Empirical study and model of warfare dynamics: Willingness to risk Available to Purchase

Economists often highlight a gross domestic product (GDP) as a key metric in determining war outcomes, despite historical exceptions, such as the Taliban’s victories over the Soviet and U.S. armies in Afghanistan—nations with vastly superior GDPs. Two critical factors that remain underexplored are the soldier’s willingness to sacrifice for their country and a country’s willingness to risk nuclear war. To address this gap, we conducted a worldwide survey to assess the maximum acceptable level of losses respondents would tolerate in their own country for varying levels of enemy losses. The findings were surprising: respondents, on average, considered 23% casualties (with a median of 10%) as an acceptable loss if it meant 100% destruction of the enemy. To determine which nuclear power might be more inclined to initiate a nuclear war, we introduce the willingness to risk ratio, defined as the ratio between the GDP that can be destroyed in enemy countries and the GDP that could be destroyed by the enemy in one’s own country. Recognizing that conventional wars can serve as a pretext for a nuclear conflict between two nuclear powers, $S$ and $S ′$⁠, we developed a network model where bravery is defined at the micro level of individual soldiers, whereas defeatism can spread contagiously throughout the network. If due to increasing aid of the nuclear power $S ′$ to a weaker country $W$⁠, the opposing nuclear power $S$ suffers heavier casualties, the probability of the nuclear catastrophe $P$ surges, prompting $S$ and $S ′$ to start weighing between a nuclear-war scenario and continuation of the proxy war. In this case, the increase of $P$ ramps up the chance that the power $S ′$⁠, geographically farther to the spot of conflict, stops supporting $W$ since it is less willing to risk nuclear war and in economic terms, $S ′$ may lose more than $S$ if the war escalates.