### Tag Archives: Game Theory

## John Nash, a Beautiful Mind | Genius 1

## MIT Glimpse (Episode 4)

I was interviewed in November 2015 by Alex Albanese on MIT Glimpse. We discussed Benford’s law, cake cutting, and online optimization. We also discussed how to pick the right toilet, why pi sucks, and why you should watch plenty of Youtube videos!

## A Mathematical Guide to Selling

How to best sell a good? Should we auction it like in movies? Since the 1960s, economists have addressed this question mathematically and found surprising results. Most notably, in 1981, Nobel prize winner Roger Myerson proved that most auctions you could think of would win you just as much as any basic auction, but that, as well, you could do better using his approach. Since, today, billions of dollars are at play in online auctions, you can imagine how hot a topic it has now become!

## The New Big Fish Called Mean-Field Game Theory

In recent years, at the interface of game theory, control theory and statistical mechanics, a new baby of applied mathematics was given birth. Now named mean-field game theory, this new model represents a new active field of research with a huge range of applications! This is mathematics in the making!

## The Biology Civil War Opposing Kin to Group Selection

In 2010, a controversial article published in Nature violently criticized the last 40 years of developments in evolutionary biology, triggering an ongoing war within the scientific community. This article explains the essence of the controversy!

## Bayesian Games: Math Models for Poker

How to better understand Poker and card games in general? Bayesian games provide the right mathematical model just for that! These correspond to games with incomplete information and include probabilistic reasonings.

## Advanced Game Theory Overview

This article gives an overview of recent developments in game theory, including evolutionary game theory, extensive form games, mechanism design, bayesian games and mean field games.

## Game Theory and the Nash Equilibrium

In the movie "A Beautiful Mind", the character is John Nash. He is one of the founders of a large and important field of applied mathematics called game theory. Game Theory is the study of human interactions. Its fallouts in economy, politics or biology are countless. This article gives you an introduction to the concepts of this amazing way of thinking.

## Evolutionary Game Theory

Evolutionary Game Theory is a relatively recent branch of game theory which studies the dynamics of games. Originally used to describe populations of species in biology, and more particularly, the consequences of their interactions to the evolution of their populations, this field now produces interesting results for economic and environmental modelings.

## Mechanism Design and the Revelation Principle

Whenever you need to make a group of people interact, you are designing a mechanism. If you want to achieve a good interaction, you need to make sure your mechanism is well designed. In this article, I'll show you main features of mechanisms through various examples. I'll also talk about a great mathematical tool for mechanism design: the revelation principle.

## Regulation of Electricity Markets

Electricity markets are not like any markets. In particular, they cannot be liberalized without regulation. In the article, I list the reasons why this market is specific and I conclude by giving you important features of a good regulation.

## Fair Division and Cake-Cutting

Cutting a cake to satisfy everyone is no piece of cake! In the article, we focus on classical definitions of fair divisions. I'll criticize those definitions and conclude by extrapolating them to fairness in society.