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

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 X1_k = player K’s policy preference on the issue; Let X2_k = 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.