Rationalist Explanations for War
International Organization, 1995 · paper · Political science
Examines why costly wars occur even among rational leaders who weigh costs and risks. Focuses on rationalist explanations of war rather than irrationality or leaders escaping its costs.
Checked: PDF from web.archive.org, fetched 5 Oct 2026. Page numbers are those of that PDF.
4 findings
Substance Lemma 2 (p. 412: 'the demand x is in the support of A's demand strategy given a message f only if there exists a c_i ∈ T such that x = p + c_i') is proved by 'deviating to x" = p + c_{i+1}'. That deviation is not feasible when p + c_{i+1} > 1, because demands lie in [0,1], and nothing restricts T to [0, 1−p]. The proof of the Proposition, which opens 'Suppose x* = p + c_k', has the same gap. A minor further point: k is used both for the constant demand in Lemma 3 ('x(f) = k') and for the type index c_k.
- p. 35 Lemma 3
x(f) = k, a constant
- p. 36 Proof of the proposition
Suppose x* = p + ck is the unique equilibrium demand
- p. 35 Appendix, Lemma 2 and its proof
deviating to x" = p + ci+1, since doing so has no effect on the risk of war.
- p. 36 Proof of the proposition, eq. (1)
Suppose x* = p + ck is the unique equilibrium demand in the game without talk.
Only the authors can say what is right here.
Judge's note: Checked pp. 410–413 (PDF 33–36) on the page images. Demands are x ∈ [0,1] (p. 411), and A's strategy is a distribution 'over [0, 1]' (p. 412). H is a distribution 'on the nonnegative real numbers' with strictly positive density (p. 410). T is a finite approximation of that distribution, and no assumption p + c_n ≤ 1 is stated. Claim 2(ii) treats the corner x* = 1 explicitly. My own working: if p + c_i < 1 < p + c_{i+1}, the move up to p + c_{i+1} that the Lemma 2 proof uses is infeasible, and the corner demand x = 1 can be strictly optimal. I checked the reviewer's example (p = 0.505, c_A = 0.1, c_i = i/100, uniform prior over 1001 types). Demanding 1 makes types i ≤ 49 fight: payoff (50*0.405 + 951)/1001 ≈ 0.970. Demanding p + c_49 = 0.995 makes types i ≤ 48 fight: payoff (49*0.405 + 952*0.995)/1001 ≈ 0.966. Every demand in (0.995, 1] has the same set of types that fight, so x = 1 is best among them. Then 1 is in the support of A's strategy (for example in babbling), yet 1 − p is not in T, so Lemma 2 is false as printed under the stated assumptions. The repair (use min{p + c_j, 1}, or assume c_n ≤ 1 − p) probably leaves the Proposition intact, but only the author can say which was intended. I add the reuse of k (Lemma 3's constant demand against the type index c_k on p. 413), which I confirmed on the images; it is cosmetic.
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Reference or label The same 1992 Berkeley Ph.D. dissertation (chap. 1) is titled "Threats to Use Force: Costly Signals and Bargaining in International Crises" in the acknowledgement note (p. 2) but "Threats to Use Force: The Role of Costly Signals in International Crises" in footnote 30 (p. 17).
- p. 2 Unnumbered acknowledgement footnote
"Threats to Use Force: Costly Signals and Bargaining in International Crises,"
- p. 17 Footnote 30
"Threats to Use Force: The Role of Costly Signals in International Crises," Ph.D. diss.
- p. 2 Unnumbered acknowledgement footnote
"Threats to Use Force: Costly Signals and Bargaining in International Crises," Ph.D. diss., University of California, Berkeley, 1992
- p. 17 Footnote 30
"Threats to Use Force: The Role of Costly Signals in International Crises," Ph.D. diss., University of California, Berkeley, 1992, chap. 1
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Judge's note: Both page images show the two titles as quoted. Author, degree, institution, year and chapter are the same, so this is one work cited two ways. The files cannot show which title is right; that is for the author to say.
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Reference or label Footnote 16 cites Perry, "An Example of Price Formation in Bilateral Situations," as "Econometrica 50 (March 1986), pp. 313–21". The March 1986 issue is volume 54.
- p. 11 Footnote 16
Econometrica 50 (March 1986), pp. 313-21
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Judge's note: Rests on outside knowledge: Perry's article appeared in Econometrica vol. 54, no. 2 (March 1986), pp. 313–21, and vol. 50 is the 1982 volume. The page image shows '50'.
