Training School on Mixed-Integer Games

Computational game theory is a rapidly growing field with many applications in the sciences and social sciences. A tractable computational environment to these challenging multi-agent optimization problems is provided by the theory of variational inequalities and monotone operators. These approaches work well for games with continuous strategy spaces and local cost functions satisfying joint monotonicity properties.

Motivated by many problems in engineering and operations research, a recent line of literature investigated the algorithmic foundations of Nash equilibrium in the presence of mixed-integer constraints on the players' action sets. Indeed, such mixed-integer formulations of games are prevalent in control and design of networked systems (traffic networks, unit-commitment problems, supply-chain problems etc...).

A key challenge in the algorithmic design for game theoretic models is that computations have to be performed locally in a distributed way, with as little central coordination as possible. Recently, many advances have been made in this direction for solving large-scale networked mixed-integer problems. The aim of this training school is to discuss possible ways to extend these seminal contributions to game-theoretic problems with potentially non-linear payoffs, so that the individual agents' problem are going to be mixed-integer non-linear optimization problems.