  This chapter addresses the question of how to efficiently solve
many-objective optimization problems in a computationally demanding black-box
simulation context. We shall motivate the question by applications in machine
learning and engineering, and discuss specific harsh challenges in using
classical Pareto approaches when the number of objectives is four or more.
Then, we review solutions combining approaches from Bayesian optimization,
e.g., with Gaussian processes, and concepts from game theory like Nash
equilibria, Kalai-Smorodinsky solutions and detail extensions like
Nash-Kalai-Smorodinsky solutions. We finally introduce the corresponding
algorithms and provide some illustrating results.
