The attrition game considered in this study is a graph based strategic game which is a movement-prohibited analogue of small-scale combat situations that arise frequently in popular real-time strategy video games. We present proofs that the attrition game, under a variety of assumptions, is a computationally hard problem in general. We also analyze the 1 vs. n unit case, for which we derive optimal target-orderings that can be computed in polynomial time and used as a core for heuristics for the general case. Finally, we present small problem instances that require randomizing moves - a fact that at first glance seems counter-intuitive.
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