It is common opinion that generalized Nash equilibrium problems are harder than Nash equilibrium problems. In this work, we show that by adding a new player, it is possible to reduce many generalized problems to standard equilibrium problems. The reduction holds for linear problems and smooth convex problems verifying a Slater-type condition. We also derive … Read more
We consider combinatorial multi-item markets and propose the notion of a ∆-regret Walras equilibrium, which is an allocation of items to players and a set of item prices that achieve the following goals: prices clear the market, the allocation is capacity-feasible, and the players’ strategies lead to a total regret of ∆. The regret is … Read more
Generalized Nash equilibrium problems with mixed-integer variables constitute an important class of games in which each player solves a mixed-integer optimization problem, where both the objective and the feasible set is parameterized by the rivals’ strategies. However, such games are known for failing to admit exact equilibria and also the assumption of all players being … Read more
Many mathematical models base on the coupling of two or more optimization problems. This paper surveys possibilities to couple two optimization problems and discusses how solutions of the different models are interrelated with each other. The considered pairs stem from the fields of standard and generalized Nash equilibrium problems, optimistic and pessimistic bilevel problems, saddle … Read more
The variational inequality (VI) problem is a fundamental mathematical framework for many classical problems. This paper introduces an algorithm that applies to arbitrary finite-dimensional VIs with general compact convex sets and general continuous functions. The algorithm guarantees global linear convergence to an approximate solution without requiring any assumptions, including the typical monotonicity. Our approach adapts … Read more
We study a two-player zero-sum inspection game with incomplete information, where an inspector deploys resources to maximize the expected damage value of detected illegal items hidden by an adversary across capacitated locations. Inspection and illegal resources differ in their detection capabilities and damage values. Both players face uncertainty regarding each other’s available resources, modeled via … Read more
Collection point networks are rapidly expanding as delivery companies and public authorities promote their implementation to consolidate deliveries and reduce urban congestion. However, rather than catering to public interest by maximizing accessibility, the placement of collection points remains primarily driven by competition among delivery companies, which seek to maximize their market share. This paper thus … Read more
We focus on multi-agent, multi-objective problems, particularly on those where the objectives admit a potential structure. We show that the solution to the potential multi-objective problem is always a noncooperative optimum for the multi-agent setting. Furthermore, we identify a class of problems for which every noncooperative solution can be computed via the potential problem. We … Read more
This paper presents a scalable algorithm for computing the best pure Nash equilibrium (PNE) in large-scale integer programming games (IPGs). While recent advances in IPG algorithms are extensive, existing methods are limited to a small number of players, typically 𝑛 = 2, 3. Motivated by a county-level aquatic invasive species (AIS) prevention problem involving 84 … Read more
Two-level hierarchical decision-making problems, where a leader’s choice influences a follower’s action, arise across key business and public-sector domains, from market design and pricing to defense. These problems are typically modeled as bilevel programs and are known to be notoriously hard to solve at scale. In single-level combinatorial optimization, especially for challenging instances, local search … Read more