A Game Theoretic Analysis of the Politics of Taking It in Turns

British Journal of Political Science

Volumn 28, Issue 2, 1998, Pages 355-387

  Ward, Hugh ^a  

^a NONE

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EID: 0345763150     PISSN: 00071234     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (51)

1. J. Hartlyn, The Politics of Coalition Rule in Colombia (Cambridge: Cambridge University Press, 1988), pp. 63-5; J. Peeler, 'Elite Settlement and Democratic Consolidation: Colombia, Costa Rica and Venezuela', in J. Higley and R. Gunther (eds), Elites and Democratic Consolidation in Latin America and Southern Europe (Cambridge: Cambridge University Press, 1992), pp. 94-5.
2. J. Hartlyn, The Politics of Coalition Rule in Colombia (Cambridge: Cambridge University Press, 1988), pp. 63-5; J. Peeler, 'Elite Settlement and Democratic Consolidation: Colombia, Costa Rica and Venezuela', in J. Higley and R. Gunther (eds), Elites and Democratic Consolidation in Latin America and Southern Europe (Cambridge: Cambridge University Press, 1992), pp. 94-5.
3. Financial Times 27 February 1996.
4. R. A. Dahl, Polyarchy: Participation and Opposition (New Haven, Conn.: Yale University Press, 1971), p. 20.
5. A. Przeworski, Democracy and the Market: Political and Economic Reform in Eastern Europe and Latin America (Cambridge: Cambridge University Press, 1991), chap. 1.
6. R. Sugden, The Economics of Rights, Cooperation, and Welfare (Oxford: Blackwell, 1986), chap. 3 especially. Sugden makes use of the idea of evolutionarily stable equilibria, drawn from the application of game-theory to biology, to show how stable conventions may evolve through trial and error learning or selection when large numbers of randomly chosen pairs of players play games.
7. On the role of formal and legal structures in bolstering older, informal practices surrounding the rotation of access to irrigation water in arid parts of Spain, see E. Ostrom, Governing the Commons: The Evolution of Institutions for Collective Action (Cambridge: Cambridge University Press, 1990), pp. 69-82. For a discussion of heirarchical, negotiated and mixed solutions to co-ordination problems, see F. W. Scharpf, 'Games Real Actors Could Play: Positive and Negative Co-ordination in Embedded Negotiation', Journal of Theoretical Politics, 6 (1994), 27-53.
8. On the role of formal and legal structures in bolstering older, informal practices surrounding the rotation of access to irrigation water in arid parts of Spain, see E. Ostrom, Governing the Commons: The Evolution of Institutions for Collective Action (Cambridge: Cambridge University Press, 1990), pp. 69-82. For a discussion of heirarchical, negotiated and mixed solutions to co-ordination problems, see F. W. Scharpf, 'Games Real Actors Could Play: Positive and Negative Co-ordination in Embedded Negotiation', Journal of Theoretical Politics, 6 (1994), 27-53.
9. My account draws heavily on B. Greenhill, The Merchant Schooners (London: Conway Press, 1988), especially pp. 117-18 and pp. 126-7.
10. On the role of community in bolstering reciprocity practices, see M. J. Taylor, Community, Anarchy and Liberty (Cambridge: Cambridge University Press, 1982).
11. A. Rapoport and A. Chammah, Prisoner's Dilemma (Ann Arbor: University of Michigan Press, 1965).
12. R. Axelrod, The Evolution of Cooperation (New York: Basic Books, 1984), p. 10.
13. M. J. Taylor, The Possibility of Cooperation (Cambridge: Cambridge University Press, 1987), pp. 75-80.
14. A notable exception is G. Tsebelis, Nested Games: Rational Choice in Comparative Politics (Berkeley: University of California Press, 1990), pp. 175-84, where the idea that institutions within consociational democracy help solidify a form of taking in turns in which each major pillar of society gets its way when the issue is crucial to its interests is explored.
