Rationality in international relations: A game-theoretic and empirical study of the U.S.-China case

World Politics

Volumn 48, Issue 3, 1996, Pages 358-390

  Langlois, Catherine C ^a   Langlois, Jean Pierre P ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

GAME THEORY; GEOPOLITICAL RELATIONS; HISTORICAL PERSPECTIVE; INTERNATIONAL RELATIONS; MODELLING APPROACH; POLITICAL STRATEGY; RATIONAL BEHAVIOUR; SINO-AMERICAN RELATIONS;

CHINA; USA;

EID: 0029750141     PISSN: 00438871     EISSN: None     Source Type: Journal    
DOI: 10.1353/wp.1996.0012     Document Type: Article

References (74)

1. An extensive survey of that literature is given by Barry O'Neill, "A Survey of Game Models of Peace and War," in Robert Aumann and Sergiu Hart, eds., Handbook of Game Theory, vol. 2 (New York: Springer-Verlag, 1992).
2. Strategies are in subgame-perfect equilibrium (SGPE) if each is best against the other(s) in any contingency. The concept of SGPE comes from Reinhart Selten, "Re-examination of the Perfectness Concept for Equilibrium Points in Extensive Games," International Journal of Game Theory 4 (1975).
3. Robert Jervis, "Realism, Game Theory, and Cooperation," World Politics 40 (April 1988).
4. Loosely speaking, this means that players share the same expectation of future interaction, thus determining the path of future play. See James D. Morrow, Game Theory for Political Science (Princeton: Princeton University Press, 1994).
5. If each side punishes its opponent for not meeting its expectation, those expectations must be identical or they will remain hopelessly out of equilibrium. This requires a coordination of expectations.
6. Our characterization of SGPEs in Appendix 2 also suggests how to test whether countervailing strategies have been adopted, by searching in the data for traces of coordination. Such tests, performed on data for U.S.-China relations for the period 1972 to 1988 and reported in Appendix 4, support the hypothesis that a pure countervailing strategy rather than any other type of strategy was adopted by the two countries during the period under consideration.
7. In 2×2 games, if C denotes cooperate, D defect, and XY the choices X by row and Y by column, a Prisoner's Dilemma structure for row means his preferences satisfy DC > CC > DD > CD. There are several Deadlock-type games. The relevant one here satisfies DD > CD > DC > CC.
8. We refer here to the noncooperative models that assume individualistic actors.
9. O'Neill (fn. 1); Steven J. Brams and D. Marc Kilgour, Game Theory and National Security (New York: Basil Blackwell, 1988).
10. See Robert Powell, Nuclear Deterrence Theory: The Search for Credibility (New York: Cambridge University Press, 1990).
11. Robert Axelrod, The Evolution of Cooperation (New York: Basic Books, 1984).
12. The folk theorem asserts that any "individually rational" outcome (i.e., no worse than the minimax) can be supported by a trigger strategy equilibrium in a repeated game. See Drew Fudenberg and Eric Maskin, "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica 54 (1986).
13. For example, it is not enough to recognize that one's opponent has chosen to play a trigger strategy (which involves collaborating as long as the other players do and reverting to noncooperative play for a fixed number of turns to punish the opponent for deviating from cooperative play). Each player must understand which particular trigger strategy has been chosen (how many punishment turns and which precise outcome is considered as the cooperative point) and chose to adopt the same one, since, if not, the strategies do not form an equilibrium.
14. George W. Downs and David M. Rocke, Tacit Bargaining, Arms Races, and Arms Control (Ann Arbor: University of Michigan Press, 1990).
15. Jervis(fn. 3).
16. While countervailing is inherently reciprocative, the additional punishment of unexpected play could lead to retaliations for cooperative initiatives!. This paradox is inherent to all trigger strategy schemes in continuous games.
17. See, among others, George W. Downs, David M. Rocke and Randolph M. Siverson, "Arms Races and Cooperation," in Kenneth A. Oye, ed., Cooperation under Anarchy (Princeton: Princeton University Press, 1986); and Kenneth A. Oye, "Explaining Cooperation under Anarchy: Hypotheses and Strategies," in Oye, ed., Cooperation under Anarchy.
