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Achieving Cooperation under Anarchy: Strategies and Institutions

  • Robert Axelrod (a1) and Robert O. Keohane (a2)


Cooperation and discord in world politics are explained to a considerable extent by the three factors discussed in the Introduction: mutuality of interest, the shadow of the future, and the number of players. Yet the context of interaction, perceptions, and strategies is also important. Issues are linked to one another through multilevel games, which may be compatible or incompatible. Whether reciprocity constitutes an effective strategy depends both on linkages among issues and on the institutions within which negotiations take place. Perceptions are always significant and often decisive. Decision makers often actively seek to change the contexts within which they act by linking issues, trying to alter others' perceptions, establishing institutions, and promoting new norms. This finding suggests the importance of linking the upward-looking theory of strategy with the downward-looking theory of regimes.



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1 Lipson, , “International Cooperation in Economic and Security Affairs,” World Politics 37 (October 1984), 123.

2 Axelrod, Robert, “Conflict of Interest: An Axiomatic Approach,” Journal of Conflict Resolution ii (March 1967), 8799; and Conflict of Interest: A Theory of Divergent Goals with Applications to Politics (Chicago: Markham, 1970).

3 Jervis, Robert, “Cooperation under the Security Dilemma,” World Politics 30 (January 1978), 167214.

4 The definition of Prisoners' Dilemma also includes one additional restriction: CC > (DC + CD)/2. This is to ensure that it is better to have mutual cooperation than to have an even chance of being the exploiter or the exploited.

5 For an earlier discussion of contemporary events, using a common analytical framework to examine both economic and security relations, see Oye, , “The Domain of Choice,” in Oye, Kenneth A., Rothchild, Donald, and Lieber, Robert J., eds., Eagle Entangled: U.S. Policy in a Complex World (New York: Longman, 1979), 333.

6 Axelrod, Robert, The Evolution of Cooperation (New York: Basic Books, 1984).

7 Axelrod, Robert, “The Rational Timing of Surprise,” World Politics 31 (January 1979), 228–46.

8 Krasner, Stephen D., ed., International Regimes (Ithaca, NY: Cornell University Press, 1983); Keohane, Robert O., After Hegemony: Cooperation and Discord in the World Political Economy (Princeton: Princeton University Press, 1984).

9 Axelrod (fn. 6).

10 Lipson (fn. 1).

11 Osgood, Robert E. and Tucker, Robert W., Force, Order and Justice (Baltimore: Johns Hopkins University Press, 1967), esp. chap. 2, “The Expansion of Force.”

12 Keohane (fn. 8), 49–132.

13 Lipson, “Bankers' Dilemmas,” in this collection, 200–225.

14 Ruggie, John G., “Continuity and Transformation in the World Polity: Toward a Neorealist Synthesis,” World Politics 35 (January 1983), 261–85.

15 Ruggie, John G., “International Regimes, Transactions and Change: Embedded Liberalism in the Postwar Economic Order,” International Organization 36 (Spring 1982), 379 416, reprinted in Krasner (fn. 8), 195–231; Hirsch, Fred, “The Ideological Underlay of Inflation,” in Goldthorpe, John and Hirsch, Fred, eds., The Political Economy of Inflation (London: Martin Robertson, 1978), 263–84.

16 Keohane (fn. 8).

17 Hoffmann, Stanley, “International Organization and the International System,” International Organization 24 (Summer 1970), 389413.

18 Ernst B. Haas refers to this as “tactical” issue-linkage, contrasting it with “substantive” issue-linkage resulting from causal knowledge. See Haas, , “Why Collaborate? Issue-linkage and International Regimes,” World Politics 32 (April 1985), 357405, at 372. For a sophisticated analysis of tactical issue-linkage, see Michael McGinnis, “Issue Linkage and the Evolution of International Cooperation,” Journal of Conflict Resolution, forthcoming.

19 Tollison, Robert E. and Willett, Thomas D., “An Economic Theory of Mutually Advantageous Issue Linkage in International Negotiations,” International Organization 33 1979). 425–49.

20 Oye(fn. 5).

21 Schelling, Thomas C., The Strategy of Conflict (New York: Oxford University Press, 1960), 177.

22 Breslauer, George W., “Why Detente Failed: An Interpretation,” in George, Alexander L. and others, Managing U.S.-Soviet Rivalry: Problems of Crisis Prevention (Boulder, CO: Westview Press, 1983), 319–40; Gaddis, John L., “The Rise, Fall and Future of Detente,” Foreign Affairs 62 (Winter 1983/1984), 354–77; Stanley Hoffmann, “Detente,” in Nye, Joseph S., ed., The Maying of America's Soviet Policy (New Haven: Yale University Press for the Council on Foreign Relations, 1984), 231–64.

