The Risk of War: An Analysis Combining Real Options and Games

Real options have been used to evaluate investment decisions with various structures, but have rarely been put into a game theoretical context. We examine the risk of war over a common resource, whose value is a geometric Brownian Motion, where one country may preemptively appropriate the resource, and the other wage war for it. We derive a closed form expression for the optimal mixed strategy that both countries should follow, and show that the resulting price level that triggers capturing the resource and subsequent war asymptotically follows a power law. The present value of the time until war is triggered also decays slowly asymptotically. In consequence, in spite of both countries’ propensity towards preemption, war may be indefinitely delayed.