We consider bilevel programs where a single leader interacts with multiple followers who are coupled by a Nash equilibrium problem at the lower level. We generalize the value function reformulation to include multiple followers. This allows us to propose a convergent method based on the sequential convex approximation paradigm, and study the (exact or inexact) … Read more
We study a class of nonlinear optimization problems with diverse practical applications, particularly in cooperative game theory. These problems are referred to as Maximum Multiplicative Programs (MMPs), and can be conceived as instances of “Optimization Over the Frontier” in multiobjective optimization. To solve MMPs, we introduce a feasibility pump-based heuristic that is specifically designed to … Read more
In this tutorial we consider single-leader-multi-follower games in which the models of the lower-level players have polyhedral feasible sets and convex objective functions. This situation allows for classic KKT reformulations of the separate lower-level problems, which lead to challenging single-level reformulations of MPCC type. The main contribution of this tutorial is to present a ready-to-use … Read more
Protecting critical infrastructure from intentional damage requires foreseeing the strategies of possible attackers. The problem faced by the defender of such infrastructure can be formulated as a Stackelberg security game. A defender must decide what specific targets to protect with limited resources, maximizing their expected utility (e.g., minimizing damage value) and considering that a second … Read more
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
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
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
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
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 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