Abstract
This paper analyzes a guns-versus-butter model in which two agents compete for control over an insecure portion of their combined output. They can resolve this dispute either peacefully through settlement or by military force through open conflict (war). Both types of conflict resolution depend on the agents’ arming choices, but only war is destructive. We find that, insofar as entering into binding contracts on arms is not possible and agents must arm even under settlement to secure a bigger share of the contested output, the absence of long-term commitments need not be essential in understanding the outbreak of destructive war. Instead, the ability to make short-term commitments could induce war. More generally, our analysis highlights how the pattern of war’s destructive effects, the degree of output insecurity and the initial distribution of resources matter for arming decisions and the choice between peace and war. We also explore the implications of transfers for peace.
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Notes
See Jackson and Morelli (2011) for a relatively recent survey of the literature. To the reasons suggested by Fearon (1995), they add (i) agency problems that arise when the leaders’ preferences are not aligned with those of their citizenry and (ii) problems in multilateral bargaining where coalitions can form to block any possible negotiated agreement that would benefit all.
See Powell (2006) for an extensive discussion of commitment problems, especially as they arise with expected shifts in power away from one party to another. Absent a means of enforcing current deals in the future, the party expecting to lose power in the future is compelled to engage in war today, despite a short-run preference for peace due to war’s destructive effects (see also Fearon 1998; Acemoglu and Robinson 2001). Others have emphasized that negotiated agreements made today can settle only a current dispute, so that maintaining peace over time requires repeated negotiations in the future. Because that involves the diversion of additional resources from production (e.g., arming), one or both sides might prefer to end the dispute today (or at least to severely weaken the opponent) by declaring war, again despite war’s destructive effects (Garfinkel and Skaperdas 2000; McBride and Skaperdas 2014).
See Garfinkel and Skaperdas (2007) for a survey of conflict models and their applications in economics.
If there were no differential destruction under open conflict, the two sides’ preferences over war and peace would be identical, with both sides always strictly preferring settlement to avoid war’s overall destructive effects. To the best of our knowledge, the implications of differential destruction for the endogenous choice between war and peace have never before been explored. Powell (1993), for example, similarly assumes differential destruction, but does not explore its implications for arming choices that would naturally influence, in turn, preferences over peace and war. While Grossman and Kim (1995) explore the implications of this assumption for defensive and predatory arming choices, their focus is on how one agent can arm sufficiently for defensive purposes to deter his rival from subsequently arming for predatory purposes.
Others have found similarly that war can emerge as an equilibrium outcome in a one-period setting, although the underlying mechanisms at play are different. Specifically, in Beviá and Corchón (2010) where war’s only costs are the resources dedicated to fighting and peace is costless, one agent might declare war as it forces a redistribution of resources in the victor’s favor, whereas peace maintains the status quo. Abstracting from arming choices but incorporating war’s destructive effects, Jackson and Morelli (2007) emphasize the role of political biases within a country, where the decision maker of the country stands to gain relatively more from a victory, to induce a war. In both analyses, assuming a proportional conflict technology (as we do), it is the poorer agent who stands to gain (on net) more from a redistribution of resources and thus is more inclined to declare war. In a one-period setting that, like ours, supposes settlement requires arming and is thus costly, Chang and Luo (2017) find that war can be preferred ex ante over settlement by both agents when war’s destructive effects depend positively on arming choices, since in this case war tends to induce less arming than settlement. Yet, that analysis does not consider the importance of the distribution of resource endowments.
See Skaperdas (1996) who axiomatizes a more general class of CSFs, \(\phi ^{i}(G^{i},G^{j})=f(G^{i})/\sum _{h=1,2}f(G^{h})\) for \(i\ne j=1,2\), where \(f(\cdot )\) is a non-negative and increasing function. Hirshleifer (1989) explores the properties of the ratio form, where \( f(G)=G^{a}\) with \(a\in (0,1]\), and of the difference form, where \(f(G)=e^{\alpha G}\) with \(\alpha >0\). For simplicity and tractability, we chose the ratio form with \(a=1\).
As discussed below, our central results to follow remain unchanged when both secure and insecure output are subject to overall destruction, \(1-\beta \).
In contrast, when the two sides settle peacefully, the transfer of output from one agent to the other involves no violent force and thus would not be subject to such additional damage.
See the proof to Proposition 1 in the online appendix.
To avoid cluttering of notation, we suppress the dependence of \({\widetilde{B}}_s^i\) on \(\kappa \), \(R^i\) and \({\bar{R}}\).
That only one agent i at most can be resource constrained follows since, by the definition of \({\bar{R}}\), \(R^j={\bar{R}}-R^i\) (\(j\ne i=1,2\)), such that \(R^i\in (0,R_L^s)\) implies \(R^j\in [R_H^s,{\bar{R}})\).
Observe from (6) that the maximum value of \(R_L^s\), which obtains when \(\kappa =0\), is precisely equal to this cutoff. Thus, for \(\kappa >0\), \(R_L^s<\frac{1}{4}{\bar{R}}\).
Once again, to avoid cluttering of notation, we suppress the dependence of \({\widetilde{B}}_c^i\) on \(\theta \), \(\gamma \), \(R^i\) and \({\bar{R}}\).
As shown in the online appendix, each agent’s arming choice can be, but need not be, monotonically related to his own endowment. In particular, we show there exists a \(\gamma _0\equiv \breve{\gamma }\left( \theta \right) \in (0,1)\) with \(\breve{\gamma }^{\prime }( \theta )<0\), such that for \(\gamma \in [\gamma _{0}\left( \theta \right) ,1)\), \(dG_{c}^{i}/dR^{i}>0\). Otherwise, we have \(\lim _{R^{i}\rightarrow R_{L}^{c}}dG_{c}^{i}/dR^{i}>0\), while \(\lim _{R^{i}\rightarrow R_{H}^{c}}dG_{c}^{i}/dR^{i}<0\). Nonetheless, the richer agent is more powerful in equilibrium.
Note that one can also visualize the effect of a decrease in \(\beta \) within Fig. 2b as a clockwise rotation of the payoff function at \(R^1=0\).
See the online appendix.
Specifically, let \(T^i\) denote the value of agent i’s resource that is contested and suppose it is independent of his endowment \(R^i\). Then, \(\beta (1-\kappa )(T^i + \gamma T^j)\) would be the value of agent i’s (\(i\ne j\)) prize under conflict and \((1-\kappa )(T^i + T^j)\) would the value of his prize under peace. The analysis goes through when we consider possible asymmetries in \(T^i\) and \(T^j\) for \(\gamma <1\). In this context, one could also consider asymmetries in the degree of security. While the functional dependence of guns on the distribution of resources and the various thresholds would change, the key insights on how destruction and the distribution of resources would affect the choice between peace and war would remain qualitatively intact.
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Acknowledgements
We thank Todd Sandler, William Shughart, Kostas Serfes, Ricardo Serrano-Padial, three anonymous referees and participants of the Eighth Conference on Political Violence and Policy (2018) at the University of Texas-Dallas, for useful comments.
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Garfinkel, M.R., Syropoulos, C. Problems of commitment in arming and war: how insecurity and destruction matter. Public Choice 178, 349–369 (2019). https://doi.org/10.1007/s11127-018-0601-x
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DOI: https://doi.org/10.1007/s11127-018-0601-x