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Wording On p. 413 the paper writes 'h(c_j, f) = h(c_j)m(f, c_j)/Pr(f) and H(c_j, f) = (1/Pr(f)) Σ_{i=0}^{j−1} h(c_i, f)'. Since h(c_i, f) is already the posterior (normalised by Pr(f)), the second expression divides by Pr(f) twice. Consistent with eq. (3), the summand should be h(c_i)m(f, c_i).
- p. 36 Proof of the proposition, line after eq. (2)
H(cj,f) = (1/Pr(f)) Σ h(ci, f)
- p. 35 Definition of posteriors
h(ci, f) ≡ Pr(cB = ci|f)
- p. 36 Appendix, proof of the Proposition, line after eq. (2)
H(cj, f) = (1/Pr(f)) Σ_{i=0}^{j−1} h(ci, f)
Only the authors can say what is right here.
Judge's note: On the p. 413 image the summand reads h(c_i, f). On p. 412, h(c_i, f) ≡ Pr(c_B = c_i | f) and H(c_i, f) ≡ Σ_{j<i} h(c_j, f). So H(c_j, f) = (1/Pr(f)) Σ h(c_i)m(f, c_i), and the printed line carries an extra 1/Pr(f). Eq. (3), obtained by multiplying by Pr(f), uses Σ h(c_i)m(f, c_i), which is the correct form. The slip is confined to this one intermediate line, and the Proposition stands.
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11 minor (typos and the like; most checked by the judge only)
Reference or label Footnote 42 cites Albertini on events "on the evening of the 27th" (July 1914) to "The Origins of the War of 1914, vol. 1, pp. 444–45", while footnotes 37–39 and 62 cite the July-crisis material to vol. 2.
- p. 21 Footnote 42
See Albertini, The Origins of the War of 1914, vol. 1, pp. 444-45.
- p. 20 Footnote 37-39
Luigi Albertini, The Origins of the War of 1914, vol. 2 (London: Oxford University Press, 1953), pp. 183-87.
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Judge's note: Rests on outside knowledge: Albertini's vol. 1 ends before Sarajevo, and vol. 2 covers the July 1914 crisis. Inside the paper, footnotes 37–39 cite vol. 2, pp. 158–187 for 18–21 July, and footnote 62 also cites vol. 2. So 'vol. 1' for 27 July looks like a volume slip. Only the authors can confirm it.
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Reference or label Footnote 64 cites Levy, "Preferences, Constraints, and Choices in July 1914," International Security 15 (Winter 1990/91), "pp. 234–36". The pages fall outside the article's page range.
- p. 30 footnote 64
International Security 15 (Winter 1990/91), pp. 234-36.
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Judge's note: Rests on outside knowledge: Levy's article occupies International Security 15(3), pp. 151–86. The page 30 image shows 'pp. 234–36'. No other page range for this article appears in the files.
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Wording Claim 2 says "the ex ante risk of war is always positive for small enough cA greater than zero", and the proof says "only in case (i) can this equal zero". Both fail at the boundary p = 1, which the model's p ∈ [0, 1] allows.
- p. 34 Claim 2 statement and last step of proof
it follows that only in case (i) can this equal zero, and for small enough cA case (i) cannot obtain.
- p. 10 Model setup
state A prevails with probability p ∈ [0, 1]
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Judge's note: Read pages 10, 33 and 34. cB has a distribution on the nonnegative reals, and B fights iff cB < x − p. With p = 1, every demand x ∈ [0,1] gives x − p ≤ 0, so Pr(fight) = H(x* − p) = H(0) = 0 for every cA > 0. Case (ii) gives x* = 1 = p, so the risk is zero outside case (i), which contradicts the proof step. For p < 1 with positive density, cases (ii) and (iii) give positive risk, so the result stands outside this degenerate boundary. Stating p < 1 would fix it.
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Wording The preventive-war text states "A will demand x_t = p2 + cB(1 − δ)" and that preventive war occurs "whenever ... δp2 − p1 > cB(1 − δ)²". This holds only if p2 + cB(1 − δ) ≤ 1, a condition that is not stated.
- p. 28 Preventive war model, text
A will demand x_t = p2 + cB (1 − δ) in the second period and in all subsequent periods t.
- p. 29 Preventive war condition
and indeed it will be whenever the following condition holds: δp2 − p1 > cB(1 − δ)².
Only the authors can say what is right here.
