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Peace and war in territorial disputes

05 Jul 2004-National Bureau of Economic Research (National Bureau of Economic Research)-Vol. 2004
TL;DR: In this article, the authors explore a class of answers to why sovereign states sometimes fail to settle territorial disputes peacefully and also why even peaceful settlements of territorial disputes rarely call for the resulting border to be unfortified.
Abstract: Why do sovereign states sometimes fail to settle territorial disputes peacefully? Also, why do even peaceful settlements of territorial disputes rarely call for the resulting border to be unfortified? This paper explores a class of answers to these questions that is based on the following premise: States can settle a territorial dispute peacefully only if (1) their payoffs from a peaceful settlement are larger than their expected payoffs from a default to war, and (2) their promises not to attack are credible. This premise directs the analysis to such factors as the advantage of attacking over both defending and counterattacking, the divisibility of the contested territory, the possibility of recurring war, the depreciation or obsolescence of fortifications, and inequality in the effectiveness of mobilized resources.

Summary (3 min read)

Introduction

  • Recognition of the problem of credibility also suggests an answer to the question of why borders are usually fortified:.
  • Fortifications can help to make a peaceful settlement credible.

Analytical Framework

  • Assume that two sovereign states, State 1 and State 2, face a newly arisen dispute over control of a valuable territory.
  • A war would give each state a non-negative probability of winning control of the entire contested territory.
  • In addition the analysis assumes that in choosing its strategy set each state takes the other state’s strategy set as given.
  • The two states put the same value on controlling the contested territory.
  • Eventually the analysis relaxes each of these working assumptions.

The Consequences of a Default to War

  • Equation (1) says that the expected payoff for State i from a default to war equals the product of the probability that it would win the war and the value of having permanent control of the contested territory, minus the amount that it would spend to mobilize resources.
  • Equation (2) incorporates both the assumption that the dispute is newly arisen and, hence, that the contested territory is initially unfortified and the working assumption that the states have the same effectiveness of amounts spent to mobilize resources.
  • 7This first-order condition, as well as other first-order conditions specified below, accords with the as- sumption that neither state faces a binding constraint on its ability to mobilize resources.
  • Equations (4) imply that in a default to war spending to mobilize resources would dissipate half of the value of having permanent control of the contested territory.

A Peaceful Settlement

  • Suppose that these states, seeking an alternative that is preferable to a default to war, were to attempt to settle their territorial dispute peacefully.
  • Specifically, suppose that these states were to consider a peaceful settlement with three provisions: If R∗i equals zero, then the border is unfortified.
  • Given the working assumption that the whole of the territory is neither more not less valuable than 8Powell (1993) considers the possibility of a peaceful settlement with a fortified border, but in this analysis he takes the division of the contested territory as given, rather than as subject to negotiation as in the present analysis.

The Expected Payoff from Attacking

  • Given that the states choose their strategy sets to maximize their expected payoffs, a promise by State i not to attack would be credible only if the expected payoff for State i from keeping its promise would at least as large as its expected payoff from breaking its promise and attacking.
  • The specification that γ is smaller than θ formalizes the assumption that attacking has an advantage over counterattacking.

Credibility Conditions

  • Equivalently the authors can express this credibility condition as (16) ki ≥ Zi, where Zi ≡ Ñi +R ∗ i V . 10 If condition (16) is satisfied, then for State i the payoff from a peaceful settlement is at least as large as the expected payoff from attacking.
  • 9,10 9 But, if condition (18) is satisfied, then the authors can presume that the promises of both states not to attack serve to allow the states to coordinate on this equilibrium.
  • Suppose that the ratio γ/θ does not satisfy condition (18).
  • If a peaceful settlement with an unfortified border would not be credible, but if amounts spent to construct fortifications would be sufficiently effective relative to amounts spent to mobilize resources for an attack, then the states can reach a peaceful settlement with a fortified border that is credible and preferable to a default to war.
  • The converse of Propositions (I) and (II) is also worth emphasizing.

Divisibility

  • The authors now turn to relaxing their working assumptions, beginning with the assumption that the whole of the territory is neither more nor less valuable than the sum of its parts.
  • Using condition (6σ) suppose that σ is equal to or smaller than one half.
  • Thus, condition (6σ) implies that, if σ were equal to or smaller than one half, then, because the winner of a war would control the entire contested territory, the payoff from a peaceful settlement, even with the resulting border unfortified, could not be larger for both states than the expected payoff from a default to war.
  • Thus, the authors have the following extension of Proposition (III): (IIIσ).
  • If the whole of the contested territory is worth sufficiently more than the sum of its parts, then the states cannot reach a peaceful settlement, with the resulting border either unfortified or fortified, that would be preferable to a default to war.

A Recurring Possibility of War

  • So far the authors have assumed that a war would settle the territorial dispute permanently.
  • Condition (18) implies that, under the assumption that the winner of a war would get permanent control of the contested territory, a credible peaceful settlement with an unfortified border would not be possible with γ equal to zero.
  • As in the standard theory of repeated games, assume that, with states facing a recurring possibility of war, as long as both states keep their promises not to attack, they can continue to make credible promises not to attack.
  • Condition (18ρ) implies the following extension of Proposition (I).

Depreciation and Obsolescence

  • The authors now turn to the working assumption that fortifications neither depreciate nor become obsolete.
  • The working assumption that fortifications neither depreciate nor become obsolete corresponds to the limiting case of δ equal to zero.
  • With fortifications having to be rebuilt periodically, the payoff for State i from a peaceful settlement that required an initial expenditure of R∗i on fortifications would be kiV − R∗i /(1− δ).
  • Depreciation and obsolescence of fortifications obviously do not affect the possibility of a credible peaceful settlement with an unfortified border.
  • The quadratic equation obtained by setting Z1+Z2, as implied by equation (19δ), equal to one implies that the minimum values of R∗1 and R ∗ 2 that would satisfy the condition,.

Unequal Effectiveness of Amounts Spent to Mobilize Resources

  • Finally the authors come to the working assumption that the two states have the same effectiveness of amounts spent to mobilize resources.
  • Consider again the possibility of a peaceful settlement with an unfortified border.
  • If, in addition, γi and γj can be unequal, then equation (9), the contest-success function that applies in the event that State i were to break its promise not to attack, becomes, with R∗j equal to zero, (9u) p̃i = θiR̃i θiR̃i + γjR∗∗j .
  • But, condition (18u) also implies that, if the average of γ2/θ1 and γ1/θ2 were equal to √ 2− 1, but if γ2/θ1 was not equal to γ1/θ2, then a credible peaceful settlement with an unfortified border would not be possible.
  • This proposition follows from the nonlinearity of the contest-success functions.

Summary

  • This paper has analyzed a choice-theoretic model in which a territorial dispute between sovereign states can afford either a peaceful settlement with an unfortified border, or, if not, perhaps a peaceful settlement with a fortified border, or possibly only a default to war.
  • The following are the main results of their analysis: A large advantage of attacking over counterattacking precludes a peaceful settlement with an unfortified border.

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