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We introduce a dynamic game of outbidding where two groups use violence to compete for evolving public support in a tug-of-war fashion. We fit the model to newly collected data on Palestinian support for Hamas and Fatah in the Israeli-Palestinian conflict and estimate each group’s desire and ability to pull public opinion in favorable directions through terrorist attacks. We use the fitted model to test the outbidding hypothesis— enhanced competitive incentives increase violence—without relying on proxies. We find asymmetric effects: making Hamas more competitive increases the violence from both groups but making Fatah more competitive decreases violence from both groups. Furthermore, we find that competition from Hamas drives Fatah’s use of violence, but not vice versa. When Fatah expects no violence from Hamas, its use of terrorism decreases by 25%, but when Hamas expects no violence from Fatah, the decrease is only 7%. In fact, competition from Fatah actually deceases attacks by Hamas when Fatah has strong public support.