The Predictioneer’s Game: Using the Logic of Brazen Self-Interest to See and Shape the Future

by Bruce Bueno De Mesquita

  Structure of the Game: Sketch of One of N2–N Stage

  Games Played Simultaneously

  A and B uncertain whether other will retaliate if coerced

  A and B uncertain whether other will coerce if given the chance

  In playing the game, each player’s initial move is to choose whether to make proposals. A proposal is expressed as a demand that another player accept some specific change in his position that is favorable to the demander. Players choose proposals designed to maximize their welfare at the end of the stage game. In practice, this means choosing proposals that make the other players indifferent between imposing costs on the demander and preferring a negotiated compromise instead. Of course, the endogenous selection of proposal values must take into account player beliefs about their rival’s type.

  Payoffs are calculated as follows:

  Let the probability that A prevails in an iteration of the game vs.

  C is the potential clout or influence of each stakeholder, S is the salience each stakeholder attaches to the issue, and U denotes utility with the first subscript indicating whose utility is being evaluated and the second vis-à-vis which other player’s approach to the issue.

  Let X1k = player K’s policy preference on the issue; Let X2k = player K’s preference over reaching agreement or being resolute on the issue.

  Let A’s utility for B’s approach to the issue with that is, the model assumes that players prefer a mix of gains based on sharing resolve or flexibility to settle and based on the issue outcome sought over fully satisfying themselves on one dimension while getting nothing on the other. The structure of the utility of proposals is comparably computed but with positions chosen endogenously rather than necessarily being either player’s policy position.

  The model assumes four sources of costs:

  (1) α, the cost of trying to coerce and meeting resistance; (2) τ, the cost of being coerced and resisting; (3) γ, the cost of being coerced and not resisting; and (4) , the cost of coercing; that is, the cost of failing to make a credible threat that leads the foe to acquiesce. It also allows all of the input variables to change (doing so in accordance with heuristic rules I impose on the game). That is, the model is designed so that player clout, salience, resolve, and position shift from iteration to iteration in response to the equilibrium conditions of the prior round of play. Because alternative heuristic rules chosen by others are likely to be as sensible and reliable as mine either for evaluating costs or for assessing how variable values change across periods of play, I do not dwell here on those aspects of the model.

  With these values in hand, here are the expected payoffs at terminal nodes in the first iteration:

  D* and R* denote, respectively, the belief that the subscripted player is a dove and a retaliator. These beliefs are updated in accordance with Bayes’ Rule. Off-the-equilibrium path beliefs are set at 0.5.

  Proposals go back and forth between players, but not all proposals are credible. They are credible if the Outcome involves B giving in to A’s coercion or if the absolute value of the proposal being made minus the target’s current position relative to the range of available policy differences is less than the current resolve score of the target, with resolve defined in the next section.

  The predicted new position of each player in a given round is determined as the weighted mean of the credible proposals it receives and the predicted outcome is the weighted mean of all credible proposals in the round, smoothed as the average of the weighted means including the adjacent rounds just before and after the round in question. The nature of the proposal in each dyadic game is determined by the equilibrium outcome expected in that stage of the game. The weighted mean reflects the credibly proposed positions weighted by clout multiplied by salience.

  Phew, I hope the math mavens enjoyed that and the rest of you didn’t mind it too much.

  Notes

  Introduction

  1. See Bruce Bueno de Mesquita, “Leopold II and the Selectorate: An Account in Contrast to a Racial Explanation,” Historical Social Research [Historische Sozialforschung] 32, no. 4 (2007): 203-21.

  2. Vernon Mallinson, “Some Sources for the History of Education in Belgium,” British Journal of Educational Studies 4, no. 1 (November 1955): 62-70.

  3. See, for instance, Joseph Conrad, Youth, and Two Other Stories (New York: McClure, Phillips, 1903); Barbara Emerson. Leopold II of the Belgians: King of Colonialism (London: Weidenfield and Nicolson, 1979); Peter Forbath, The River Congo (New York: Harper and Row, 1977); and Adam Hochschild, King Leopold’s Ghost (Boston: Mariner Books, 1999).

  4. The discussion that follows is based on the logic and evidence provided in Bruce Bueno de Mesquita, Alastair Smith, Randolph M. Siverson, and James D. Morrow, The Logic of Political Survival (Cambridge, Mass.: MIT Press, 2003). See especially chapter 7. See also Bruce Bueno de Mesquita and Alastair Smith, “Political Survival and Endogenous Institutional Change,” Comparative Political Studies 42, no. 2 (February 2009): 167-97.

