10,252 research outputs found
Viability analysis of the first-order mean field games
The paper is concerned with the dependence of the solution of the
deterministic mean field game on the initial distribution of players. The main
object of study is the mapping which assigns to the initial time and the
initial distribution of players the set of expected rewards of the
representative player corresponding to solutions of mean field game. This
mapping can be regarded as a value multifunction. We obtain the sufficient
condition for a multifunction to be a value multifunction. It states that if a
multifunction is viable with respect to the dynamics generated by the original
mean field game, then it is a value multifunction. Furthermore, the
infinitesimal variant of this condition is derived.Comment: 35 page
Complementability of exponential systems
We prove that any incomplete system of complex exponentials in is a subset of some complete and minimal system of
exponentials. In addition, we prove analogous statement for systems of
reproducing kernels in de Branges spaces.Comment: 6 page
Approximate solutions of continuous-time stochastic games
The paper is concerned with a zero-sum continuous-time stochastic
differential game with a dynamics controlled by a Markov process and a terminal
payoff. The value function of the original game is estimated using the value
function of a model game. The dynamics of the model game differs from the
original one. The general result applied to differential games yields the
approximation of value function of differential game by the solution of
countable system of ODEs.Comment: 23 page
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