相关论文: Complexity Theory, Game Theory, and Economics: The…

In this thesis, we survey techniques and results from the study of Complexity Theory and Games. We then apply these techniques to obtain new results for previously unstudied games. Our contributions in the games Hexiom, Cut the Rope, and…

We want to make progress toward artificial general intelligence, namely general-purpose agents that autonomously learn how to competently act in complex environments. The purpose of this report is to sketch a research outline, share some of…

This is an expanded version of the lecture given at the AMS Short Course on Mean Field Games, on January 13, 2020 in Denver CO. The assignment was to discuss applications of Mean Field Games in finance and economics. I need to admit upfront…

Economies are complex man-made systems where organisms and markets interact according to motivations and principles not entirely understood yet. The increasing dissatisfaction with the postulates of traditional economics i.e. perfectly…

This chapter presents a brief review of complexity research in mathematics education. We argue how research on complexity, as it pertains to mathematics education, can be viewed as an epistemological discourse, an historical discourse, a…

With increasing game size, a problem of computational complexity arises. This is especially true in real world problems such as in social systems, where there is a significant population of players involved in the game, and the complexity…

This note presents reflections drawn from my recent experiences in teaching a course on mathematics and sustainability, with a particular emphasis on raising awareness of the topic and its broader implications. The lectures were structured…

This document collects the lecture notes from my course "Communication Complexity (for Algorithm Designers),'' taught at Stanford in the winter quarter of 2015. The two primary goals of the course are: 1. Learn several canonical problems…

In this chapter the complex systems are discussed in the context of economic and business policy and decision making. It will be showed and motivated that social systems are typically chaotic, non-linear and/or non-equilibrium and therefore…

Matching games naturally generalize assignment games, a well-known class of cooperative games. Interest in matching games has grown recently due to some breakthrough results and new applications. This state-of-the-art survey provides an…

Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…

The theory of computational complexity focuses on functions and, hence, studies programs whose interactive behavior is reduced to a simple question/answer pattern. We propose a broader theory whose ultimate goal is expressing and analyzing…

Cooperative games provide a framework to study cooperation among self-interested agents. They offer a number of solution concepts describing how the outcome of the cooperation should be shared among the players. Unfortunately, computational…

This volume contains the proceedings of the International Workshop on Developments in Implicit Computational complExity (DICE 2010), which took place on March 27-28 2010 in Paphos, Cyprus, as a satellite event of the Joint European…

Computational aspects of solution notions such as Nash equilibrium have been extensively studied, including settings where the ultimate goal is to find an equilibrium that possesses some additional properties. Furthermore, in order to…

This article summarises a Web-book on "Complexity" that was developed to introduce undergraduate students to interesting complex systems in the biological, physical and social sciences, and the common tools, principles and concepts used for…

Compositional Game Theory is a new, recently introduced model of economic games based upon the computer science idea of compositionality. In it, complex and irregular games can be built up from smaller and simpler games, and the equilibria…

$ $[This paper is a (self contained) chapter in a new book, Mathematics and Computation, whose draft is available on my homepage at https://www.math.ias.edu/avi/book ]. We survey some concrete interaction areas between computational…

Scribe notes from the 2012 Barbados Workshop on Computational Complexity. A series of lectures on Analysis of Boolean Functions by Ryan O'Donnell, with a guest lecture by Per Austrin.

Mathematics is often perceived as difficult or inaccessible, yet meaningful engagement can arise in unexpected places. In this article we describe a multi-year exploration of mathematical outreach through games, puzzles, exhibitions, and…