15. So called because no one can recall who first proved the result. For reviews of the literature, see H. Sabourian, 'Repeated Games: A Survey', in F. Hahn (ed.), The Economics of Missing Markets, Information, and Games (Oxford: Oxford University Press, 1989); and D. Fudenberg and J. Tirole, Game Theory (Cambridge, Mass.: MIT Press, 1992), chap. 5.
16. So called because no one can recall who first proved the result. For reviews of the literature, see H. Sabourian, 'Repeated Games: A Survey', in F. Hahn (ed.), The Economics of Missing Markets, Information, and Games (Oxford: Oxford University Press, 1989); and D. Fudenberg and J. Tirole, Game Theory (Cambridge, Mass.: MIT Press, 1992), chap. 5.
17. Taylor, The Possibility of Cooperation, p. 80.
18. R. Selten, 'Re-examination of the Perfectness Concept for Equilibrium Points in Extensive Games', International Journal of Game Theory, 4 (1975), 25-55.
19. Fudenberg and Tirole, Game Theory, p. 149.
20. J. Friedman, 'A Non Cooperative Equilibrium for Supergames', Review of Economic Studies, 38 (1971), 1-12.
21. 2) must hold - a highly unlikely occurrence. The threat implicit in B is not credible except along this knife-edge.
22. The essential features for ensuring subgame perfect equilibria are that players tempted to make a short-term gain by departing from the pattern should be punished and that there should be some
23. A. Lijphart, Democracies: Patterns of Majoritarian and Consensus Government in Twenty-One Countries (New Haven, Conn.: Yale University Press, 1984), chap. 1.
24. Another option here would be model the process as a Markov chain over the system states CD and DC, so that allowance could be made for such effects as incumbency bias in defining transition probabilities. Arguments about convergence in two-party systems might suggest that e = 1/2. However, the argument here is neither restricted to one-dimensional competition where voters have single-peaked preferences nor to pure office-seeking parties. There is no presupposition that all voters vote rationally, and differences in the size of blocks of identifiers may be related to different values of e.
25. ∞, rounds are still defined by the period before an election would have been held under the constitution that prevailed before the breakdown of democracy.
26. Whether we are dealing with a democracy if e is too low is an important normative issue. See K. Strom, 'Democracy as Political Competition', in G. Marks and L. Diamond, eds, Reexamining Democracy: Essays in Honor of Seymour Martin Lipset (Newbury Park, Calif.: Sage, 1992). The literature on democratic transitions suggests that moderate reformers must not have an overwhelming probability of winning future elections if stability is to be assured. See A. Przeworski, 'The Games of Transition', in S. Mainwaring, G. O'Donnell and J. S. Valenzuela, eds, Issues in Democratic Consolidation (Notre Dame, Ind.: University of Notre Dame Press, 1992), pp. xxx-xxx, at p. 121; G. O'Donnell and P. C. Schmitter, Transitions From Authoritarian Rule: Tentative Conclusions about Uncertain Democracies (Baltimore, Md.: The Johns Hopkins University Press, 1986), pp. 62-3. My conclusion here is similar to that reached by Przeworski - see Democracy and the Market, pp. 30-1.
27. Whether we are dealing with a democracy if e is too low is an important normative issue. See K. Strom, 'Democracy as Political Competition', in G. Marks and L. Diamond, eds, Reexamining Democracy: Essays in Honor of Seymour Martin Lipset (Newbury Park, Calif.: Sage, 1992). The literature on democratic transitions suggests that moderate reformers must not have an overwhelming probability of winning future elections if stability is to be assured. See A. Przeworski, 'The Games of Transition', in S. Mainwaring, G. O'Donnell and J. S. Valenzuela, eds, Issues in Democratic Consolidation (Notre Dame, Ind.: University of Notre Dame Press, 1992), pp. xxx-xxx, at p. 121; G. O'Donnell and P. C. Schmitter, Transitions From Authoritarian Rule: Tentative Conclusions about Uncertain Democracies (Baltimore, Md.: The Johns Hopkins University Press, 1986), pp. 62-3. My conclusion here is similar to that reached by Przeworski - see Democracy and the Market, pp. 30-1.
