6 papers
On the Minimum Number of Linear Pieces Required to Approximate Nonlinear Functions under an Accuracy Constraint
Aloïs Duguet, Sandra Ulrich Ngueveu, François Lamothe
The approximation of nonlinear functions by piecewise linear functions is a tool commonly used when dealing with mixed-integer nonlinear problems. Typically, by replacing nonlinear…
When do Mixed-Integer Games Admit Rational Equilibria?
Aloïs Duguet, Tobias Harks, Martin Schmidt +1
We consider mixed-integer linear-quadratic generalized Nash equilibrium problems, i.e., games in which each player solves a mixed-integer program subject to linear constraints in h…
Branch-and-Cut for Computing Approximate Equilibria of Mixed-Integer Generalized Nash Games
Aloïs Duguet, Tobias Harks, Martin Schmidt +1
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 bo…
Minimal Regret Walras Equilibria for Combinatorial Markets
Aloïs Duguet, Tobias Harks, Martin Schmidt +1
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 ach…
Branch-and-Cut for Mixed-Integer Nash Equilibrium Problems
Aloïs Duguet, Tobias Harks, Martin Schmidt +1
We study Nash equilibrium problems with mixed-integer variables in which each player solves a mixed-integer optimization problem parameterized by the rivals' strategies. We disting…
Computing Approximate Nash Equilibria for Integer Programming Games
Aloïs Duguet, Margarida Carvalho, Gabriele Dragotto +1
We propose a framework to compute approximate Nash equilibria in integer programming games with nonlinear payoffs, i.e., simultaneous and non-cooperative games where each player so…