A Jacobi-type Newton method for Nash equilibrium problems with descent guarantees

A common strategy for solving an unconstrained two-player Nash equilibrium problem with continuous variables is applying Newton’s method to the system of nonlinear equations obtained by the corresponding first-order necessary optimality conditions. However, when taking into account the game dynamics, it is not clear what is the goal of each player when considering that they … Read more

Multilinear formulations for computing Nash equilibrium of multi-player matrix games

We present multilinear and mixed-integer multilinear programs to find a Nash equilibrium in multi-player strategic-form games. We compare the formulations to common algorithms in Gambit, and conclude that a multilinear feasibility program finds a Nash equilibrium faster than any of the methods we compare it to, including the quantal response equilibrium method, which is recommended … Read more

An equivalent mathematical program for games with random constraints

This paper shows that there exists a Nash equilibrium of an n-player chance-constrained game for elliptically symmetric distributions. For a certain class of payoff functions, we suitably construct an equivalent mathematical program whose global maximizer is a Nash equilibrium. Article Download View An equivalent mathematical program for games with random constraints

Games with joint chance constraints under mixture distributions

We consider an n-player non-cooperative game where each player has expected value payoff function and her strategy set is defined by a joint chance constraint. The random constraint vectors are independent. We propose a subset of probability distributions from elliptical family of distributions. We consider the case when the probability distribution of each random constraint … Read more

Games with distributionally robust joint chance constraints

This paper studies an n-player non-cooperative game with strategy sets defined by stochastic linear constraints. The stochastic constraints of each player are jointly satisfied with a probability exceeding a given threshold. We consider the case where the row vectors defining the constraints are independent random vectors whose probability distributions are not completely known and belong … Read more

Assessment of Climate Agreements over the Long Term with Strategic Carbon Dioxyde Removal Activity

In this paper we extend a game theoretic meta-model used to assess the future of Paris agreement to the time horizon 2100 and we include in the strategic decisions of the negotiating coalitions the use of Carbon Dioxyde Removal (CDR) technologies. The meta-game model is calibrated through statistical emulation of GEMINI-E3, a world computable general … Read more

A characterization of Nash equilibrium for the games with random payoffs

We consider a two player bimatrix game where the entries of the payoff matrices are random variables. We formulate this problem as a chance-constrained game by considering that the payoff of each player is defined using a chance constraint. We consider the case where the entries of the payoff matrices are independent normal/Cauchy random variables. … Read more

Distributionally robust chance-constrained games: Existence and characterization of Nash equilibrium

We consider an n-player finite strategic game. The payoff vector of each player is a random vector whose distribution is not completely known. We assume that the distribution of a random payoff vector of each player belongs to a distributional uncertainty set. We define a distributionally robust chance-constrained game using worst-case chance constraint. We consider … Read more

Existence of Nash equilibrium for Chance-Constrained Games

We consider an n-player strategic game with finite action sets. The payoffs of each player are random variables. We assume that each player uses a satisficing payoff criterion defined by a chance-constraint, i.e., players face a chance- constrained game. We consider the cases where payoffs follow normal and elliptically symmetric distributions. For both cases we … Read more

Global Optimization via Slack Variables

This paper presents a method for finding global optima to constrained nonlinear programs via slack variables. The method only applies if all functions involved are of class C1 but without any further qualification on the types of constraints allowed; it proceeds by reformulating the given program into a bi-objective program that is then solved for … Read more