We study the fair and truthful allocation of m divisible public items among n agents, each with distinct preferences for the items. To aggregate agents’ preferences fairly, we focus on finding a core solution. For divisible items, a core solution always exists and can be calculated by maximizing the Nash welfare objective. However, such a … Read more
We study weighted, capacitated cost-sharing games on parallel-link networks, also known as bin packing games. We focus on an integer-splittable variant in which items of varying sizes can be divided into integer units and assigned to bins with heterogeneous capacities and costs. Although this setting has practical relevance, it remains largely unexplored in the context … Read more
Generalized Nash equilibrium problems with mixed-integer variables form an important class of games in which each player solves a mixed-integer optimization problem with respect to her own variables and the strategy space of each player depends on the strategies chosen by the rival players. In this work, we introduce a branch-and-cut algorithm to compute exact … Read more
Graphs of minimal point mappings of parametric optimization problems appear in the definition of feasible sets of bilevel optimization problems and of semi-infinite optimization problems, and the intersection of multiple such graphs defines (generalized) Nash equilibria. This paper shows how minimal point graphs of nonconvex parametric optimization problems can be written with the help of … Read more
Inspired by collaborative initiatives in the military domain, we analyze a setting in which multiple different players (e.g., Ministries of Defence) have to carry out preventive maintenance jobs. Each player is responsible for one job, with a job-specific minimal frequency and with maintenance costs, consisting of a job-specific variable component and a fixed component, which … Read more
This paper presents a game-theoretical framework for data classification and network discovery, focusing on pairwise influences in multivariate choices. The framework consists of two complementary games in which individuals, connected through a signed weighted graph, exhibit network similarity. A voting rule captures the influence of an individual’s neighbors, categorized as attractive (friend-like) or repulsive (enemy-like), … Read more
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 number … 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 from … Read more