18. See, among others, George W. Downs, David M. Rocke and Randolph M. Siverson, "Arms Races and Cooperation," in Kenneth A. Oye, ed., Cooperation under Anarchy (Princeton: Princeton University Press, 1986); and Kenneth A. Oye, "Explaining Cooperation under Anarchy: Hypotheses and Strategies," in Oye, ed., Cooperation under Anarchy.
19. Francis A. Beer, "Games and Metaphors, "Journal of Conflict Resolution 30 (1986).
20. Axelrod(fn. 11).
21. See Charles W. Ostrom, "Evaluating Alternative Foreign Policy Decision-Making Models: An Empirical Test between Arms Race Models and an Organizational Politics Model," Journal of Conflict Resolution 21 (1977); Steven J. Majeski and David Jones, "Arms Race Modeling: Causality Analysis and Model Specification," Journal of Conflict Resolution 25 (1981); and Kendall D. Moll and Gregory Luebbert, "Arms Race and Military Expenditure Models: A Review," Journal of Conflict Resolution 24 (1980).
22. See Charles W. Ostrom, "Evaluating Alternative Foreign Policy Decision-Making Models: An Empirical Test between Arms Race Models and an Organizational Politics Model," Journal of Conflict Resolution 21 (1977); Steven J. Majeski and David Jones, "Arms Race Modeling: Causality Analysis and Model Specification," Journal of Conflict Resolution 25 (1981); and Kendall D. Moll and Gregory Luebbert, "Arms Race and Military Expenditure Models: A Review," Journal of Conflict Resolution 24 (1980).
23. See Charles W. Ostrom, "Evaluating Alternative Foreign Policy Decision-Making Models: An Empirical Test between Arms Race Models and an Organizational Politics Model," Journal of Conflict Resolution 21 (1977); Steven J. Majeski and David Jones, "Arms Race Modeling: Causality Analysis and Model Specification," Journal of Conflict Resolution 25 (1981); and Kendall D. Moll and Gregory Luebbert, "Arms Race and Military Expenditure Models: A Review," Journal of Conflict Resolution 24 (1980).
24. See William J. Dixon, "Reciprocity in United States-Soviet Relations: Multiple Symmetry or Issue Linkage?" American Journal of Political Science 30 (1986); and Michael D. Ward, "Cooperation and Conflict in Foreign Policy Behavior," International Studies Quarterly 26 (1982). See also Dina Zinnes, "Three Puzzles in Search of a Researcher," International Studies Quarterly 24 (1980); Bruce Russett, The Prisoner's Insecurity: Nuclear Deterrence, the Arms Race and Arms Control (San Francisco: W. H. Freeman, 1983); and Walter Isard and Charles Anderton, "Arms Race Models: A Survey and Synthesis," Conflict Management and Peace Science 8, no. 2 (1985).
25. See William J. Dixon, "Reciprocity in United States-Soviet Relations: Multiple Symmetry or Issue Linkage?" American Journal of Political Science 30 (1986); and Michael D. Ward, "Cooperation and Conflict in Foreign Policy Behavior," International Studies Quarterly 26 (1982). See also Dina Zinnes, "Three Puzzles in Search of a Researcher," International Studies Quarterly 24 (1980); Bruce Russett, The Prisoner's Insecurity: Nuclear Deterrence, the Arms Race and Arms Control (San Francisco: W. H. Freeman, 1983); and Walter Isard and Charles Anderton, "Arms Race Models: A Survey and Synthesis," Conflict Management and Peace Science 8, no. 2 (1985).
26. See William J. Dixon, "Reciprocity in United States-Soviet Relations: Multiple Symmetry or Issue Linkage?" American Journal of Political Science 30 (1986); and Michael D. Ward, "Cooperation and Conflict in Foreign Policy Behavior," International Studies Quarterly 26 (1982). See also Dina Zinnes, "Three Puzzles in Search of a Researcher," International Studies Quarterly 24 (1980); Bruce Russett, The Prisoner's Insecurity: Nuclear Deterrence, the Arms Race and Arms Control (San Francisco: W. H. Freeman, 1983); and Walter Isard and Charles Anderton, "Arms Race Models: A Survey and Synthesis," Conflict Management and Peace Science 8, no. 2 (1985).
27. See William J. Dixon, "Reciprocity in United States-Soviet Relations: Multiple Symmetry or Issue Linkage?" American Journal of Political Science 30 (1986); and Michael D. Ward, "Cooperation and Conflict in Foreign Policy Behavior," International Studies Quarterly 26 (1982). See also Dina Zinnes, "Three Puzzles in Search of a Researcher," International Studies Quarterly 24 (1980); Bruce Russett, The Prisoner's Insecurity: Nuclear Deterrence, the Arms Race and Arms Control (San Francisco: W. H. Freeman, 1983); and Walter Isard and Charles Anderton, "Arms Race Models: A Survey and Synthesis," Conflict Management and Peace Science 8, no. 2 (1985).
