Smooth Game

For a game whose strategy sets are convex subsets of Hilbert spaces, the game is smooth if, for every player $i$ and fixed $s_{-i}$, the map $$ s_i\mapsto g_i(s_i,s_{-i}) $$ is $C^1$. It is concave if these maps are concave.

References

• [MFoGT, Def. 4.7.5] Laraki, Renault, and Sorin, Mathematical Foundations of Game Theory. Smooth and concave Hilbert games.