28. Whether we are dealing with a democracy if e is too low is an important normative issue. See K. Strom, 'Democracy as Political Competition', in G. Marks and L. Diamond, eds, Reexamining Democracy: Essays in Honor of Seymour Martin Lipset (Newbury Park, Calif.: Sage, 1992). The literature on democratic transitions suggests that moderate reformers must not have an overwhelming probability of winning future elections if stability is to be assured. See A. Przeworski, 'The Games of Transition', in S. Mainwaring, G. O'Donnell and J. S. Valenzuela, eds, Issues in Democratic Consolidation (Notre Dame, Ind.: University of Notre Dame Press, 1992), pp. xxx-xxx, at p. 121; G. O'Donnell and P. C. Schmitter, Transitions From Authoritarian Rule: Tentative Conclusions about Uncertain Democracies (Baltimore, Md.: The Johns Hopkins University Press, 1986), pp. 62-3. My conclusion here is similar to that reached by Przeworski - see Democracy and the Market, pp. 30-1.
29. There are, however, considerable differences between my own analysis and Przeworski's: (i) his analysis does not establish game-theoretic conditions for stability, because the full range of alternative strategies to adhering to the current election results is not considered; (ii) he does not analyse the credibility of the threat strategies that in his model implicitly face those who consider not adhering to an election result; (iii) he does not consider the implications of the multiplicity of equilibria that may exist, including power-sharing and equilibria associated with different rules giving different probabilities of success, so his model does not capture the commitment problem discussed in the next section.
30. The literature on transitions stresses that the constraints on the powers of government to reshape society, enshrined in broader social pacts, must not push the benefits of office holding, y, too low for moderate reformers, or else they will not play by the rules. See Przeworski, 'The Games of Transition', p. 127. Past experience of conflicts, which would arguably lead to lower values of w, seems to put pressure on elites to accept taking it in turns. See Burton, Higley and Gunther, 'Introduction: Elite Transformation and Domestic Regimes', p. 14; O'Donnell and Schmitter, Transitions From Authoritarian Rule, p. 31. In the model as (w - z) - the opportunity cost of accepting an election result which leaves you without office - increases, stability becomes less likely. Convergence between the ideologies of elites should reduce (w - z)and such convergence is known to be one factor promoting stability. See Burton, Higley and Gunther, 'Introduction: Elite Transformation and Domestic Regimes', pp. 24-30.
31. The literature on transitions stresses that the constraints on the powers of government to reshape society, enshrined in broader social pacts, must not push the benefits of office holding, y, too low for moderate reformers, or else they will not play by the rules. See Przeworski, 'The Games of Transition', p. 127. Past experience of conflicts, which would arguably lead to lower values of w, seems to put pressure on elites to accept taking it in turns. See Burton, Higley and Gunther, 'Introduction: Elite Transformation and Domestic Regimes', p. 14; O'Donnell and Schmitter, Transitions From Authoritarian Rule, p. 31. In the model as (w - z) - the opportunity cost of accepting an election result which leaves you without office - increases, stability becomes less likely. Convergence between the ideologies of elites should reduce (w - z)and such convergence is known to be one factor promoting stability. See Burton, Higley and Gunther, 'Introduction: Elite Transformation and Domestic Regimes', pp. 24-30.
32. The literature on transitions stresses that the constraints on the powers of government to reshape society, enshrined in broader social pacts, must not push the benefits of office holding, y, too low for moderate reformers, or else they will not play by the rules. See Przeworski, 'The Games of Transition', p. 127. Past experience of conflicts, which would arguably lead to lower values of w, seems to put pressure on elites to accept taking it in turns. See Burton, Higley and Gunther, 'Introduction: Elite Transformation and Domestic Regimes', p. 14; O'Donnell and Schmitter, Transitions From Authoritarian Rule, p. 31. In the model as (w - z) - the opportunity cost of accepting an election result which leaves you without office - increases, stability becomes less likely. Convergence between the ideologies of elites should reduce (w - z)and such convergence is known to be one factor promoting stability. See Burton, Higley and Gunther, 'Introduction: Elite Transformation and Domestic Regimes', pp. 24-30.
