International Relations, Modeling, National Security

Rock-Paper-Scissors and Arms Races Part 1

I have always been fascinated by military innovation and the ways in which individuals and organizations perceive and adapt to threats and opportunities in their environments.  One of the important lessons from game theory, biology, and military history is the fragility of dominant positions – there is rarely a dominant strategy that trumps all possible options available to one’s rivals.  While arms races may be escalatory and appear as games of one-upmanship, this is an imprecise interpretation of their dynamics.  It is true that rivals tend to acquire larger, faster, more powerful tanks, planes, ships, etc., but the actual story is a more subtle one where competitors seek to offset each other’s advantages, sometimes by imitation, developing or buying armaments of similar types, while at other times they may seek to innovate and counter an adversary’s advances, for example by developing air-defense systems to offset improvements in a rival’s air forces.  Moreover, while weapons themselves receive a great deal attention, the actual competition is between military organizations, of which their tools are only a piece of the larger story that includes organizational change, doctrine, training, operational concepts, finance, recruitment, and more.  When viewed in total, arms races become collective pursuits that involve entire military organizations, and touch on all aspects of their economies, ideology, science and technology, demography, geography, and culture.  Decisions to eschew particular options can be as consequential as what is pursued.

Complete models of military innovations and military revolutions, particularly quick and sudden alterations in the practice of war and politics, have been difficult to formalize and remain predominantly the work of historians and case study oriented social scientists.  I have seen very little mathematical or computational models that capture the multidimensional character of arms races – while there exists a wide range of fascinating formal models that deal with particular aspects of these issues such as deterrence, warning and crisis stability, the periodization of warfare, etc.  Indeed, my original dissertation topic examined military revolutions as an undertheorized aspect of international relations theory and sought to draw from evolution and ecology to formalize these concepts.  While I could never cross certain translational boundaries with respect to distinctions between geneotypes/phenotypes, and organisms/species in working to model the international system as an ecology of armed groups, I nevertheless found great interest and promise in one particular model from evolutionary game theory – Rock-Paper-Scissors (RPS).

RPS is a very simple game that displays a particularly important trait – there is no dominant strategy.  Playing Rock will beat Scissors but lose to Paper; Paper will beat Rock but lose to Scissors; and Scissors will beat Paper but lose to Rocks.  Thus, contrary to Bart Simpson’s famous saying that “nothing beats rock,” every strategy can win and every strategy can lose.  Famously, this dynamics has shown up in populations of lizards, and has been seen in ancient warfare as well with the inability of heavy infantry, light infantry, heavy cavalry, and light cavalry to consistently dominate rival military forces of different types based on geography and offense and defense.  More recently, the recognition that nuclear war was a qualitatively different type of military engagement than conventional war, followed by similar recognition that insurgencies and terrorism are also qualitatively distinct has challenged the notion of a spectrum of conflict that runs a continuous gamut from low-intensity to high-intensity – that implied if one could dominate conflicts at the high-end of the spectrum it was implicitly true that it could dominate the low-end as well.  Instead, warfare is a discrete phenomenon with particular break-points that enable signaling, escalation, negotiation, termination, and strategically and behaviorally distinct regimes.

A simple model of adaptive arms races, as opposed to escalatory ones, can treat three discrete forms of conflict as a game of RPS, where the strategies are the development and use of micro-scale military forces that operate within communities such as insurgents, terrorists, and police forces; a second option is the employment of organized armies that can control populations and territory; finally, a third strategy is the development and use of strategic forces that employ long-range strikes against an adversary’s infrastructure, communications, logistics, leadership and economy.  In each case, one type of military force can deter or defeat another, but none dominates.  Local forces can be contained and even defeated by armies, but can survive and frustrate forces that depend on long-range strikes.  Alternatively, long-range strikes can deter and undermine the organization of large armies, but cannot do much to sever the ties between local military forces and the communities they are embedded in.  While this is a highly stylized simple characterization of warfare between competing types of military forces, it provides a simple mapping onto already formalized models that explain cycles in populations of competitors and the persistence of weak strategies or actors based on ecological conditions.

My next several postings will adapt the RPS model to warfare and study how changes in its configuration reveal insights into the dynamics of military competition.


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