  5. Petty dictators typically also have a pot of money that can be spent at their sole discretion. Democratic leaders have far less authority over spending. Discretionary funds can be used to benefit the citizenry or can be socked away in a secret bank account. One way to recognize civic-mindedness is to see how many benefits the public has compared to expectations, given the type of regime. Singapore’s Lee Kwan Yew and Chinas Deng Xiaoping, for instance, seem to have been genuinely civic-minded. They implemented effective public policies while sustaining the loyalty of their essential supporters. Kim Jong Il, Robert Mugabe, and Supreme Leader Ali Khamenei, in contrast and to varying degrees, seem not so civic-minded. See Bueno de Mesquita, Smith, Siverson, and Morrow, Logic of Political Survival.

  6. Stanley Feder, “Factions and Policon: New Ways to Analyze Politics,” in H. Bradford Westerfield, ed., Inside CIA’s Private World: Declassified Articles from the Agency’s Internal Journal, 1955—1992 (New Haven: Yale University Press, 1995), and James L. Ray and Bruce M. Russett, “The Future as Arbiter of Theoretical Controversies: Predictions, Explanations and the End of the Cold War,” British Journal of Political Science 26, no. 4 (October 1996): 441-70.

  Chapter 1: What Will It Take to Put You in This Car Today?

  1. See the Jobs Rated Almanac ratings at http://www.egguevara.com/shopping/articles/jobsrated.html.

  2. If you think body language is not important, do a search online for “negotiation and body language.” You will find article after article about how close sellers should place themselves to buyers, how they should use their hands and arms, facial expressions, etc. to improve the price they get and the odds of closing deals.

  Chapter 2: Game Theory 101

  1. John von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior (Princeton: Princeton University Press, 1947).

  2. Sylvia Nasar, A Beautiful Mind: The Life of Mathematical Genius and Nobel Laureate John Nash (New York: Simon & Schuster, 1998). For progressively more thorough and technical introductions to game theory, starting with a completely readable nontechnical treatment, see Avinash K. Dixit and Barry J. Nalebuff, Thinking Strategically: The Competitive Edge in Business, Politics and Everyday Life (New York: W. W. Norton, 1991); James D. Morrow, Game Theory for Political Scientists (Princeton: Princeton University Press, 1994); Martin J. Osborne, An Introduction to Game Theory (Oxford: Oxford University Press, 2003); and Drew Fudenberg and Jean Tirole, Game Theory (Cambridge, Mass.: MIT Press, 1991).

  3. Six dollars per day falls in the middle of the World Banks estimate of per capita income for Iraq in 2007. Unlike for most countries, for Iraq the World Bank is not able to provide a firm number. Other estimates seem to be based on the World Banks range.

  4. Brian Kolodiejchuk, ed., Mother Teresa: Come Be My Light—The Private Writings of the Saint of Calcutta (New York: Doubleday, 2007).

  5. See Irene Hau-siu Chow, Victor P. Lau, Thamis Wíng-chun Lo, Zhenquan Sha, and He Yun, “Service Quality in Restaurant Oper
ations in China: Decision- and Experiential-Oriented Perspectives,” International Journal of Hospitality Management 26, no. 3 (September 2007): 698-710.

  6. For the math mavens out there, the circle is a special case in which each dimension is of equal importance to the player. If one dimension is more important than the other, then we should draw an ellipse, each of whose radii reflects the relative importance of the issues. I skip this complicating detail here.

  7. Those mathematically inclined and interested in delving more deeply into how it is possible for rational decision makers to move from any policy combination to any other, see Richard McKelvey, “Intransitivities in Multidimensional Voting Models and Some Implications for Agenda Control,” Journal of Economic Theory 12 (1976): 472-82; Richard McKelvey, “General Conditions for Global Intransitivities in Formal Voting Models,” Econometrica 47 (1979): 1085-1112; and Norman Schofield, “Instability of Simple Dynamic Games,” Review of Economic Studies 45 (1978): 575-94.