33. The literature on transitions stresses that the constraints on the powers of government to reshape society, enshrined in broader social pacts, must not push the benefits of office holding, y, too low for moderate reformers, or else they will not play by the rules. See Przeworski, 'The Games of Transition', p. 127. Past experience of conflicts, which would arguably lead to lower values of w, seems to put pressure on elites to accept taking it in turns. See Burton, Higley and Gunther, 'Introduction: Elite Transformation and Domestic Regimes', p. 14; O'Donnell and Schmitter, Transitions From Authoritarian Rule, p. 31. In the model as (w - z) - the opportunity cost of accepting an election result which leaves you without office - increases, stability becomes less likely. Convergence between the ideologies of elites should reduce (w - z)and such convergence is known to be one factor promoting stability. See Burton, Higley and Gunther, 'Introduction: Elite Transformation and Domestic Regimes', pp. 24-30.
34. J. C. Harsanyi and R. Selten, A General Theory of Equilibrium Selection in Games (Cambridge, Mass.: MIT Press, 1988).
35. T. C. Schelling, The Strategy of Conflict (Cambridge, Mass.: Harvard University Press, 1960).
36. 2) ≥ ax/(1 - a) which is equivalent to a ≥ (x - z)/(y - x). This condition is strong enough to ensure taking it in turns to free-ride is an equilibrium if (x - z)/(y - x) ≥ (w - z)/(y - w) or x(y - z) ≥ w(y ≥ z), which is true since x > w.
37. I conjecture that members of the classes {CD, CC} and {DC, CC} will be met with more rarely empirically than members of the class {CD, DC} because they are liable to be seen as unfair to the player who always has to co-operate, as the other player's payoff is always at least as high if not higher.
38. A possibility discussed in relation to rotating credit associations in T. Besley, S. Coate and G. Lonry, 'The Economics of Rotating Savings and Credit Associations', American Economic Review 83 (1993), 792-810, p. 793.
39. Compare J. M. Colomer, 'Transitions By Agreement: Modelling the Spanish Way', American Political Science Review, 85 (1991), 1283-302; Przeworski, Democracy and the Market, chap. 1; Przeworski, 'The Games of Transition'; G. Marks, 'Rational Sources of Chaos in Democratic Transitions', in Marks and Diamond, eds, Reexamining Democracy; Y. Cohen, Radicals, Reformers and Reactionaries: The Prisoner's Dilemma and the Collapse of Democracy in Latin America (Chicago: University of Chicago Press, 1994); J. M. Colomer and M. Pascual, 'The Polish Games of Transition', Communist and Post Communist Studies, 27 (1994), 275-94.
40. Compare J. M. Colomer, 'Transitions By Agreement: Modelling the Spanish Way', American Political Science Review, 85 (1991), 1283-302; Przeworski, Democracy and the Market, chap. 1; Przeworski, 'The Games of Transition'; G. Marks, 'Rational Sources of Chaos in Democratic Transitions', in Marks and Diamond, eds, Reexamining Democracy; Y. Cohen, Radicals, Reformers and Reactionaries: The Prisoner's Dilemma and the Collapse of Democracy in Latin America (Chicago: University of Chicago Press, 1994); J. M. Colomer and M. Pascual, 'The Polish Games of Transition', Communist and Post Communist Studies, 27 (1994), 275-94.
41. Compare J. M. Colomer, 'Transitions By Agreement: Modelling the Spanish Way', American Political Science Review, 85 (1991), 1283-302; Przeworski, Democracy and the Market, chap. 1; Przeworski, 'The Games of Transition'; G. Marks, 'Rational Sources of Chaos in Democratic Transitions', in Marks and Diamond, eds, Reexamining Democracy; Y. Cohen, Radicals, Reformers and Reactionaries: The Prisoner's Dilemma and the Collapse of Democracy in Latin America (Chicago: University of Chicago Press, 1994); J. M. Colomer and M. Pascual, 'The Polish Games of Transition', Communist and Post Communist Studies, 27 (1994), 275-94.
