Section: Scientific Foundations

Algorithmic Game Theory

Game theory aims at discussing situations of competition between rational players [101] . After the seminal works of Emile Borel and John von Neumann, one key events was the publication in 1944 of the book   [106] by John von Neumann and Oskar Morgenstern. Game theory then spent a long period in the doldrums. Much effort was devoted at that time towards the mathematics of two-person, zero-sum games.

For general games, the key concept of Nash equilibrium was proposed in the early 50s by John Nash in [98] , but it was not until the early 70s that it was fully realized what a powerful tool Nash has provided in formulating this concept. This is now a central concept in economics, biology, sociology and psychology to discuss general situations of competition, as attested for example by several Nobel prizes of economics.

Algorithmic game theory differs from game theory by taking into account algorithmic and complexity aspects. Indeed, historically main developments of classical game theory have been realized in a mathematical context, without true considerations on effectiveness of constructions.

Game theory and algorithmic game theory have large domains of applications in theoretical computer science: it has been used to understand complexity of computing equilibria [93] , the loss of performance due to individual behavior in distributed algorithmics  [45] , the design of incentive mechanisms  [99] , the problems related to the pricing of services in some protocols  [64] ...