  8. For a careful study of steroid use that is broadly consistent with the values used in this example, see Jenny Jakobsson Schulze, Jonas Lundmark, Mats Garle, Ilona Skílvíng. Lena Ekström, and Anders Rane, “Doping Test Results Dependent on Genotype of Uridine Diphospho-Glucuronosyl Transferase 2B17, the Major Enzyme for Testosterone Glucuronidation,” Journal of Clinical Endocrinology & Metabolism 93, no. 7 (July 2008): 2500-2506. Based on the values in this study, about 9 percent of a random sample from the population would falsely test positive. I assume 10 percent.

  9. Bayes’ Theorem allows us to answer the question “What is the probability a person is of a particular type (such as a performance enhancing steroid user) given that they say or do something in particular (such as test positive for steroids)?” To answer this question we must solve the following calculation: Let P stand for probability, R for being a steroid user, S for testing positive, and ˜R for being the type of baseball player who does not use steroids. The straight line symbol | is read as “given.” Then P(R | S) = read as “the probability of being a steroid user given that you tested positive (P[R | S]) equals the probability of testing positive given that you are a steroid user times the probability of being a steroid user divided by that same quantity plus the probability of testing positive given that you are not a steroid user times the probability that you are not a steroid user.” Thus, the calculation is conditioned on the two sets of people who test positive: those who use steroids and those who don’t. In the baseball example this translates into

  Chapter 3: Game Theory 102

  1. The first major efforts to show that arms races lead to war are the work of Lewis Fry Richardson, a distinguished meteorologist who predicted World War I but, using the same logic, failed to anticipate World War II. See his Arms and Insecurity (Chicago: Quadrangle, 1960). The literature tying arms races to war is vast but almost universally fails to consider that arms purchases are anticipatory, or, in game-theory lingo, they are endogenous, strategic decisions.

  2. The subject of renegotiation-proofness has attracted the interest of many economists, leading to a vast literature. Some seminal papers include Dilip Abreu, David Pearce, and Ennio Stacchetti, “Renegotiation and Symmetry in Repeated Games,” Journal of Economic Theory 60, no. 2 (1993): 217-40; Jean-Pierre Benoit and Vijay Krishna, “Renegotiation in Finitely Repeated Games,” Econometrica 61 (1993): 303-23; and James Bergin and W. Bentley MacLeod, “Efficiency and Renegotiation in Repeated Games,” Journal of Economic Theory 61, no. 1 (1993): 42-73.

  3. The seminal work on this question dates back to the eighteenth-century French philosopher, mathematician, and nobleman the Marquis de Condorcet. Regrettably, the latter characteristic—he opposed beheading the king and queen—cost him his life during the French Revolution. There is a wonderful statue of him on the left bank of the Seine, not too far from Notre Dame. I always pay homage to him when I am in Paris. His insights were built upon in the second half of the twentieth century to establish the modern understanding of voting methods. See, for instance, Kenneth Arrow, Social Choice and Individual Values (New York: John Wiley and Sons, 1951); William H. Riker, Liberalism Against Populism (New York: Freeman, 1982); Richard D. McKelvey and Norman Schofield, “Structural Instability of the Core,” Journal of Mathematical Economics 15, no. 3 (June 1986): 179-98; and Gary W. Cox, Making Votes Count (New York: Cambridge University Press, 1997).

  Chapter 4: Bombs Away

  1. Stanley Feder, “Factions and Policon: New Ways to Analyze Politics,” in H. Bradford Westerfield, ed., Inside CIA’s Private World: Declassified Articles from the Agency’s Internal Journal, 1955—1992 (New Haven: Yale University Press, 1995).

  2. This is a casual statement of the median voter theorem, one of the most important concepts in understanding issue resolutions. See Duncan Black, The Theory of Committees and Elections (Cambridge: Cambridge University Press, 1958), and Anthony Downs, An Economic Theory of Democracy (New York: Harper, 1957).

  3. This second first-cut prediction relies on the mean voter theorem. See Andrew Caplin and Barry Nalebuff, “Aggregation and Social Choice: A Mean Voter Theorem,” Econometrica 59 (1991): 1-23; and Norman Schofield, “The Mean Voter Theorem: Necessary and Sufficient Conditions for Convergent Equilibrium,” Review of Economic Studies 74 (2007): 965-80.

  4. See Bruce Bueno de Mesquita, “Ruminations on Challenges to Prediction with Rational Choice Models,” Rationality and Society 15, no. 1 (2003): 136-47; and Robert Thomson, Frans N. Stokman, and Christopher H. Achen, eds., The European Union Decides (Cambridge: Cambridge University Press, 2006).

