Blanc SIMI 1 - Sciences de l'information, de la matière et de l'ingénierie : Mathématiques et interactions

Long term behaviour for discrete and continuous time dynamic games – JEUDY

Submission summary

The purpose is to obtain several breakthroughs in the analysis of long-run stochastic or differential games, with an emphasis on information issues. These questions are particularly relevant in economic theory. The main idea is to combine techniques coming from continuous time and from discrete time. To do so, we bring together mathematicians and economists who have experience either in continuous or discrete time approaches. The problems can be roughly classified into two domains: the zero-sum games, for which the mathematical analysis is the more advanced, and the non-zero sum games, which are more relevant in terms of economical applications, although the technical issues are much more challenging.
1 Zero Sum Dynamic Games
1-1 Long time behaviour of averaged games
We will investigate the long standing conjecture on the existence of the asymptotic value for infinitely repeated zero sum stochastic games with compact actions and states.
1-2 Stochastic game with incomplete information.
We would like to prove the existence of the asymptotic values in absorbing and recursive games with incomplete information on both sides and in stochastic games with incomplete information.We wish to identify the continuous time version of such games or the PDE that characterizes the asymptotic value for the Mertens-Zamir system. We wish to extend the already known existence and characterization of the asymptotic value for discounted games to the limit of the average value for finitely repeated game and to continuous time splitting game. We want to understand this influence in differential games.
1-3 Strategic use of information in stochastic and differential games
The main question is how the players use their private information. The subtle issue is that a player, in order to take advantage of his private information, has to reveal it to the other players. Many fundamental questions remain open: It has been conjectured that there exists a uniform maxmin for infinitely repeated zero-sum stochastic games where the first player has more information than the second one. Splitting game quantify the amount of information each player is disclosing at each step. The existence and characterization of the discounted value, as the discount factor goes to zero, has been well understood. Our aim is to extend this to the limit of the average value.
2 Non Zero-Sum Dynamic Games
2.1-Non Zero-Sum games with incomplete information.
In economics, much attention has been paid independently to social learning and to strategic experimentation. The former typically looks at the long-run behavior of non-strategic agents organized in a network. The latter looks at the optimal behaviour of strategic agents facing a decision problem with risk, like a multi-armed bandit problem. From a game-theoretic viewpoint, both setups share the feature that there is no direct interaction - the interaction between players is mediated through information. From a strategic viewpoint, such games are therefore easier to study than games with general payoff functions. This allows the investigation of more complex informational setups.
Nothing is known on Non-zero-sum differential games with lack of information ---even in the linear-quadratic case---, and the collaboration of experts in game theory and differential games is mandatory to tackle such a difficult task.
2.2 Refinements of Nash equilibria in dynamic games
We want to study sequential equilibria when players play optimal actions at every information set. The problem is to give a definition of expected payoff conditional on a zero probability event which is compatible with the incentives of the player We want to clarify the definition and to see how far we can push the existence results of subgame-perfect and sequential equilibria. For differential games, we will investigate games with particular structure to understand the existence/stability of subgame-perfect Nash equilibria.

Project coordination

Marc QUINCAMPOIX (UNIVERSITE DE BRETAGNE OCCIDENTALE) – marc.quincampoix@univ-brest.fr

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

Partner

PREG CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE - DELEGATION REGIONALE ILE-DE-FRANCE SECTEUR OUEST ET NORD
UBO UNIVERSITE DE BRETAGNE OCCIDENTALE
GREMAQ CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE - DELEGATION REGIONALE MIDI-PYRENEES
GREGHEC CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE - DELEGATION REGIONALE ILE-DE-FRANCE SECTEUR OUEST ET NORD

Help of the ANR 200,000 euros
Beginning and duration of the scientific project: - 48 Months

Useful links

Explorez notre base de projets financés

 

 

ANR makes available its datasets on funded projects, click here to find more.

Sign up for the latest news:
Subscribe to our newsletter