Learning unknown additive normal form games

In this paper we introduce the class of additive normal form games, which is a subset of normal form games. In additive normal form games, the actions of each agent contribute some amount to the final payoff of all the agents. The contributions of the agents are assumed to be additive. We discuss the necessary and sufficient conditions for a normal form game to be an additive normal form game and show exactly how a normal form game may be converted to our additive representation. We observe that additive games always have either a dominant strategy equilibrium or weakly dominant strategy equilibria, although the equilibria may not always be Pareto optimal. Various learning techniques are applied to unknown repeated additive games, with Q-learning being the most successful.