We consider a two-player Nash game in which each player represents a fleet of unmanned aerial vehicles. Each fleet is supposed to distribute information among fleet members, while simultaneously trying to prevent the opposite fleet from achieving this. Using the electro-magnetic spectrum’s properties, we model each fleet’s task as a nonlinear Nash game. By reformulating … Read more
\(\) We consider the theoretical computational complexity of finding locally optimal solutions to bilevel linear optimization problems (BLPs), from the leader’s perspective. We show that, for any constant \(c > 0\), the problem of finding a leader’s solution that is within Euclidean distance \(c^n\) of any locally optimal leader’s solution, where \(n\) is the total … Read more
We study a Stackelberg game in which a government positions rapid response teams and thereafter a terrorist attacks a location on a line segment. We assume the damage associated to such an attack to be time dependent. We show that there exists a subgame perfect Nash equilibrium that balances the possible damage on all intervals … Read more
\(\) We study submodular optimization in adversarial context, applicable to machine learning problems such as feature selection using data susceptible to uncertainties and attacks. We focus on Stackelberg games between an attacker (or interdictor) and a defender where the attacker aims to minimize the defender’s objective of maximizing a k-submodular function. We allow uncertainties arising … Read more
Security agencies throughout the world use bodyguards to protect government officials and public figures. In this paper, we consider a two-person zero-sum game between a defender who allocates such bodyguards to protect several targets and an attacker who chooses one target to attack. Because the number of feasible bodyguard allocations grows quickly as either the … Read more
\(\) This paper is devoted to study the convergence rates of a second-order dynamical system and its corresponding discretizations associated with a nonsmooth bilinearly coupled convex-concave saddle point problem. We derive the convergence rate of the primal-dual gap for the second-order dynamical system with asymptotically vanishing damping term. Based on the implicit discretization, we propose … Read more
A common strategy for solving an unconstrained two-player Nash equilibrium problem with continuous variables is applying Newton’s method to the system 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 they are taking their current … Read more
Partial inverse combinatorial optimization problems are bilevel optimization problems in which the leader aims to incentivize the follower to include a given set of elements in the solution of their combinatorial problem. If the set of required elements defines a complete follower solution, the inverse combinatorial problem is solvable in polynomial time as soon as … Read more
Congestion games allow to model competitive resource sharing in various distributed systems. Pure Nash equilibria, that are stable outcomes of a game, could be far from being socially optimal. Our goal is to identify combinatorial structures that limit the inefficiency of equilibria. This question has been mainly investigated for congestion games defined over networks. Instead, … Read more
We propose an extension of matrix games where the row player may select rows and remove columns, subject to a budget constraint. We present an exact mixed-integer linear programming (MILP) formulation for the problem, provide analytical results concerning its solution, and discuss applications in the security domain. Our computational experiments show heuristic approaches on average … Read more