Chapter 42 Foundations of strategic equilibrium This chapter examines the conceptual foundations of the concept of strategic equilibrium and its various variants and refinements. The emphasis is very much on the underlying ideas rather than on any technical details.After an examination of some pre equilibrium ideas in particular the concept of rationalizability the concept of strategic (or Nash) equilibrium is introduced. Various interpretations of this concept are discussed and a proof of the existence of such equilibria is sketched.Next the concept of correlated equilibrium is introduced. This concept can be thought of as retaining the self enforcing aspect of the idea of equilibrium while relaxing the independence assumption.Most of the remainder of the chapter is concerned with the ideas underlying the refinement of equilibrium: admissibility and iterated dominance; backward induction; forward induction; and ordinality and various invariances to changes in the player set. This leads to a consideration of the concept of strategic stability a strong refinement satisfying these various ideas.Finally there is a brief examination of the epistemic approach to equilibrium and the relation between strategic equilibrium and correlated equilibrium.