28. See William J. Dixon, "Reciprocity in United States-Soviet Relations: Multiple Symmetry or Issue Linkage?" American Journal of Political Science 30 (1986); and Michael D. Ward, "Cooperation and Conflict in Foreign Policy Behavior," International Studies Quarterly 26 (1982). See also Dina Zinnes, "Three Puzzles in Search of a Researcher," International Studies Quarterly 24 (1980); Bruce Russett, The Prisoner's Insecurity: Nuclear Deterrence, the Arms Race and Arms Control (San Francisco: W. H. Freeman, 1983); and Walter Isard and Charles Anderton, "Arms Race Models: A Survey and Synthesis," Conflict Management and Peace Science 8, no. 2 (1985).
29. Zinnes (fn. 21).
30. See John R. Freeman, John T. Williams, and Tse-Min Lin, "Vector Autoregression and the Study of Politics," American Journal of Political Science 33 (November 1989).
31. See Joshua S. Goldstein and John Freeman, "U.S.-Soviet-Chinese Relations: Routine Reciprocity, or Rational Expectations?" American Political Science Review 85 (March 1991); and idem, Three-Way Street: Strategic Reciprocity in World Politics (Chicago: University of Chicago Press, 1990).
32. See Joshua S. Goldstein and John Freeman, "U.S.-Soviet-Chinese Relations: Routine Reciprocity, or Rational Expectations?" American Political Science Review 85 (March 1991); and idem, Three-Way Street: Strategic Reciprocity in World Politics (Chicago: University of Chicago Press, 1990).
33. See John Williams and Michael McGinnis, "Sophisticated Reaction in the U.S.-Soviet Arms Race: Evidence of Rational Expectations," American Journal of Political Science 32 (November 1988).
34. See Michael McGinnis and John Williams, "Change and Stability in Superpower Rivalry," American Political Science Review 83 (December 1989).
35. Goldstein and Freeman (fn. 24,1990 and 1991); and Joshua S. Goldstein, "Great Power Cooperation under Conditions of Limited Reciprocity: From Empirical to Formal Analysis," International Studies Quarterly 39 (December 1995).
36. See James E. Shapiro et al., Direct Investment and Joint Ventures in China: A Handbook for Corporate Negotiators (New York: Quorum Books, 1991).
37. Ibid.
38. Gary Milholin and Gerard White, Bombs from Beijing: A Report on China's Nuclear and Missile Exports, report prepared for the House Foreign Affairs Committee, U.S. Congress, May 1991.
39. See Greg O'Leary, "China's Foreign Relations: The Reintegration of China into the World Economy," in Bill Brugger, ed., China since the Gang of Four (London: Crown Helm, 1980).
40. Well-known mixed-motive 2×2 games include the Prisoner's Dilemma, Chicken, and the Stag Hunt.
41. William G. Miller, The People's Republic of China's United Front Tactics in the United States, 1972-1988 (Bakersfield, Calif.: Charles Schlacks, 1988).
42. Golam W. Choudhury, China in World Affairs: The Foreign Policy of the PRC since 1970 (Boulder, Colo.: Westview Press, 1982).
43. Miller (fn. 33).
44. Harrison Wagner, "The Theory of Games and the Problem of International Cooperation," American Political Science Review 77 (1983), argues that games such as Harmony and Deadlock should be considered before any mixed-motive game. And in a game such as Deadlock, the very meaning of the term cooperate becomes questionable: if both sides prefer the defect-defect outcome, is this not mutual accommodation?
45. Goldstein and Freeman (fn. 24, 1990 and 1991).
46. ch = 1/2- UC/12, CU being the coded WEIS series representing Chinese behavior.
47. Countervailing does not require a Prisoner's Dilemma structure in order to succeed. Indeed, our empirical estimates for the pre-open-door period (1972-78) point to a different game that, although listed in exhaustive studies, has received little attention; see Steven J. Brams, Theory of Moves (Cambridge: Cambridge University Press, 1994). That game has a Nash equilibrium in which both sides defect, leaving one side (China) with its best outcome and the other (U.S.) with its next to worst. But countervailing succeeds in promoting a relatively cooperative outcome while providing an SGPE in that game.
