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Antimicrobial resistance is a threat to global health, aggravated by the use of antimicrobials in livestock production. Mitigating the growing economic costs related to antimicrobial use in livestock production requires strong global coordination, and to that end policy makers can leverage global and national food animal trade policies, such as bans and user fees. Evaluation of such policies requires representing the interactions between competing producers in the global meat market, which is usually out of the scope of statistical models. For that, we developed a game-theoretic food system model of global livestock production and trade between 18 countries and aggregate world regions. The model comprises the largest producing and consuming countries, the explicit interconnections between countries, and the use of antimicrobials in food animal production. Our model allows us to provide policy insights beyond standard literature and assess the trade-off between trade, cost of a policy, and antimicrobials-induced productivity. We studied three scenarios: global increased user fees on antimicrobials, a global ban of meat imports from Brazil, and a decrease in China's meat consumption. We found that a user fee that increases the price of antimicrobials by 50% globally leads to a 33% reduction in global antimicrobial use. However, participation of developing and emerging countries in the coordination scheme is jeopardized, since they become less competitive for meat sales compared to developed countries. When meat imports from Brazil are banned globally, importers of Brazil's meat would turn primarily to the U.S. to supplement their demand. Lastly, meeting China's medium-term lower meat consumption target would not affect global antimicrobial use, but could increase China's antimicrobial use by 11%. We highlighted the importance of trade for the outcome of a policy and concluded that global cooperation is required to align the incentives of all countries toward tackling antimicrobial resistance.