We introduce a general multi-defender Stackelberg security game where multiple independent defenders jointly protect a same set of targets from being attacked by a common attacker.In the game,Strong Stackelberg Equili...We introduce a general multi-defender Stackelberg security game where multiple independent defenders jointly protect a same set of targets from being attacked by a common attacker.In the game,Strong Stackelberg Equilibrium is fundamentally problematic,because the notion of‘break-ing ties in defender’s favour’is no longer well defined,as we must specify which defender will receive the favour.To address this issue,we define a new equilibrium concept under a newly defined tie-breaking rule.We characterise Logit Stackelberg Multi-Defender Equilibrium,corre-sponding to a logit tie-breaking rule,as well as an equivalent Nash Equilibrium among defenders,and exhibit algorithms for computing the equilibrium solutions.We find that Logit Stackelberg Multi-Defender Equilibrium and its’equivalent Nash Equilibrium may not exist,which motivates us to find an approximate equilibrium.We design a revised exclusion algorithm to find the approximateε-Nash Equilibrium in which no defender gains more thanεby deviating.展开更多
基金supported by the National Natural Science Foun-dation of China[grant numbers 61572095,61877007]Department of Science and Technology of Shanxi Province[grant numbers 20210302124303,202203021222251].
文摘We introduce a general multi-defender Stackelberg security game where multiple independent defenders jointly protect a same set of targets from being attacked by a common attacker.In the game,Strong Stackelberg Equilibrium is fundamentally problematic,because the notion of‘break-ing ties in defender’s favour’is no longer well defined,as we must specify which defender will receive the favour.To address this issue,we define a new equilibrium concept under a newly defined tie-breaking rule.We characterise Logit Stackelberg Multi-Defender Equilibrium,corre-sponding to a logit tie-breaking rule,as well as an equivalent Nash Equilibrium among defenders,and exhibit algorithms for computing the equilibrium solutions.We find that Logit Stackelberg Multi-Defender Equilibrium and its’equivalent Nash Equilibrium may not exist,which motivates us to find an approximate equilibrium.We design a revised exclusion algorithm to find the approximateε-Nash Equilibrium in which no defender gains more thanεby deviating.
