The results obtained with the model show that the truth may be even less convenient: as the model reveals, the dynamics among the fighting groups can be extremely sensitive to initial conditions and parameter values. It is generally believed that the fate of complex conflicts cannot be predicted because data are too scarce and unreliable. But they are also shown to remain valid under more realistic assumptions, i.e., when groups follow mixed strategies.
They are obtained under the assumption that groups follow either defense strategies (their recruitment process depends only on their losses) or attack strategies (their recruitment depends only on the injuries they inflict to their enemies). The results can be summarized with two statements: “brute force is often rewarding” and “defensive strategies are stabilizing (they lead to constant violence dynamics) while attack strategies are destabilizing (they can lead to periods of violence alternated with periods of relative peace)”. Third, when a conflict is trapped in a non-stationary stalemate, the model suggests when a short but heavy military intervention should be performed in order to have the highest chances of eradicating the enemies. Second, the model shows how outcomes depend on initial conditions. Stalemates can be stationary or have recurrent ups and downs in the army sizes and in the inflicted and suffered losses. The idealized model we propose indicates that stalemates, i.e., conflicts with no winner, arise. Thus, traditional descriptive conceptual models, like those suggested long ago by Lanchester and Richardson (for a review, see ), are of limited help. Armed conflicts often involve more than two groups, which typically differ in their military characteristics and recruitment policies. The interest in mathematical models of armed conflicts has increased in the last decades owing to the wide prevalence and complex nature of such conflicts.
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