Judge's note: I reworked the steps from page images 28–29. B is indifferent when 1−x = 1−p2−cB(1−δ), giving x2 = p2+cB(1−δ). Attack beats acquiescing with x1=0 iff (1−p1)/(1−δ)−cB > 1+δ(1−x2)/(1−δ), which reduces to δp2−p1 > cB(1−δ)². The algebra is correct for an interior demand. But issue resolutions lie in [0,1], and costs are only assumed positive. Checked counterexample: δ=0.5, p1=0.1, p2=0.9, cB=1. Then x2 would be 1.4, so A demands 1 and B acquiesces (0 > −0.8). In period 1, acquiescing gives 1 and war gives 0.8, so there is no war, although the printed condition holds (0.35 > 0.25). The reasoning needs an unstated interior assumption; the main result stands for interior cases.
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Typo Footnote 5 spells Blainey's first name "Geoffry"; the text on p. 391 spells it "Geoffrey Blainey's well-known and often-cited argument".
- p. 6 Footnote 5
Geoffry Blainey, The Causes of War
- p. 14 Main text, 'Disagreements about relative power'
Geoffrey Blainey's well-known and often-cited argument
- p. 6 footnote 5
Geoffry Blainey
- p. 14 Disagreements about relative power
Geoffrey Blainey's well-known
Judge's note: Both images confirm the two spellings, so this is not an extraction artefact. The paper itself uses 'Geoffrey' in the text.
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Typo Footnote 5: "See Fritz Fisher, Germany's Aims in the First World War (New York: Norton, 1967)". The historian's surname is Fischer.
- p. 6 Footnote 5
See Fritz Fisher, Germany's Aims in the First World War
- p. 6 Footnote 5
See Fritz Fisher, Germany's Aims in the First World War (New York: Norton, 1967).
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Judge's note: Rests on outside knowledge: the author of Germany's Aims in the First World War is Fritz Fischer. The page image shows 'Fisher'.
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Typo Nalebuff's article is spelled "Brinksmanship and Nuclear Deterrence: The Neutrality of Escalation" in footnote 21 but "Brinkmanship and Nuclear Deterrence" in footnote 36.
- p. 14 Footnote 21
Nalebuff, "Brinksmanship and Nuclear Deterrence: The Neutrality of Escalation,"
- p. 20 Footnote 36
Nalebuff, "Brinkmanship and Nuclear Deterrence"
- p. 14 footnote 21
Brinksmanship and Nuclear Deterrence
- p. 20 footnote 36
Brinkmanship
Judge's note: Both page images show the two spellings. It is the same article: footnote 36 is the short form of footnote 21. The two spellings should be made the same.
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Typo Footnote 24: "Ralph K. White, Nobody Wanted War: Misperception in Vietnam and Other Wars (New York: Doubleday/Anchor), chap. 7" gives no publication year, unlike the other book citations.
- p. 15 Footnote 24
(New York: Doubleday/Anchor), chap. 7
Judge's note: The page image confirms that no year appears inside the parentheses. Lebow, in the same footnote, has '1981'.
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Typo Footnote 63: "Samuel Williamson, 'The Origins of World War I,' Journal of Interdisciplinary History (Spring 1988), pp. 795–818" gives no volume number, unlike the other journal citations.
- p. 30 Footnote 63
Journal of Interdisciplinary History (Spring 1988), pp. 795-818
Judge's note: The page 30 image confirms that no volume appears. Footnote 64 on the same page, for example, gives 'International Security 15'. The volume number itself (18) would rest on outside knowledge.
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Typo The proof of Claim 2 labels its cases "(i)", "(ii)", then "(3) any x* ∈ [p, 1] that solves", while the claim's statement uses (iii).
- p. 34 Proof of Claim 2
then x* = 1 maximizes uA(x); (3) any x* ∈ [p, 1] that solves
- p. 34 Proof of Claim 2, enumeration of cases
(3) any x* ∈ [p, 1] that solves
Judge's note: The page 34 image confirms '(3)' in the proof, where the statement of the claim has '(iii) otherwise'.
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Typo On p. 413 the definition 'where Pr(f) = Σ_{c∈T} h(c)m(f, c)) is the probability that B chooses f' has an unmatched closing parenthesis.
- p. 36 Proof of the proposition
Pr(f) = Σc∈T h(c)m(f, c))
Judge's note: The p. 413 image (PDF p. 36) shows 'h(c)m(f, c))' with an extra ')' and no matching opening parenthesis in the clause.
Second check: none (judge only)