Related papers: Optimal transport and Cournot-Nash equilibria
We propose a stochastic first-order algorithm to learn the rationality parameters of simultaneous and non-cooperative potential games, i.e., the parameters of the agents' optimization problems. Our technique combines (i.) an active-set step…
In this paper we present optimization problems with biconvex objective function and linear constraints such that the set of global minima of the optimization problems is the same as the set of Nash equilibria of a n-player general-sum…
We consider generalized Nash equilibrium problems (GNEPs) with non-convex strategy spaces and non-convex cost functions. This general class of games includes the important case of games with mixed-integer variables for which only a few…
The designs of many large-scale systems today, from traffic routing environments to smart grids, rely on game-theoretic equilibrium concepts. However, as the size of an $N$-player game typically grows exponentially with $N$, standard game…
We consider structural and algorithmic questions related to the Nash dynamics of weighted congestion games. In weighted congestion games with linear latency functions, the existence of (pure Nash) equilibria is guaranteed by potential…
We prove that every finite two-person shortest path game, where the local cost of every move is positive for each player, has a Nash equilibrium (NE) in pure stationary strategies, which can be computed in polynomial time. We also extend…
A game-theoretic framework for time-inconsistent stopping problems where the time-inconsistency is due to the consideration of a non-linear function of an expected reward is developed. A class of mixed strategy stopping times that allows…
In this article, we consider generalized Nash games where the associated constraint map is not necessarily self. The classical Nash equilibrium may not exist for such games and therefore we introduce the notion of best approximate solution…
In this article we consider a special class of Nash equilibrium problems that cannot be reduced to a single player control problem. Problems of this type can be solved by a semi-smooth Newton method. Applying results from the established…
In this paper, we consider the problem of finding a Nash equilibrium in a multi-player game over generally connected networks. This model differs from a conventional setting in that players have partial information on the actions of their…
We study a network congestion game of discrete-time dynamic traffic of atomic agents with a single origin-destination pair. Any agent freely makes a dynamic decision at each vertex (e.g., road crossing) and traffic is regulated with given…
We present a general convex relaxation approach to study a wide class of Unbalanced Optimal Transport problems for finite non-negative measures with possibly different masses. These are obtained as the lower semicontinuous and convex…
In this work, we provide a structural characterization of the possible Nash equilibria in the well-studied class of security games with additive utility. Our analysis yields a classification of possible equilibria into seven types and we…
We study the inefficiency of equilibria for various classes of games when players are (partially) altruistic. We model altruistic behavior by assuming that player i's perceived cost is a convex combination of 1-\alpha_i times his direct…
The distributed computation of equilibria and optima has seen growing interest in a broad collection of networked problems. We consider the computation of equilibria of convex stochastic Nash games characterized by a possibly nonconvex…
For a mean field game model with a major and infinite minor players, we characterize a notion of Nash equilibrium via a system of so-called master equations, namely a system of nonlinear transport equations in the space of measures. Then,…
We investigate the linear quadratic stochastic optimal control problems in infinite dimension without Markovian restriction for coefficients. The necessary and sufficient conditions for open-loop optimal controls are presented. We prove the…
We present polynomial-time algorithms as well as hardness results for equilibrium computation in atomic splittable routing games, for the case of general convex cost functions. These games model traffic in freight transportation, market…
Zero-sum games arise in a wide variety of problems, including robust optimization and adversarial learning. However, algorithms deployed for finding a local Nash equilibrium in these games often converge to non-Nash stationary points. This…
This paper considers a class of generalized convex games where each player is associated with a convex objective function, a convex inequality constraint and a convex constraint set. The players aim to compute a Nash equilibrium through…