Existence and solution methods for equilibria

Equilibrium problems provide a mathematical framework which includes optimization, variational inequalities, fixed-point and saddle point problems, and noncooperative games as particular cases. This general format received an increasing interest in the last decade mainly because many theoretical and algorithmic results developed for one of these models can be often extended to the others through the unifying language provided by this common format. This survey paper aims at covering the main results concerning the existence of equilibria and the solution methods for finding them.

► This survey paper covers the main results about existence and methods for equilibria.
► The existence results are divided into groups according to the required assumptions.
► The methods are classified depending on the kind of solved problems at each iteration.
► We stress the role of coercivity, monotonicity, and convexity assumptions.