectures, focusing on the communication and computational complexity of computing equilibria; and the Lunar Lectures, focusing on applications of complexity theory in game theory and economics. No background in game theory is assumed.Comment: Revised v2 from December 2019 corrects some errors in and adds some recent citations to v1 Revised v3 corrects a few typos in v

Models and applications of Optimal Transport in Economics, Traffic and Urban Planning

Some optimization or equilibrium problems involving somehow the concept of optimal transport are presented in these notes, mainly devoted to applications to economic and game theory settings. A variant model of transport, taking into account traffic congestion effects is the first topic, and it shows various links with Monge-Kantorovich theory and PDEs. Then, two models for urban planning are introduced. The last section is devoted to two problems from economics and their translation in the language of optimal transport

Neuroeconomics: How Neuroscience Can Inform Economics

Neuroeconomics uses knowledge about brain mechanisms to inform economic analysis, and roots economics in biology. It opens up the "black box" of the brain, much as organizational economics adds detail to the theory of the firm. Neuroscientists use many tools— including brain imaging, behavior of patients with localized brain lesions, animal behavior, and recording single neuron activity. The key insight for economics is that the brain is composed of multiple systems which interact. Controlled systems ("executive function") interrupt automatic ones. Emotions and cognition both guide decisions. Just as prices and allocations emerge from the interaction of two processes—supply and demand— individual decisions can be modeled as the result of two (or more) processes interacting. Indeed, "dual-process" models of this sort are better rooted in neuroscientific fact, and more empirically accurate, than single-process models (such as utility-maximization). We discuss how brain evidence complicates standard assumptions about basic preference, to include homeostasis and other kinds of state-dependence. We also discuss applications to intertemporal choice, risk and decision making, and game theory. Intertemporal choice appears to be domain-specific and heavily influenced by emotion. The simplified ß-d of quasi-hyperbolic discounting is supported by activation in distinct regions of limbic and cortical systems. In risky decision, imaging data tentatively support the idea that gains and losses are coded separately, and that ambiguity is distinct from risk, because it activates fear and discomfort regions. (Ironically, lesion patients who do not receive fear signals in prefrontal cortex are "rationally" neutral toward ambiguity.) Game theory studies show the effect of brain regions implicated in "theory of mind", correlates of strategic skill, and effects of hormones and other biological variables. Finally, economics can contribute to neuroscience because simple rational-choice models are useful for understanding highly-evolved behavior like motor actions that earn rewards, and Bayesian integration of sensorimotor information

Distributed Computing with Adaptive Heuristics

We use ideas from distributed computing to study dynamic environments in which computational nodes, or decision makers, follow adaptive heuristics (Hart 2005), i.e., simple and unsophisticated rules of behavior, e.g., repeatedly "best replying" to others' actions, and minimizing "regret", that have been extensively studied in game theory and economics. We explore when convergence of such simple dynamics to an equilibrium is guaranteed in asynchronous computational environments, where nodes can act at any time. Our research agenda, distributed computing with adaptive heuristics, lies on the borderline of computer science (including distributed computing and learning) and game theory (including game dynamics and adaptive heuristics). We exhibit a general non-termination result for a broad class of heuristics with bounded recall---that is, simple rules of behavior that depend only on recent history of interaction between nodes. We consider implications of our result across a wide variety of interesting and timely applications: game theory, circuit design, social networks, routing and congestion control. We also study the computational and communication complexity of asynchronous dynamics and present some basic observations regarding the effects of asynchrony on no-regret dynamics. We believe that our work opens a new avenue for research in both distributed computing and game theory.Comment: 36 pages, four figures. Expands both technical results and discussion of v1. Revised version will appear in the proceedings of Innovations in Computer Science 201

Game Theory and its Applications

Game theory is the mathematical study of strategic decision making in situations of conflict. In game theory, a single interaction is defined as a game, and those involved in the decision-making are called the players, who are assumed to act rationally. This paper will explore the basic ideas of game theory, including the ideas of payoffs and outcomes; classification of games as zero-sum or nonzero-sum; types of strategies and counterstrategies and the idea of dominance. Game theory has many applications in subjects such as economics, international relations and politics, and psychology as it can be used to analyze and predict the behavior and decisions of the players. This paper will apply game theory to the decisions made by the players during the Triwizard Tournament in Harry Potter and the Goblet of Fire

Economics and mathematical theory of games

The theory of games is a branch of applied mathematics that is used in economics, management, and other social sciences. Moreover, it is used also in military science, political science, international relations, computer science, evolutionary biology, and ecology. It is a field of mathematics in which games are studied. The aim of this article is to present matrix games and the game theory. After the introduction, we will explain the methodology and give some examples. We will show applications of the game theory in economics. We will discuss about advantages and potential disadvantages that may occur in the described techniques. At the end, we will represent the results of our research and its interpretation