From: John Conover <john@email.johncon.com>

Subject: Isn't the budget process a Zero-Sum Game?

Date: Sat, 6 Apr 1996 17:58:53 -0800

Suppose that the annual corporate budget of a company (government agency, etc.,) is finite, and has to be divided up by the various operating entities in the company for next year's fiscal operations. Isn't this a "prescription" for a "prisoners dilemma" scenario? I think the budget process may be a near perfect, very real, example of a zero-sum, multi-player game worthy of study. I mean, there certainly is an incentive for the players, (divisional VP's, etc.,) to defect and request, (justify/rationalize/politicize,) getting the largest piece of the budget pie as possible, even if a strategy of cooperation among the executive staff would yield a better payoff for the corporation as a whole. See the attachment for the rationalization and implications. Any observations on how Business Process Reengineering addresses these issues differently than "conventional" organizations would be greatly appreciated. John BTW, what prompted this posting was several recent meetings that I attended to determine "sweat equity" budgets in a company-same as the budget process-and promptly watched things degenerate into shin kicking and sand throwing "contest." After listening to "rational" arguments from all vested sides, and pondering things, (I apologize for that,) I began consider that such outcomes are inevitable from a game-theoretic standpoint. -- John Conover, john@email.johncon.com, http://www.johncon.com/ Attachment: As an over simplified illustration of the budget process being a two person, zero-sum game, consider a company with two divisions, A and B, with the executives of each division deliberating the fraction of the budget that will go to each division. The fiscal budget payoff table might look like: B Cooperates B Defects +------------------------+ A Cooperates | 2,2 | 0,3 | +--------------+---------+ A Defects | 3,0 | 1,1 | +--------------+---------+ Which might be interpreted as: 1) if A and B cooperate, they each get 2 million dollars, 1.5 million from the corporate budget, and 0.5 million each for synergistic (ie., cooperative,) operations. Presumably, this is the "best" alternative for the corporation, as a whole. 2) If A or B, but not both, opt for the total budget of 3 million, (ie., one or the other plays a defection strategy,) then the defectionist will get the 3 million, and the other will get 0, (since, presumably, one can not operate without the other, the defectionist will not get 4 million, as in 1), above.) 3) If they both defect, then they each get 1 million, which is the 1.5 million from the budget, and a loss of 0.5 million for not operating in a synergistic fashion. 1) Operating in a cooperative, synergistic fashion, both A and B get 2 million each, the highest cumulative "score" available for the game. 2) There is an incentive for both players to defect from this strategy. Which happens to be the requirements of a zero-sum game, (with two players, in this simple case.) The reasons that both players will choose a defection strategy can be found by looking at A's logical process in determining which strategy (cooperation, or defection,) would be most beneficial. 1) If A cooperates, and B cooperates, A gets 2 million. 2) If A cooperates, and B defects, A gets 0 million, the lowest "score in the game." 3) If A defects, and B cooperates, A gets 3 million, the highest "score" in the game. 4) If A defects, and B defects, A gets 1 million, and avoids getting the lowest "score" in the game. Likewise for player B. Note that A playing a defection strategy is the "rational" choice. No matter what B chooses to do, A is better off choosing a strategy of defection. So, player B, using the same rationale, decides to defect, also, making the 1,1 solution the "rational" and inevitable outcome of the budget process, (at least in the non-iterated version of the "game.") The above table is from "Prisoner's Dilemma," William Poundstone, Doubleday, New York, New York, 1992, pp. 120. For a more formal presentation, see "Games and Decisions," R. Duncan Luce and Howard Raiffa, John Wiley & Sons, New York, New York, 1957, pp. 56. For a general presentation and history, see, http://william-king.www.drexel.edu/top/class/histf.html.

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