Title: Monotone Near-Zero-Sum Games
Primary area: optimization
Keywords: Non-zero-sum games; monotone games

Abstract: Zero-sum and non-zero-sum (aka general-sum) games are relevant in a wide range of applications. 
While general non-zero-sum games are computationally hard, researchers focus
on the special class of monotone games for gradient-based algorithms.
However, there is a substantial gap between the gradient complexity of monotone zero-sum and monotone general-sum games. 
Moreover, in many practical scenarios of games the zero-sum assumption needs to be relaxed.
To address these issues, we define a new intermediate class of monotone near-zero-sum games that contains monotone zero-sum games as a special case. Then, we present a novel algorithm that transforms the near-zero-sum games into a sequence of zero-sum subproblems, improving the gradient-based complexity for the class. Finally, we demonstrate the applicability of this new
class to model practical scenarios of games motivated from the literature.