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In multi-agent settings with mixed incentives, methods developed for zero-sumgames have been shown to lead to detrimental outcomes. To address this issue,opponent shaping (OS) methods explicitly learn to influence the learningdynamics of co-players and empirically lead to improved individual andcollective outcomes. However, OS methods have only been evaluated inlow-dimensional environments due to the challenges associated with estimatinghigher-order derivatives or scaling model-free meta-learning. Alternativemethods that scale to more complex settings either converge to undesirablesolutions or rely on unrealistic assumptions about the environment orco-players. In this paper, we successfully scale an OS-based approach togeneral-sum games with temporally-extended actions and long-time horizons forthe first time. After analysing the representations of the meta-state andhistory used by previous algorithms, we propose a simplified version calledShaper. We show empirically that Shaper leads to improved individual andcollective outcomes in a range of challenging settings from literature. Wefurther formalize a technique previously implicit in the literature, andanalyse its contribution to opponent shaping. We show empirically that thistechnique is helpful for the functioning of prior methods in certainenvironments. Lastly, we show that previous environments, such as the CoinGame,are inadequate for analysing temporally-extended general-sum interactions.

Scaling Opponent Shaping to High Dimensional Games