- Award ID(s):
- 2014816
- PAR ID:
- 10316599
- Date Published:
- Journal Name:
- 60th IEEE Conference on Decision and Control (CDC)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
We consider the stochastic generalized Nash equilibrium problem (SGNEP) where a set of self-interested players, subject to certain global constraints, aim to optimize their local objectives that depend on their own decisions and the decisions of others and are influenced by some random factors. A distributed stochastic generalized Nash equilibrium seeking algorithm is proposed based on the Douglas-Rachford operator splitting scheme, which only requires local communications among neighbors. The proposed scheme significantly relaxes assumptions on co-coercivity and contractiveness in the existing literature, where the projected stochastic subgradient method is applied to provide approximate solutions to the augmented best-response subproblems for each player. Finally, we illustrate the validity of the proposed algorithm through a Nash-Cournot production game.more » « less
-
We consider the stochastic generalized Nash equilibrium problem (SGNEP) where a set of self-interested players, subject to certain global constraints, aim to optimize their local objectives that depend on their own decisions and the decisions of others and are influenced by some random factors. A distributed stochastic generalized Nash equilibrium seeking algorithm is proposed based on the Douglas-Rachford operator splitting scheme, which only requires local communications among neighbors. The proposed scheme significantly relaxes assumptions on co-coercivity and contractiveness in the existing literature, where the projected stochastic subgradient method is applied to provide approximate solutions to the augmented best-response subproblems for each player. Finally, we illustrate the validity of the proposed algorithm through a Nash-Cournot production game.more » « less
-
In this paper, we develop distributed computation algorithms for Nash equilibriums of linear quadratic network games with proven differential privacy guarantees. In a network game with each player's payoff being a quadratic function, the dependencies of the decisions in the payoff function naturally encode a network structure governing the players' inter-personal influences. Such social influence structure and the individual marginal payoffs of the players indicate economic spillovers and individual preferences, and thus they are subject to privacy concerns. For distributed computing of the Nash equilibrium, the players are interconnected by a public communication graph, over which dynamical states are shared among neighboring nodes. When the players' marginal payoffs are considered to be private knowledge, we propose a distributed randomized gradient descent algorithm, in which each player adds a Laplacian random noise to her marginal payoff in the recursive updates. It is proven that the algorithm can guarantee differential privacy and convergence in expectation to the Nash equilibrium of the network game at each player's state. Moreover, the mean-square error between the players' states and the Nash equilibrium is shown to be bounded by a constant related to the differential privacy level. Next, when both the players' marginal payoffs and the influence graph are private information, we propose two distributed algorithms by randomized communication and randomized projection, respectively, for privacy preservation. The differential privacy and convergence guarantees are also established for such algorithms.more » « less
-
Markov games model interactions among multiple players in a stochastic, dynamic environment. Each player in a Markov game maximizes its expected total discounted reward, which depends upon the policies of the other players. We formulate a class of Markov games, termed affine Markov games, where an affine reward function couples the players’ actions. We introduce a novel solution concept, the soft-Bellman equilibrium, where each player is boundedly rational and chooses a soft-Bellman policy rather than a purely rational policy as in the well-known Nash equilibrium concept. We provide conditions for the existence and uniqueness of the soft-Bellman equilibrium and propose a nonlinear least-squares algorithm to compute such an equilibrium in the forward problem. We then solve the inverse game problem of inferring the players’ reward parameters from observed state-action trajectories via a projected-gradient algorithm. Experiments in a predator-prey OpenAI Gym environment show that the reward parameters inferred by the proposed algorithm outper- form those inferred by a baseline algorithm: they reduce the Kullback-Leibler divergence between the equilibrium policies and observed policies by at least two orders of magnitude.more » « less
-
Yllka Velaj and Ulrich Berger (Ed.)
This paper considers a two-player game where each player chooses a resource from a finite collection of options. Each resource brings a random reward. Both players have statistical information regarding the rewards of each resource. Additionally, there exists an information asymmetry where each player has knowledge of the reward realizations of different subsets of the resources. If both players choose the same resource, the reward is divided equally between them, whereas if they choose different resources, each player gains the full reward of the resource. We first implement the iterative best response algorithm to find an ϵ-approximate Nash equilibrium for this game. This method of finding a Nash equilibrium may not be desirable when players do not trust each other and place no assumptions on the incentives of the opponent. To handle this case, we solve the problem of maximizing the worst-case expected utility of the first player. The solution leads to counter-intuitive insights in certain special cases. To solve the general version of the problem, we develop an efficient algorithmic solution that combines online convex optimization and the drift-plus penalty technique.