48. When trying to define an initial date, the question is how far back one should consider past events and political regimes to be relevant to the day-to-day management of a relationship. By focusing on stationary strategies, we avoid this problem, although it is possible to reconstruct strategies that account for a starting date (see fn. 41).
49. 0 will be optimal against the U.S. countervailing strategy we describe below.
50. t's by a tough U.S. stand, the discounted values in (4) decrease as a result.
51. Recall that this means that play prescribed by such strategies maximizes discounted payoff regardless of the prior developments of the game.
52. us, > 0. But it is possible to relax this restriction and to consider Deadlock-type games.
53. t-1 as in (3a). Of course, the two approaches are equivalent.
54. Again we emphasize that payoff structures other than the Prisoner's Dilemma can be successfully dealt with using our countervailing approach. In other game structures the fear and temptation concepts do not necessarily apply and other relationships emerge.
55. All other remarks made about the robustness of the countervailing strategy (3a) extend to (14b). In particular, no U.S. strategy could promote a better steady state for the U.S.
56. us could also be written as a sum. The particular form chosen is for notational convenience when writing out China's move at time (t + 1) as a function of the past history of play.
57. ch. Such cross terms allow for estimation of a wider variety of payoff functions. However, the inferred coefficient on the cross term for the payoff functions were not found to be significantly different from zero.
58. The denominator 6 in the k-term accounts for the range. The use of monthly data leads to aggregation of events and a widening of the range of the data. This would magnify the denominator 6 and would not affect the rest of our analysis. Of course, we still need to assume some bounded interval to guarantee the boundedness of payoffs required by the theorem in Appendix 2.
59. An autoregression following (18) will identify the parameters of a countervailing strategy. As the main theorem in Appendix 2 demonstrates, strategies that form SGPEs are either countervailing or coordinated. If the players do not adopt a countervailing strategy but instead coordinate play, then the data should reveal punishing responses by each player. As mentioned above, we provide, in Appendix 3, a test of the hypothesis that China and the U.S. could be coordinating their moves rather than implementing countervailing strategies. The data do not support the hypothesis of coordination.
60. In that case, countervailing would not succeed in providing an SGPE. A finding of negative b-coefficients for both sides would therefore refute the countervailing hypothesis.
61. Jack E. Vincent, Project Theory (Landam: University Press of America, 1979); Goldstein and Freeman (fn. 24, 1990).
62. Joshua S. Goldstein, "A Conflict-Cooperation Scale for WEIS Events Data," Journal of 'Conflict Resolution 36, no. 2 (1992).
63. Such a restriction does not imply that the effects of an aggressive move will necessarily evaporate after six months. First, if the defector persists in an aggressive position, countervailing will continue and even deepen with time. And if the defector moves back to cooperation, the countervailing responses will only slowly reestablish cooperation.
64. See William Greene, Econometric Analysis (New York: Macmillan, 1993).
65. See Clive Granger and Paul Newbold, "Spurious Regressions in Econometrics," Journal of Econometrics 2 (1974).
66. It turns out that when the equations estimated for the period 1972 to 1978 are used to explain subsequent years, a break in the data is apparent about 1979 and is confirmed by a formal Chow test.
67. Even under the standard assumption of normal distribution for the coefficients estimated in (20), the resulting distribution of the b-coefficients is not normal since their derivation involves nonlinear transformations.
68. Brams (fn. 39).
69. Goldstein and Freeman (fn. 24, 1990 and 1991).
70. Goldstein and Freeman (fn. 21, 1991); and Goldstein (fn. 27, 1994).
71. 2).
72. i functions.
73. t+1, we may use either one in the equality of the second line of (31).
74. us≥0.