  Chapter 5: Napkins for Peace

  1. For a not-too-technical explanation of what goes on inside the model, see Bruce Bueno de Mesquita, Predicting Politics (Columbus: Ohio State University Press, 2002).

  2. Bruce Bueno de Mesquita, “Multilateral Negotiations: A Spatial Analysis of the Arab-Israeli Dispute,” International Organization (Summer 1990): 317-40.

  3. See http://news.bbc.co.uk/1/hi/world/middle_east/1763912.stm.

  4. Anthony H. Cordesman, The Israel-Palestinian War: Escalating to Nowhere (Westport, Conn.: Praeger, 2005): 219.

  Chapter 6: Engineering the Future

  1. For an early, foundational study applying war-of-attrition games, see John Maynard Smith and Geoffrey A. Parker, “The Logic of Asymmetric Contests,” Animal Behaviour 24 (1976): 159-75. See also Anatol Rapaport, Two Person Game Theory (Ann Arbor: University of Michigan Press, 1966).

  2. See, for instance, James D. Fearon, “Rationalist Explanations for War,” International Organization 49 (1995): 379-414.

  Chapter 7: Fast-Forward the Present

  1. For a deeper exploration of some surprising implications of commitment problems and the pursuit of peace with adversaries, in particular peace with terrorists, see Ethan Bueno de Mesquita, “Conciliation, Counter-Terrorism, and Patterns of Terrorist Violence,” International Organization 59, no. 1 (2005): 145-76.

  2. The actual calculation predicting the impact of deaths (the horizontal axis) on tourism (the vertical axis) is based on the logarithm of deaths to capture order-of-magnitude changes. Doubling the lives lost from 10 deaths to 20, for instance, represents a more noticeable change than going from 190 to 200 deaths even though the absolute change is the same. Logarithms capture the magnitude of change so that equal spaces reflect equal percentage increments in lost lives.

  3. Limitations on the availability of data constrain the number of years I can cover. Violence and tourism are both measured quarterly. The Palestinians suffer the lion’s share of violent deaths. The graph looks very much the same if only Palestinian deaths are plotted rather than all violent deaths resulting from the conflict. Data on Israeli tourism are from the Bank of Israel and can be found at http://www.bankisrael.gov.il/series/en/catalog/tourism/tourist entries/. Data on violent deaths are from David Fielding, “How Does Violent Conflict Affect Investment Location Decisions?” Journal of Peace Research 41, no. 4 (2004): 465-84.

  4. See “Palestinian Central Bureau of S
tatistics Press Release for the Hotel Survey, Fourth Quarter 2005,” found at www.pcbs.pna.org/Portals/_pcbs/PressRelease/HOTEL0405.pdf.

  Chapter 8: How to Predict the Unpredictable

  1. See John Lewis Gaddis, “International Relations Theory and the End of the Cold War,” International Security 17, no. 3 (Winter 1992): 323-73; and James Ray and Bruce Russett, “The Future as Arbiter of Theoretical Controversies: Predictions, Explanations and the End of the Cold War,” British Journal of Political Science 26, no. 4 (October 1996): 441-70.

  2. Bruce Bueno de Mesquita, “Measuring Systemic Polarity,” Journal of Conflict Resolution (June 1975): 187-215; and Michael F. Altfeld and Bruce Bueno de Mesquita, “Choosing Sides in Wars,” International Studies Quarterly (March 1979): 87-112.

  3. EUGene’s data can be accessed at http://www.eugenesoftware.org/.

  4. See Bruce Bueno de Mesquita, “The End of the Cold War: Predicting an Emergent Property,” Journal of Conflict Resolution 42, no. 2 (April 1998): 131-55.

  Chapter 9: Fun with the Past

  1. See Xenophon, Hellenica, Book VI, Chapter IV, downloaded from http://www.fordham.edu/halsall/ancient/371leuctra.html).

  2. Edward Kritzler, Jewish Pirates of the Caribbean: How a Generation of Swashbuckling Jews Carved Out an Empire in the New World in Their Quest for Treasure, Religious Freedom—and Revenge (New York: Doubleday, 2008).

  3. Niall Ferguson, The Pity of War: Explaining World War I (New York: Basic Books, 2000).