Related papers: Asymptotic Properties of Optimal Trajectories in D…
We study the intermediate asymptotic behavior of solutions to the first-order mean field games system with a local coupling, when the initial density is a compactly supported function on the real line, and the coupling is of power type.…
We generalize gradient descent with momentum for optimization in differentiable games to have complex-valued momentum. We give theoretical motivation for our method by proving convergence on bilinear zero-sum games for simultaneous and…
We consider a dynamic programming problem with arbitrary state space and bounded rewards. Is it possible to define in an unique way a limit value for the problem, where the "patience" of the decision-maker tends to infinity ? We consider,…
We study the long-run properties of optimal control problems in continuous time, where the running cost of a control problem is evaluated by a probability measure over R_+. Li, Quincampoix and Renault [DCDS-A, 2016] introduced an asymptotic…
We study distributed computation in synchronous dynamic networks where an omniscient adversary controls the unidirectional communication links. Its behavior is modeled as a sequence of directed graphs representing the active (i.e. timely)…
In this paper we study an infinite-horizon persistent monitoring problem in a two-dimensional mission space containing a finite number of statically placed targets, at each of which we assume a constant rate of uncertainty accumulation.…
We introduce the notion of universal graphs as a tool for constructing algorithms solving games of infinite duration such as parity games and mean payoff games. In the first part we develop the theory of universal graphs, with two goals:…
We introduce the concept of attainable sets of payoffs in two-player repeated games with vector payoffs. A set of payoff vectors is called {\em attainable} if player 1 can ensure that there is a finite horizon $T$ such that after time $T$…
A succesful method to describe the asymptotic behavior of a discrete time stochastic process governed by some recursive formula is to relate it to the limit sets of a well chosen mean differential equation. Under an attainability condition,…
We show that evolutionarily stable states in general (nonlinear) population games (which can be viewed as continuous vector fields constrained on a polytope) are asymptotically stable under a multiplicative weights dynamic (under…
We analyse a version of the policy iteration algorithm for the discounted infinite-horizon problem for controlled multidimensional diffusion processes, where both the drift and the diffusion coefficient can be controlled. We prove that,…
A general framework of evolutionary dynamics under heterogeneous populations is presented. The framework allows continuously many types of heterogeneous agents, heterogeneity both in payoff functions and in revision protocols and the entire…
In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…
This paper considers discounted infinite horizon mean field games by extending the probabilistic weak formulation of the game as introduced by Carmona and Lacker (2015). Under similar assumptions as in the finite horizon game, we prove…
We conjecture that the distribution of the edge-disjoint union of two random regular graphs on the same vertex set is asymptotically equivalent to a random regular graph of the combined degree, provided it grows as the number of vertices…
This paper uses recent results on continuous-time finite-horizon optimal switching problems with negative switching costs to prove the existence of a saddle point in an optimal stopping (Dynkin) game. Sufficient conditions for the game's…
In this paper, we investigate a partially observable zero sum games where the state process is a discrete time Markov chain. We consider a general utility function in the optimization criterion. We show the existence of value for both…
In~[1],authors considered a general finite horizon model of dynamic game of asymmetric information, where N players have types evolving as independent Markovian process, where each player observes its own type perfectly and actions of all…
Adaptive dynamic programming is a collective term for a variety of approaches to infinite-horizon optimal control. Common to all approaches is approximation of the infinite-horizon cost function based on dynamic programming philosophy.…
Many sequential decision problems can be formulated as Markov Decision Processes (MDPs) where the optimal value function (or cost-to-go function) can be shown to satisfy a monotone structure in some or all of its dimensions. When the state…