Algorithms for Cameras View-Frame Placement Problems in the Presence of an Adversary and Distributional Ambiguity

In this paper, we introduce cameras view-frame placement problem (denoted by CFP) in the presence an adversary whose objective is to minimize the maximum coverage by p cameras in response to input provided by n autonomous agents in a remote location. We allow uncertainty in the success of attacks, incomplete information of the probability distribution … Read more

Fighting Terrorism: How to position Rapid Response Teams?

In light of recent terrorist attacks, we introduce and study a Stackelberg game between a government and a terrorist. In this game, the government positions a number of heavily-armed rapid response teams on a line segment (e.g., a long boulevard or shopping avenue) and then the terrorist attacks a location with the highest damage. This … Read more

Cooperative locker locations games

More and more people are ordering products online, having their parcels delivered to their homes. This leads to more congestion, which negatively impacts the environment as well as public health and safety. To reduce these negative impacts, carriers can use parcel lockers to consolidate and serve their customers. The implementation of a locker network can, … Read more

A PDE-Constrained Generalized Nash Equilibrium Approach for Modeling Gas Markets with Transport

We investigate a class of generalized Nash equilibrium problems (GNEPs) in which the objectives of the individuals are interdependent and the shared constraint consists of a system of partial differential equations. This setup is motivated by the modeling of strategic interactions of competing firms, which explicitly take into account the dynamics of transporting a commodity, … Read more

Inefficiency of pure Nash equilibria in network congestion games: the impact of symmetry and graph structure

We study the inefficiency of pure Nash equilibria in symmetric unweighted network congestion games. We first explore the impact of symmetry on the worst-case PoA of network congestion games. For polynomial delay functions with highest degree p, we construct a family of symmetric congestion games over arbitrary networks which achieves the same worst-case PoA of … Read more

A branch-and-bound algorithm for non-convex Nash equilibrium problems

This paper introduces a spatial branch-and-bound method for the approximate computation of the set of all epsilon-Nash equilibria of continuous box-constrained non-convex Nash equilibrium problems. We explain appropriate discarding and fathoming techniques, provide a termination proof for a prescribed approximation tolerance, and report our computational experience. Article Download View A branch-and-bound algorithm for non-convex Nash … Read more

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

Two-stage distributionally robust noncooperative games: Existence of Nash equilibrium and its application to Cournot-Nash competition

Two-stage distributionally robust stochastic noncooperative games with continuous decision variables are studied. In such games, each player solves a two-stage distributionally robust optimization problem depending on the decisions of the other players. Existing studies in this area have been limited with strict assumptions, such as linear decision rules, and supposed that each player solves a … 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

CliSAT: a SAT-based exact algorithm for hard maximum clique problems

Given a graph, the maximum clique problem (MCP) asks for determining a complete subgraph with the largest possible number of vertices. We propose a new exact algorithm, called CliSAT, to solve the MCP to proven optimality. This problem is of fundamental importance in graph theory and combinatorial optimization due to its practical relevance for a … Read more