Deterrence Through Response Curves: An Empirical Analysis of the Gaza-Israel Conflict

We use response curves in a repeated game to analyze key aspects of mutual deterrence: escalation, de-escalation, incomplete deterrence, and deterrence by denial. In this approach, episodes of violence are due to interacting response curves, which disincentivize opponents from attacking through both deterrence and compellence. Both sides punish attacks to maintain credibility in future episodes, disincentivizing larger attacks and yielding nonviolent lulls. We empirically estimate those curves using detailed incident data from the Israel-Gaza conflict between 2007 and 2017. Our estimates match the dynamics of the raw data: very frequent episodes of low lethality violent exchange. Response curves are stable and probably Markovian. They exhibit a posture consistent with incomplete deterrence: i.e., episodes de-escalate, but to a violent equilibrium. Israeli missile defense shifts the Gazan response curve to a less aggressive posture, as predicted by theory.