@conference {1504448,
	title = {A Unified Method for Handling Discrete and Continuous Uncertainty in Bayesian Stackelberg Games },
	booktitle = {International Conference on Autonomous Agents and Multiagent Systems (AAMAS)},
	year = {2012},
	abstract = {Given their existing and potential real-world security applications,
Bayesian Stackelberg games have received significant research interest [3, 12, 8]. In these games, the defender acts as a leader, and
the many different follower types model the uncertainty over discrete attacker types. Unfortunately since solving such games is an
NP-hard problem, scale-up has remained a difficult challenge.
This paper scales up Bayesian Stackelberg games, providing a
novel unified approach to handling uncertainty not only over discrete follower types but also other key continuously distributed real
world uncertainty, due to the leader{\textquoteright}s execution error, the follower{\textquoteright}s
observation error, and continuous payoff uncertainty. To that end,
this paper provides contributions in two parts. First, we present a
new algorithm for Bayesian Stackelberg games, called HUNTER,
to scale up the number of types. HUNTER combines the following five key features: i) efficient pruning via a best-first search of
the leader{\textquoteright}s strategy space; ii) a novel linear program for computing tight upper bounds for this search; iii) using Bender{\textquoteright}s decomposition for solving the upper bound linear program efficiently;
iv) efficient inheritance of Bender{\textquoteright}s cuts from parent to child; v)
an efficient heuristic branching rule. Our experiments show that
HUNTER provides orders of magnitude speedups over the best existing methods to handle discrete follower types. In the second part,
we show HUNTER{\textquoteright}s efficiency for Bayesian Stackelberg games
can be exploited to also handle the continuous uncertainty using
sample average approximation. We experimentally show that our
HUNTER-based approach also outperforms latest robust solution
methods under continuously distributed uncertainty.},
	author = {Yin, Zhengyu and Tambe, Milind}
}
