The theory of games and the balance of power

World Politics

Volumn 38, Issue 4, 1986, Pages 546-576

  Wagner, R Harrison ^a  

^a NONE

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[No Author keywords available]

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EID: 84975994663     PISSN: 00438871     EISSN: 10863338     Source Type: Journal    
DOI: 10.2307/2010166     Document Type: Article

References (20)

1. Waltz, Theory of International politics (Reading, MA: Addison-Wesley, 1979), 117.
2. Leonce Donnadieu, Essai sur la theorie de l'é quilibre (Paris: A. Rousseau, 1900).
3. Riker, The Theory of Political Coalitions (New Haven: Yale University Press, 1962).
4. Partha Chatterjee, Arms, Alliances, and Stability (Delhi: Macmillan Company of India, 1975).
5. Morton Kaplan, Towards Professionalism in International Theory: Macrosystem Analysis (New York: Free Press, 1979).
6. Evidence for this assertion is presented in R. Harrison Wagner, “The Theory of Games and the Balance of Power,” Annual Meetings of the American Political Science Association, Washington, DC, September 1984 (subsequently revised).
7. Claude, Power and International Relations (New York: Random House, 1962), 112–13.
8. Friedrich von Gentz, Fragments Upon the Balance of Power in Europe (London: M. Peltier, 1806), 56–70
9. Donnadieu (fn. 2), 4.
10. Organski, World Politics (New York: Knopf, 1958), 271–338
11. A.F.K. Organski and Jacek Kugler, The War Ledger (Chicago: University of Chicago Press, 1980), 13–63.
12. Arthur Lee Burns, “From Balance to Deterrence: A Theoretical Analysis,” World Politics 9 (July 1957), 494–529.
13. For a discussion of this and related issues, see David Kreps and Robert Wilson, “Sequential Equilibria,” Econometrica 50 (July 1982), 863–94. I would like to acknowledge Robert Powell's help in defining the endpoints of this game and the players' payoff functions.
14. Burns (fn. 11). See also Morton Kaplan, Arthur Burns, and Richard Quandt, “Theoretical Analysis of the Balance of Power,” Behavioral Science 5 (July 1960), 240–52.
15. Both Robert Powell and Emerson Niou have independently pointed out to me that, if the victim is allowed to make a preemptive transfer of just enough resources to the unopposed attacker to give it R/2 units, it will lose fewer resources, and will thus prefer to make this transfer. Moreover, if the opposed attacker would like to acquire resources peacefully, then it, too, will prefer this outcome, and this, rather than the outcome described in the text, is the only equilibrium. (For a development of this idea, see Emerson M. S. Niou and Peter C. Ordeshook, “A Theory of the Balance of Power,” Journal of Conflict Resolution, forthcoming.) But what is necessary for the existence of this alternative equilibrium is not simply voluntary transfers, but transfers to which the opposed attacker has no opportunity to respond. Otherwise the reasoning in the text applies, and both the victim and the opposed attacker will prefer to join against the unopposed attacker if it tries to take advantage of the victim's offer. While the rules of the game do not allow voluntary transfers, therefore, the reasoning in the text is consistent with any means of transferring resources from the victim to the unopposed ally that allows the opposed ally to make a counter-offer before the transfer is completed.
16. The quantity of resources with which the victim is left is thus determined by the relation between the rate at which unopposed attackers can absorb resources from their victims and the time required for states to retarget their resources. That is the (somewhat artificial) implication of the particular assumptions made earlier. The specific form of the conclusion is less important than the general point: that the inability of states to prevent their allies from taking advantage of the division of their victims is an important factor in preserving the independence of the victims. The conflict between the U.S. and the U.S.S.R. that arose out of the question of the division of Germany is perhaps a relevant example. See R. Harrison Wagner. “The Decision to Divide Germany and the Origins of the Cold War,” International Studies Quarterly 24 (June 1980), 155–90.
17. Robert Gilpin, War and Change in World Politics (Cambridge and New York: Cambridge University Press, 1981).
18. Waltz (fn. 1), 164.
19. See, for example, Robert Jervis, “Cooperation under the Security Dilemma,” World Politics 30 (January 1978), 167–214.
20. In order to avoid misunderstandings, let me emphasize what should be obvious: that the game analyzed in this article is quite different from either a single-play or a repeated Prisoners' Dilemma game, and therefore the literature on international cooperation based on the analysis of Prisoners' Dilemma games is not relevant to the issues examined here. See also R. Harrison Wagner, “The Theory of Games and the Problem of International Cooperation,” American Political Science Review 77 (June 1983), 330–46.