Risk Averse Stackelberg Security Games with Quantal Response

In this paper, we consider a Stackelberg security game SSG where a defender can simultaneously protect m out of n targets with $$n>m$$ from an adversary that uses a quantal response QR to decide which target to attack. The main contribution consists in introducing risk aversion in the defender's behavior by using an entropic risk measure. Our work extends the work in [20] to a model that considers a risk averse defender. In addition we improve the algorithms used in [20] by reducing the number of integer variables, outlining how this adapts to arbitrary linear constraints. Computational results are presented on large scale artificial instances, showing the qualitative advantages of using a risk measure rather than the expected value.

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