42. Compare J. M. Colomer, 'Transitions By Agreement: Modelling the Spanish Way', American Political Science Review, 85 (1991), 1283-302; Przeworski, Democracy and the Market, chap. 1; Przeworski, 'The Games of Transition'; G. Marks, 'Rational Sources of Chaos in Democratic Transitions', in Marks and Diamond, eds, Reexamining Democracy; Y. Cohen, Radicals, Reformers and Reactionaries: The Prisoner's Dilemma and the Collapse of Democracy in Latin America (Chicago: University of Chicago Press, 1994); J. M. Colomer and M. Pascual, 'The Polish Games of Transition', Communist and Post Communist Studies, 27 (1994), 275-94.
43. Compare J. M. Colomer, 'Transitions By Agreement: Modelling the Spanish Way', American Political Science Review, 85 (1991), 1283-302; Przeworski, Democracy and the Market, chap. 1; Przeworski, 'The Games of Transition'; G. Marks, 'Rational Sources of Chaos in Democratic Transitions', in Marks and Diamond, eds, Reexamining Democracy; Y. Cohen, Radicals, Reformers and Reactionaries: The Prisoner's Dilemma and the Collapse of Democracy in Latin America (Chicago: University of Chicago Press, 1994); J. M. Colomer and M. Pascual, 'The Polish Games of Transition', Communist and Post Communist Studies, 27 (1994), 275-94.
44. Compare J. M. Colomer, 'Transitions By Agreement: Modelling the Spanish Way', American Political Science Review, 85 (1991), 1283-302; Przeworski, Democracy and the Market, chap. 1; Przeworski, 'The Games of Transition'; G. Marks, 'Rational Sources of Chaos in Democratic Transitions', in Marks and Diamond, eds, Reexamining Democracy; Y. Cohen, Radicals, Reformers and Reactionaries: The Prisoner's Dilemma and the Collapse of Democracy in Latin America (Chicago: University of Chicago Press, 1994); J. M. Colomer and M. Pascual, 'The Polish Games of Transition', Communist and Post Communist Studies, 27 (1994), 275-94.
45. O'Donnell and Schmitter, Transitions from Authoritarian Rule, p. 15.
46. See M. Burton, R. Gunther and J. Higley, 'Elites and Democratic Consolidation in Latin America and Southern Europe: An Overview', in Higley and Gunther, eds, Elites and Democratic Consolidation in Latin America and Southern Europe, p. 334; Przeworski, 'The Games of Transition', pp. 116-26.
47. See M. Burton, R. Gunther and J. Higley, 'Elites and Democratic Consolidation in Latin America and Southern Europe: An Overview', in Higley and Gunther, eds, Elites and Democratic Consolidation in Latin America and Southern Europe, p. 334; Przeworski, 'The Games of Transition', pp. 116-26.
48. T. Hobbes, Leviathan, edited by C. B. Macpherson (Harmondsworth, Middx.: Penguin, 1968), p. 196, pp. 204-5.
49. H. Ward, 'Testing the Waters: Taking Risks to Gain Reassurance in Public Goods Games', Journal of Conflict Resolution, 33 (1989), 274-308, p. 281.
50. For reviews of the relevant literature and related topics, see H. Nurmi, 'Problems in the Theory of Institutional Design: An Overview', Journal of Theoretical Politics, 5 (1993), 523-40; R. E. Goodin, ed., The Theory of Institutional Design (Cambridge: Cambridge University Press, 1995).
51. For reviews of the relevant literature and related topics, see H. Nurmi, 'Problems in the Theory of Institutional Design: An Overview', Journal of Theoretical Politics, 5 (1993), 523-40; R. E. Goodin, ed., The Theory of Institutional Design (Cambridge: Cambridge University Press, 1995).