Mean-field games with absorption is a class of games, that have been introduced in Campi and Fischer (2018) and that can be viewed as natural limits of symmetric stochastic differential games with a large number of players who, interacting through a mean-field, leave the game as soon as their private states hit some given boundary. In this paper, we push the study of such games further, extending their scope along two main directions. First, a direct dependence on past absorptions has been introduced in the drift of players' state dynamics. Second, the boundedness of coefficients and costs has been considerably relaxed including drift and costs with linear growth. Therefore, the mean-field interaction among the players takes place in two ways: via the empirical sub-probability measure of the surviving players and through a process representing the fraction of past absorptions over time. Moreover, relaxing the boundedness of the coefficients allows for more realistic dynamics for players' private states. We prove existence of solutions of the mean-field game in strict as well as relaxed feedback form. Finally, we show that such solutions induce approximate Nash equilibria for the N-player game with vanishing error in the mean-field limit as $N \to \infty$. This talk is based on a joint work with M. Ghio and G. Livieri (SNS Pisa).
N-player games and mean-field games with smooth dependence on past absorptions
XXVIII European Workshop on Economic Theory
The XXVIII. European Workshop on Economic Theory (EWET 2019) is hosted by the Finance Group @ Humboldt. It will take place at the School of Business and Economics, Humboldt University, in the city center of Berlin from June 13 to June 15. The workshop is a forum for researchers interested in the latest developments in economic theory and mathematical economics. Participants present and discuss recent results in areas such as general equilibrium theory, decision theory, information economics, game theory, bargaining and matching, financial markets, and social choice. Here is a link to the official webpage.