The Nash equilibrium concept will be close to vacuous in games featuring multiple Nash equilibria because it will offer no determinate guide to action. This chapter is concerned with how game theory has attacked this apparent indeterminacy. In these circumstances rational players, it seems, will need some way of discarding equilibria if they are to ‘operationalise’ the Nash equilibrium solution. This sets the agenda for the Nash Refinement Project which began life with a notion of ‘stability’ the purpose of which was to help players discard some Nash equilibria as ‘unstable’. We begin the next section with an investigation of this notion of ‘stability’.