From the text: The literature on the existence of Nash equilibrium in discontinuous games has blossomed since the seminal contribution of P. Dasgupta and E. Maskin [Rev. Econ. Stud. 53, 1–26 (1986; Zbl 0578.90098)]. The present symposium brings together a number of recent developments. Throughout this introduction, it is assumed that any game \(G=(X_i,u_i)_{i \in N}\) under consideration has a finite player set, \(N\), that each player \(i \in N\) has a nonempty, compact, and convex set of pure strategies \(X_i\) that is a subset of a linear topological space, and has bounded payoff function \(u_i:X \to \mathbb R\), where \(X=\times_{i \in N} X_i\). Not all papers in the symposium are always so restrictive as this. Indeed, some authors occasionally do not require strategy sets to be convex nor do they always require the existence of utility representations of the players’ preferences over strategy profiles. Such exceptions will be noted in this introduction only when absolutely necessary. Also, “Nash equilibrium” will always mean pure strategy Nash equilibrium.