Abstract
Inspired by recent terrorist attacks on cereal production fields in Iraq, we introduce and study two types of Stackelberg games. In these games, the leader wants to maximize its production (e.g., cereal), while the follower tries to destroy this production as much as possible. In the first model, the leader can protect its production by spreading his production resources over multiple regions. In the second model, the leader can also decide to allocate some extra protection resources to the regions. For both games, we are interested in a follower’s and leader’s optimal strategy. We characterise optimal strategies for the follower and present two linear time algorithms (one for each game) that find an optimal strategy for the leader.
Highlights
Cereal production, in particular wheat and barley, is the principal agricultural activity in Iraq, accounting for 70% to 85% of the cultivated area
Inspired by recent terrorist attacks on cereal production fields in Iraq, we introduce and study two types of Stackelberg games
For the first model we present a linear time algorithm that finds an optimal production strategy for the leader
Summary
In particular wheat and barley, is the principal agricultural activity in Iraq, accounting for 70% to 85% of the cultivated area. The first one focuses on finding techniques or methods to solve the underlying bilevel optimization problems efficiently (see, e.g., Cappanera & Scaparra, 2011; Gutin et al, 2014; Israeli & Wood, 2002; Jiang & Liu, 2018; Liberatore, Scaparra, & Daskin, 2011; Scaparra & Church, 2008a; Scaparra & Church, 2008b; Starita & Scaparra, 2016; Washburn & Wood, 1995) Complementary to these computational-oriented studies, there exists a stream of literature that focuses on the analytical tractability of Stackelberg games (see, e.g., Bier, Oliveros, & Samuelson, 2007; Hausken & Zhuang, 2011; Powell, 2009; Shan & Zhuang, 2013; Zhuang & Bier, 2011).
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