23 Oye (fn. 5), 17.

24 Winham, Gilbert, “Robert Strauss, the MTN, and the Control of Faction,” Journal of World Trade Law 14 (September-October 1985).

25 George, Alexander and Smoke, Richard, Deterrence in American Foreign Policy (New York: Columbia University Press, 1974).

26 Keohane, Robert O., “The Big Influence of Small Allies,” Foreign Policy, No. 2 (Spring 1971), 161–82.

27 Axelrod (fn. 6).

28 Consider the example of Stag Hunt, defined by the preference ordering of both players as CC > DC > DD > CD. If Player A is credibly committed to a strategy of reciprocity, beginning with cooperation, fi's incentives to cooperate are enhanced. A's commitment to cooperate ensures that B will not be double-crossed (which would leave B with the worst payoff). Furthermore, A's commitment to retaliate against defection ensures that any defection by B would lead, after the first move, not to B's second-best outcome (DC), but to its third-best outcome (DD). The game of Chicken provides another appropriate case in point. In Chicken, mutual cooperation is only the second-best outcome for both players, but mutual defection is worst for both. Thus, DC > CC > CD > DD. A credible strategy of reciprocity by Player A in Chicken ensures B of its second-best outcome if it cooperates, and guarantees that continual defection will in the long run provide it with its worst payoff. Assuming that fi's shadow of the future is sufficiently long, it should respond toil's strategy of reciprocity by cooperating.

29 Cline, “‘Reciprocity’: A New Approach to World Trade Policy?” Institute for International Economics, Policy Analyses in International Economics 2 (Washington: September 1982), 25.

30 Axelrod (fn. 6), 138.

31 For example, Tversky, Amos and Kahneman, Daniel, “Judgment under Uncertainty: Heuristics and Biases,” Science 185 (September 1974), 1112–31 Nisbet, Richard and Ross, Lee, Human Inference: Strategies and Shortcomings of Social Judgment (Englewood Cliffs, NJ: Prentice-Hall, 1985).

32 See references cited in fn. 22.

33 Evans, , The Kennedy Round in American Trade Policy: The Twilight of the GATT? (Cambridge: Harvard University Press, 1971), 3132.

34 See Keohane, Robert O., “Reciprocity in International Relations,” International Organization 40 (Winter 1986).

35 Axelrod (fn. 6), 138.

36 Jervis (fn. 31).

37 For example, Tversky, Amos and Kahneman, Daniel, “Judgment under Uncertainty: Heuristics and Biases,” Science 185 (September 1974), 1124–31 Nisbet, Richard and Ross, Lee, Human Inference: Strategies and Shortcomings of Social Judgment (Englewood Cliffs, NJ: Prentice-Hall, 1985).

38 Simon, , The Sciences of the Artificial (Cambridge: MIT Press, 2d ed. 1982), chap. 4,“The Architecture of Complexity,“p. 99.

39 Krasner (fn. 8), 3.

40 Keohane (fn. 8), chaps. 8–9.

41 Ibid., esp. chaps. 5–7.

42 Ruggie (fn. 15).

43 Aggarwal, Vinod, “The Unraveling of the Multi-Fiber Arrangement, 1981: An Examination of Regime Change,” International Organization 37 (Autumn 1983), 617–46; Yoffie, David B., Power and Protectionism: Strategies of the Newly Industrializing Countries (New York: Columbia University Press, 1983).

44 Young, Oran R., “Regime Dynamics: The Rise and Fall of International Regimes,” International Organization 36 (Spring 1982), 277–98; reprinted in Krasner (fn. 8), 93–114.

45 In After Hegemony (fn. 8), Robert Keohane has sought to show how game theory (which is “upward-looking”) can be combined fruitfully with the “downward-looking” theories of public goods and market failure to develop a functional theory of international regimes. But he has not formalized his theory, and has applied it only to the post-World War II international political economy.

* We would like to thank the other authors in this project for their helpful suggestions. Robert Axelrod gratefully acknowledges the financial support of the National Science Foundation and the Harry Frank Guggenheim Foundation.

Achieving Cooperation under Anarchy: Strategies and Institutions

  • Robert Axelrod (a1) and Robert O. Keohane (a2)


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