We show that the long time average of solutions of first order mean field game systems in finite horizon is governed by an ergodic system of mean field game type. The well-posedness of the latter system and the uniqueness of the ergodic constant rely on weak KAM theory. Copyright Springer...

This paper introduces a mean field modeling framework for consumption-accumulation optimization. The production dynamics are generalized from stochastic growth theory by addressing the collective impact of a large population of similar agents on efficiency. This gives rise to a stochastic...

We give an example of a zero-sum stochastic game with four states, compact action sets for each player, and continuous payoff and transition functions, such that the discounted value does not converge as the discount factor tends to 0, and the value of the n-stage game does not converge as n...

This note contains a detailed derivation of the equations of the recent mean field games theory (abbr. MFG), developed by M. Huang, P.E. Caines, and R.P. Malhamé on one hand and by J.-M. Lasry and P.-L. Lions on the other, associated with a class of stochastic differential games, where the...

Multi-person stopping games with players’ priorities are considered. Players observe sequentially offers Y <Subscript>1</Subscript>,Y <Subscript>2</Subscript>,… at jump times T <Subscript>1</Subscript>,T <Subscript>2</Subscript>,… of a Poisson process. Y <Subscript>1</Subscript>,Y <Subscript>2</Subscript>,… are independent identically distributed random variables. Each accepted offer Y <Subscript> n </Subscript> results in a reward G <Subscript> n </Subscript>=Y <Subscript> n </Subscript>...</subscript></subscript></subscript></subscript></subscript></subscript></subscript></subscript></subscript>

Congested traffic problems on very dense networks lead, at the limit, to minimization problems posed on measures on curves as shown in Baillon and Carlier (Netw. Heterog. Media 7:219–241, <CitationRef CitationID="CR2">2012</CitationRef>). Here, we go one step further by showing that these problems can be reformulated in terms of the...</citationref>

We introduce asymptotic analysis of stochastic games with short-stage duration. The play of stage k, k≥0, of a stochastic game Γ <Subscript> δ </Subscript> with stage duration δ is interpreted as the play in time kδ≤t(k+1)δ and, therefore, the average payoff of the n-stage play per unit of time is the sum of...</subscript>

We establish the existence of Nash equilibria in a large class of differential games. More specifically, we show that certain differential games are compact and better reply secure when the strategy space is equipped with the weak topology. Therefore, we can claim that such games must have Nash...

In this paper, we study a class of time-inconsistent analogs (in the sense of Hu et al. (Time-inconsistent stochastic linear–quadratic control. Preprint, <CitationRef CitationID="CR13">2012</CitationRef>) which is originated from the mean-variance portfolio selection problem with state-dependent risk aversion in the context of financial...</citationref>

We extend the notion of Evolutionarily Stable Strategies introduced by Maynard Smith and Price (Nature 246:15–18, <CitationRef CitationID="CR6">1973</CitationRef>) for models ruled by a single fitness matrix A, to the framework of stochastic games developed by Lloyd Shapley (Proc. Natl. Acad. Sci. USA 39:1095–1100, <CitationRef CitationID="CR13">1953</CitationRef>) where, at...</citationref></citationref>