On Nash-equilibria of approximation-stable games

One of the goals of algorithmic game theory is to develop efficient methods for predicting the behaviour of self-interested agents in a given scenario, or game. A common approach is to attempt to compute an (approximate) Nash equilibrium, a behaviour such that agents have little incentive to deviate. Yet this computation appears to be quite difficult in general. In this work, we define and study games that are approximation-stable, meaning that all approximate equilibria predict similar behaviour. By analysing their properties, we show that finding approximate equilibria is substantially easier in such stable games.