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Many economic games and machine learning approaches can be cast as competitive optimization problems where multiple agents are minimizing their respective objective function, which depends on all agents' actions. While gradient descent is a reliable basic workhorse for single-agent optimization, it often leads to oscillation in competitive optimization. In this work we propose polymatrix competitive gradient descent (PCGD) as a method for solving general sum competitive optimization involvingarXiv:2111.08565v1 fatcat:afc7wklgrjcede3cy7h4ionz4e