A note on robust Nash equilibria in games with uncertainties

In this short note, we investigate extensions of Nash equilibria when players have some uncertainties upon their payoffs mappings, the behavior (or the type, number or any other characteristics) of their opponents. These solutions are qualified either as robust, ambiguous, partially specified or with uncertainty aversion, depending on the context. We provide a simple necessary and sufficient condition that guarantees their existence and we show that this is actually a selection of conjectural (or self-confirming) equilibria. We finally conclude by how this concept can and should be defined in games with partial monitoring in order to preserve existence properties.