A game-theoretic analysis of international trade and political conflict over external territories

See, e.g., Findlay and O’Rourke (2010), who discuss the general issues of natural resources, conflict and trade from an historical perspective. For other contributions that investigate resource-based disputes, see, e.g., Acemoglu et al. (2012), and Garfinkel et al. (2015).

For studies that present empirical evidence on the correlation between trade, conflict and related issues, see, e.g., Polachek (1992), Barbieri (1996), Barbieri and Levy (1999), Reuveny and Kang (1998), Polachek et al. (1999), Barbieri and Schneider (1999), Anderton and Carter (2001), Mansfield and Pollins (2001, 2003), Levy and Barbieri (2004), Kim and Rousseau (2005), and Glick and Taylor (2010).

The book by Mansfield and Pollins (2003) contains studies of the trade and conflict debate. The contribution by Oneal and Russett (1999) supports Polachek (1980) and shows that strengthening the extent of trade openness between contending countries effectively can reduce their conflicts in terms of overall armament expenditures. Nevertheless, some studies (e.g., Kim and Rousseau 2005) find that the pacifying effect of greater trade openness can be neutral; other studies (e.g., Barbieri 1996) find that extensive trade linkages may increase the probability of armed conflicts. Barbieri and Levy (1999) show that war does not have significant impacts on trading relationships between adversaries.

Conflicts between nations for valuable resources reflect international competition for rents through non-market means. We hypothesize that each nation has an aggregate payoff function and devotes efforts or resources into international rent-seeking activities (i.e., fighting) for more resources. We abstract our analysis from destruction costs. For studies on conflict that takes into account the endogeneity of destruction costs see, e.g., Sanders and Walia (2014), and Chang et al. (2015), and Chang and Luo (2017).

The modeling approach herein thus stands in contrast to the traditional assumption of "small open economies" in neoclassical international trade analysis, wherein trading nations accept the prices of tradable goods in their world markets under perfect competition.

We thank an anonymous referee for valuable suggestions to consider reinforcement of borders as part of arming expenditures. This makes trade costs to be determined endogenously determined by arming choices. To focus on disputes over an external territory, our analysis abstracts from conflict over national endowments, which are taken to be secured. That is, the analysis abstracts from border issues of the contending countries. Our simple analysis considers arming expenditures by each country as the number of guns required for occupying the territory so as to acquire its valuable resource or intermediate input for final good production. The term "trade costs" refers to the purely economic costs of engaging in bilateral trade according to the traditional international economics analysis. One advantage of this traditional treatment of trade costs is to see how economic decisions (in exporting and importing different final goods) affects military decisions (in terms of conflict-related resources allocated to armaments production). For ease of showing the relationship between trade decisions and military decisions, we consider trade costs to be exogenous in the analysis. The endogeneity of trade costs would add analytical complexity. We wish to pursuit this interesting extension in our future research.

For the case of symmetry in all dimensions that shall be discussed in the latter part of this section, we see that this inequality condition implies that \(Z < 4G,\) where \(G = G_{A} = G_{B} .\) The inequality condition then indicates that \(G > {Z \mathord{\left/ {\vphantom {Z 4}} \right. \kern-0pt} 4}.\) That is, each country's arming is strictly greater than a quarter of its national resource endowment.

That condition guarantees that the equilibrium prices and quantities of the final goods are positive under symmetry.

Note that country A's arming reaction curve, \(G_{A}^{S} (G_{B} ),\) is implicitly defined by its FOC that \({{\partial \varPi_{A} } \mathord{\left/ {\vphantom {{\partial \varPi_{A} } {\partial G_{A} }}} \right. \kern-0pt} {\partial G_{A} }} = 0\) and country B's arming reaction curve, \(G_{B}^{S} (G_{A} ),\) is implicitly defined by its FOC that \({{\partial \varPi_{B} } \mathord{\left/ {\vphantom {{\partial \varPi_{B} } {\partial G_{B} }}} \right. \kern-0pt} {\partial G_{B} }} = 0.\)

We thank an anonymous referee for valuable suggestions to discuss whether the arming levels are strategic substitutes or strategic complements. We find that they are strategic complements under symmetry. For the case in which there is asymmetry in national endowments, the arming levels may be strategic substitutes. We present the case of asymmetry in Sect. 3.

The parameter \(\delta\) may be used to represent the country size differential between A and B in that the higher the value of \(\delta\) the greater the size of country A relative to country B.

We owe thanks to an anonymous referee in providing us this important point for further study.

Garfinkel and Syropoulos (2017) examine the case where two adversaries do not trade with each other but do engage in trade with a third country. For issues on how the equilibrium outcome of a two-party conflict is altered by the strategic involvement of an outside party, see Chang et al. (2007), Chang and Sanders (2009), Sanders and Walia (2014). But these three studies do not consider the possibility of bilateral trade between adversaries.