The Trade-Offs of Fighting and Investing: A Model of the Evolution of War and Peace¹

¹A previous version of this paper was presented at the 2007 International Studies Association Meeting in Chicago, Illinois and at the Reopening the Black Box of War: Politics and the Conduct of War Conference, hosted by Scott Gartner at the University of California at Davis, October 26th–28th, 2006. This research is based on work by Morey (2002). We thank Scott Gartner for organizing this conference, prompting us to return to this line of research, and providing excellent feedback. We also thank Cary Covington, Douglas Dion, Caroline Hartzell, Brian Lai, Lukas Pfaff, Kenneth Schultz, Ezra Sidran, Branislav Slantchev, Patricia Sullivan, and two anonymous reviewers for helpful comments and suggestions. All errors remain our own. Authors appear in alphabetical order.

Abstract

International competition occurs in many different forms. Just as a state would be in danger if it allowed its opponent to gain a military advantage, one that falls behind a rival in an economic contest similarly faces risks. States must weigh the trade-offs between economic and military growth, as well as deciding on the best strategy to follow should war erupt. We use a formal, dynamic model to explicitly capture the trade-offs that states face in their search for security and dominance. The deductions from the model demonstrate that by considering the long-run results of a peacetime rivalry, weaker states might conclude that their only hope of winning or surviving a rivalry lies in fighting a counterforce war, explain why and how stalemates evolve during counterforce wars, and indicate that targeting industrial objectives shortens the duration of wars.

Keywords:

• competition
• dynamic model
• strategy
• trade-offs
• war

Notes

¹A previous version of this paper was presented at the 2007 International Studies Association Meeting in Chicago, Illinois and at the Reopening the Black Box of War: Politics and the Conduct of War Conference, hosted by Scott Gartner at the University of California at Davis, October 26th–28th, 2006. This research is based on work by Morey (2002). We thank Scott Gartner for organizing this conference, prompting us to return to this line of research, and providing excellent feedback. We also thank Cary Covington, Douglas Dion, Caroline Hartzell, Brian Lai, Lukas Pfaff, Kenneth Schultz, Ezra Sidran, Branislav Slantchev, Patricia Sullivan, and two anonymous reviewers for helpful comments and suggestions. All errors remain our own. Authors appear in alphabetical order.

¹Our mathematical model is a necessary first step toward the more complicated formalization of a process Maoz and Siverson (2008, this issue) see as the ideal representation of strategy dynamics. In particular, they are interested in a situation in which mid-war shifts in strategy can occur.

³ Morton (1999) also reminds us that the test of a model's assumption is not how accurately they reflect reality. Instead, the measure of an assumption is how well it helps to understand behavior.

⁴In fact, efforts to increase a state's carrying capacity drive many explanations of state expansion. For instance, Jervis (1978) argues that states seeking security may attempt to expand as a way to gain more resources that will allow them to better protect themselves. It is estimated that during the Second World War, occupied territories increased the proportion of production available to the German government by 59% (United States Strategic Bombing Survey, 1945, 21)

⁵For now, we set aside the possibility that allies can increase a state's military capacity.

⁶While Clausewitz reasons that total losses for both sides is a function of the sum of forces, we argue that the damage to one side is a function of the product of forces. Nonetheless, the underlying principle, that the magnitude of damages is produced by the interaction of two sides, is the same.

⁷In order to capture the effect of targeting another state's resource base, we added − ρ _j r _i m _i to Equation 6, forming Equation 10. As ρ _j , r _i , or m _i increases, holding the other two constant, the rate of destruction increases.

⁸See Appendix 1 for the parameter values of the simulations. The values for the parameters are fixed across all simulations in order to determine how changes in the variables alter dyadic behavior. If the parameters and initial conditions changed in every simulation, it would difficult to determine what was actually driving results.

⁹Aside from requiring them to be positive, we set no limits on the values of the variables. Values less than or equal to zero have no meaning in this model because it is not possible to have negative spending or resources. Once the simulations begin, we do not bound the values the variables may take on, as long as they remain greater than zero, thus we do not place any bounds on the relationship between the dyad members.

¹⁰Initial conditions are the values of the variables at t = 0, before and after t = 0 the values of the variables can assume any positive value.

¹¹See Kadera (1998 and 2001) for other examples of simulations of differential equations in international relations research.

¹²There is no agreed-upon standard for the minimum number of simulations required to test a model. Reviewing past published works using this method shows a wide range in the total number of simulations, from a low of 15 to a high of 50. Unless the initial conditions are some how biased (non-random) there is no grounds for assuming more simulations would provide for different outcomes. Similar arguments are used regarding sample size in regression analyses.

¹³We can also compare the industrial war results with those for counterforce war and for peacetime rivalry. In the last column of Figure 1, the simulations indicate that j is no better off than it was in the other two scenarios. Its initial resource advantage (which comes about from reverse-time simulations) erodes, so it is left the underdog both economically and militarily.

¹⁴ Organski and Kugler (1980) find that the rising power is more likely to initiate conflict to speed the transition.

¹⁵This does assume that both states can directly attack the resources of the other power. It is possible for only one state to be able to fight an industrial war while the other must attempt to force a military victory. It is hoped that future alterations to the model will be able to incorporate this form of asymmetric advantage.

¹⁶Hirshleifer's (1988) model accounts for the degree to which states appropriate resources from the enemy or produce economic goods, and might therefore serve as a template for how to incorporate mixed forms of competition into the model.