## Budget as a Zero-Sum Game? LO6477

John Conover (john@johncon.johncon.com)
Sat, 6 Apr 1996 14:15:29 -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 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 Learning Organizations address 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. I have some ideas on how to circumvent the
"inevitability," using concepts of LO, but would like to hear other
opinions, first.

John Conover

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.

Or something along those lines. From which, it can be deduced:

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.

```--

John Conover, 631 Lamont Ct., Campbell, CA., 95008, USA.
VOX 408.370.2688, FAX 408.379.9602
john@johncon.com

Learning-org -- An Internet Dialog on Learning Organizations
For info: <rkarash@karash.com> -or- <http://world.std.com/~lo/>
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