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In this paper, we study the notion of adversarial Stackelberg value for two-player non-zero sum games played on bi-weighted graphs with the mean-payoff and the discounted sum functions. The adversarial Stackelberg value of Player 0 is the largest value that Player 0 can obtain when announcing her strategy to Player 1 which in turn responds with any of his best response. For the mean-payoff function, we show that the adversarial Stackelberg value is not always achievable but ε-optimal strategiesdoi:10.4230/lipics.icalp.2020.127 dblp:conf/icalp/FiliotGR20 fatcat:im4spvt3pfgyxjbe2g5cbiklzy