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² Organski and Kugler (fn. 1), 23.

³ Gilpin (fn. 1), 198.

⁴ Organski and Kugler (fn. 1), 19, 23.

⁵ Gilpin (fn. 1), 198, 186–87.

⁶ Ibid., 198–99.

⁷ Organski and Kugler (fn. 1), 46.

⁸ For similar views of the causes of systemic wars, see, for instance, Midlarsky, Manus, The Onset of World War (Boston: Unwin Hyman, 1988)Google Scholar; Thompson (fn. 1).

⁹ Selten, Reinhardt, “Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games,” International Journal of Game Theory 4, no. 1 (1975), 25–55.CrossRefGoogle Scholar

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¹¹ Lalman (fn. 10).

¹² The algebraic representation of the game's payoffs is found in Bruce Bueno de Mesquita and Lalman, David, War and Reason (New Haven: Yale University PressGoogle Scholar, forthcoming).

¹³ See ibid, for a more technical treatment of the relationship between the costs of war and the equilibrium conditions for war.

¹⁴ For proofs of the theorem, see ibid., and Mesquita, Bruce Bueno de and Lalman, David, “The Road to War is Strewn with Peaceful Intentions,” in Ordeshook, Peter, ed., Models of Strategic Choice in Politics (Ann Arbor: University of Michigan Press, 1989), 253–66.Google Scholar

¹⁵ For ease of presentation, assume that state B is risk-neutral or risk-averse. Let B be uncertain about its own and state A's subjective probability of success. Let B believe with probability β that A's probability of success is low enough that A will not retaliate if attacked. Then, using the notation explained in the Appendix, whether A actually prefers to retaliate or not, B will try to exploit A if β > [α^B + φ^B] / [I − (P^B)(G^B − L^B)]; and A, anticipating this exploitation, will prefer to start a war. A formal proof of this argument can be found in Bueno de Mesquita and Lalman (fn. 12).

¹⁶ The Treaty of Gastein was supposed to settle the remaining questions of sovereignty over Schleswig and Holstein that resulted from the Austro-Prussian defeat of Denmark in 1864. Article 1 of the treaty stipulates that the common right obtained by the high contracting parties by Article 3 of the Treaty of Vienna of the 30th of October, 1864, is transferred, as respects the Duchy of Holstein, to his Majesty the Emperor of Austria, and as respects the Duchy of Schleswig, to his Majesty the King of Prussia, without prejudice to the continuation of these rights of both Powers to the whole of both Duchies [emphasis added]. See Malet, Alexander, The Overthrow of the Germanic Confederation by Prussia in 1866 (London: Longmans, Green, 1870), 106–10.Google Scholar

¹⁷ The Economist, June 16, 1866, p. 699.

¹⁸ See, for instance, Hamerow, Theodore S., ed., The Age of Bismarck: Documents and Interpretations (New York: Harper & Row, 1973)Google Scholar; Holborn, Hajo, “Bismarck: Realpolitik,” Journal of the History of Ideas 21 (January-March 1960), 84–98CrossRefGoogle Scholar; and Simon, W. M., Germany in the Age of Bismarck (London: George Allen & Unwin, 1968).Google Scholar

¹⁹ Simon (fn. 18), 30 and 29 (emphasis added).

²⁰ Crankshaw, Edward, Bismarck (London: Macmillan, 1981), 197, 200.Google Scholar

²¹ For the characterization of crises, see Lalman (fn. 10); Powell (fn. 10); Brams, Steven and Marc Kilgour, D., “Are Crises Rational? A Game-Theoretic Analysis,” presented at the World Congress of the International Political Science Association, Washington, DC, August 28-September 1, 1988Google Scholar; Banks, Jeffrey, “Equilibrium Behavior in Crisis Bargaining Games,” photo dup. (1989), University of Rochester.Google Scholar

²² Department of Military History of the Prussian Staff, The Campaign of 1866 in Germany, trans. Colonel Von Wright and Captain Henry Hozier (London, 1907), 3. A similar sentiment regarding the Austrian penchant for exploitative behavior in negotiations is reflected in Taylor, A.J.P., The Habsburg Monarchy, 1809–1918 (Chicago: University of Chicago Press, 1976), 123–38.Google Scholar

²³ Crankshaw (fn. 20), 201.

²⁴ See A.J.P. Taylor (fn. 22), 133, for an illuminating discussion of Francis Joseph's treatment of the Croats in negotiations in December 1866; even after the Seven Weeks' War, Francis Joseph continued to use coercion in dealing with rivals he perceived to be much weaker.

