This paper gives an overview of the existence and computation of equilibrium in nonlinear n-person games. After some introductory examples, sufficient existence results are presented in both cases of single-valued and multiple-valued best responses. The uniqueness of the equilibrium is also shown under general conditions. A special iterative method is discussed for the computation of the unique equilibrium based on a variational inequality, and a single-objective optimization model is introduced to provide the equilibria. An example of repeated oligopolies completes the paper.
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Szidarovszky, F. (2008). Nonlinear Games. In: Chinchuluun, A., Pardalos, P.M., Migdalas, A., Pitsoulis, L. (eds) Pareto Optimality, Game Theory And Equilibria. Springer Optimization and Its Applications, vol 17. Springer, New York, NY. https://doi.org/10.1007/978-0-387-77247-9_4
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