How can a small group of insurgents believe they can overcome the government by turning violent, even if the government is strongly superior? When does a conflict develop towards a peaceful conflict resolution, terrorism, a guerilla war, or a widely spread conventional civil war? We develop a formal model for rebels and government and derive optimal choices. Further, we focus on three elements as important ingredients of a "destabilization war". All three of these - large random events, time preference (which we relate to ideology), and choice of duration of fight - are rarely considered in formal conflict theory. We can answer the above two questions with game theory analysis. First, insurgents rise up because they believe in the effect of destabilization through permanent challenging attacks. Large randomness is an important ally of rebels. While each single attack may have low impact, maybe at some time a large random event could lead to success. Hence, duration of activities is a constitutive element of this kind of violent conflict. Patience (low time preference), which may reflect the degree of ideological motivation of rebels, is crucial. Second, the mode of warfare or conflict resolutions that develops is generally path-dependent and conditioned on the full set of options (including compromise). Various conditions (level of funding, ease of recruitment, access to weapons) favor in a complex way different modes of warfare or a peaceful compromise. Unlike in a "one battle war" with no time dimension, in a "continuing violent conflict" economic instruments become very powerful in terms of guiding conflict resolution in a certain direction.
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