²⁵ Showalter, Dennis E., Railroads and Rifles: Soldiers, Technology and the Unification of Germany (Hamden, CT: Archon Books, 1975), 52–73Google Scholar, 105–39; quote at 123.

²⁶ Ibid.; Pflanze, Otto, ed., The Unification of Germany, 1848–1871 (New York: Holt, Rinehart & Winston, 1968)Google Scholar; Simon (fn. 18); Palmer, Alan, Bismarck (London: Weidenfeld & Nicolson, 1976)Google Scholar; Hamerow (fn. 18); Grützner, Friedhelm, Die Politik Bismarcks, 1862 bis 1871 in der deutschen Geschichtsschreibung [The politics of Bismarck: 1862 to 1871 in German historiography] (Frankfurt am Main: Verlag Peter Lang, 1986).Google Scholar

²⁷ Kennedy (fn. 1), 163.

²⁸ Malet (fn. 16), XXII.

²⁹ Palmer (fn. 26), III.

³⁰ Taylor (fn. 22), 129.

³¹ Comparable indicators for Vienna cannot be utilized as the Austrian discount rate was fixed by the government rather than by auction and was not permitted to fluctuate frequently.

³² The Economist, April 7, 1866, p. 414, and May 5, 1866, p. 535.

³³ Simon echoes the sentiment of many historians when he writes, “it is important to remember that it was by no means a foregone conclusion that Prussia would win; pessimism was widespread in the Prussian camp, and the Austrian government was confident of victory” (fn. 18), 30–31. See also Taylor (fn. 22), 126, regarding expectations from the Austrian perspective, and Showalter (fn. 25), 121, for a general view of Prussian weaknesses.

³⁴ Taylor (fn. 22), 126ff.

³⁵ Michaelis, Herbert, “Königgrätz, 1866: Defeat of Liberalism and Universalism,” in Pflanze (fn. 26), 106–13.Google Scholar

³⁶ Taylor (fn. 22), 141. See also Simon (fn. 18) on the formation of Austria-Hungary as a consequence of the Seven Weeks' War.

³⁷ Grützner (fn. 26), 80. “Tatsächlich stürzte eine Welt ein, die Welt des Wiener Kongresses” (author's translation).

³⁸ Crankshaw (fn. 20), 219, 220–21.

³⁹ Illustrated London News 29 (July 14, 1866), quoted in Craig, Gordon A., The Battle of Königgrätz: Prussia's Victory over Austria, 1866 (Philadelphia: Lippincott, 1964).Google Scholar

⁴⁰ The Spectator (London) 39 (July 7, 1866), quoted in Craig (fn. 39).

⁴¹ Grützner (fn. 26), 80. “Die säkulare Bedeutung des Jahres 1866 unterschätzen viele deutsche Historiker der älteren Generation. … Dagegen wird heute der deutsche-französische Krieg eher als Epilog einer bereits 1866 inaugurierten Politik eingeordnet” (author's translation).

⁴² See, for instance, Simon (fn. 18), 22–38; Crankshaw (fn. 20), 189–223; Taylor (fn. 22), 123–40; Grützner (fn. 26), 80–117; Michaelis (fn. 35).

⁴³ The data for this assessment are drawn from Small, Melvin and David Singer, J., Resort to Arms: International and Civil Wars, 1816–1980 (Beverly Hills, CA: ).Google Scholar

⁴⁴ For a more detailed analysis of the anticipated costs of conflict in light of the theoretical expectations derived from the game, see Bueno de Mesquita and Lalman (fn. 12), and Mesquita, Bruce Bueno de, “Big Wars, Little Wars: Avoiding Selection Bias,” International Inter actions 16Google Scholar (forthcoming).

⁴⁵ See, for instance, Garnham, David, “Power Parity and Lethal International Violence,” journal of Conflict Resolution 20 (September 1976), 379–94CrossRefGoogle Scholar; Weede, Erich, “Overwhelming Preponderance as a Pacifying Condition among Contiguous Asian Dyads,” Journal of Conflict Resolution 20 (September 1976), 395–412CrossRefGoogle Scholar; Houweling, Henk and Siccarna, Jan, “Power Transitions as a Cause of War,” Journal of Conflict Resolution 32 (March 1988), 7–102CrossRefGoogle Scholar; Kim, Woosang, “Power, Alliance, and Major Wars, 1816–1975,” Journal of Conflict Resolution 33 (June 1989), 255–73.CrossRefGoogle Scholar

⁴⁶ For a full explanation and justification of these assumptions, see Bueno de Mesquita and Lalman (fn. 12).