In a basic Stackelberg security game (SSG), a defender can simultaneously protect m out of n targets with n > m from an adversary that observes the defense strategy and attacks where most convenient for him. We consider a more realistic model where 1) The defender faces several different opponents, 2) The adversaries are not completely rational and follow a quantal response (QR) to decide which target to attack, and 3) We introduce risk aversion in the defender's behavior by minimizing an entropic risk measure instead of an expected loss. Our contribution is as follows: 1) We show that we can find the risk-minimizing defense policy by solving a nonconvex nonlinear optimization problem, 2) We present an approximated problem (MINR) tailored for SSG that is a convex mixed Integer nonlinear program, 3) We propose a general purpose methodology (CELL) to optimize nonconvex and nonseparable fractional programming problems via Mixed Integer linear Programming (MIP) approximations, 4) We show that both problems provide lower bounds for SSG as well as arbitrarily good incumbents, and 5) We present cutting plane methods to solve them to optimality with an off the shelf MIP solver. We test both algorithms on a large bedset of mid-sized instances and show that MINR clearly dominates CELL and is able to produce-on average-solutions that are within 2% of optimality in 2 hours. We finish by showing the empirical qualitative advantages of introducing risk aversion into the defender's behavior.