Patience (game theory)

from Wikipedia, the free encyclopedia

Patience is the ability or willingness to wait or endure something calmly and in control. In game theory , the term is used in many areas of the social sciences . For example, in models of the principal-agent theory for negotiations as in salary negotiations.

Negotiation process

Offers and counter-offers are exchanged during a negotiation . A negotiation, such as a salary negotiation, is a sequential game.

One possible outcome is a compromise. This could consist in halving the payout to be distributed. Such a 50-50 division corresponds to the general understanding of "fairness". To find out which decision is the best, game theory falls back on decision trees or game trees. The different variants are played through to the end and closed from the end to find out which decision is the best. For many common negotiation types, the 50-50 split mentioned above is the solution that results from closing back.

The fact that time is money is a critical factor in negotiations because the "cake" to be distributed (i.e., the payout) shrinks as the negotiations drag on. Even so, it can happen that the parties disagree because both parties believe the cost of the negotiation would be outweighed by a more favorable outcome (higher payout). "Charles Dickens' 'Black House' illustrates the extreme case: The dispute over the Jarndyce estate dragged on for so long that the entire fortune was eaten up by lawyers."

The back lock technique can also be used when the problem does not have a fixed endpoint. "This approach was first developed by the economist Ariel Rubinstein , and the solution we are discussing is often referred to in his honor as the Rubinstein negotiated solution ."

example

A company in the steel industry is on strike after unsuccessful salary negotiations. If agreed, the company could generate $ 3 million a week in profit. The division of this sum is being negotiated. The negotiations take place once a week, with each side taking turns submitting an offer. Thus, a sequential game is considered.

Every week without an agreement therefore costs three million dollars, so an immediate agreement is in the interests of both parties. The only question is: under what conditions? The side that waits more impatiently for an agreement would have to make the first or the bigger one. A close look at the facts confirms this and allows a precise prediction of the proportions of the two parties.

For both parties, a dollar today is worth a dollar tomorrow because it could be invested and earn interest or a dividend. For the negotiating partners, there are additional aspects that exacerbate the impatience factor. In every week without an agreement, there is, for example, the risk that old and loyal customers will switch to the competition, so that the company is threatened with closure. In this case, workers and managers would have to look for new jobs that might be paid less, management stock options would become worthless and the union's reputation would be damaged. The advantage of an immediate agreement over an agreement in the next week is precisely the probability that this scenario will occur during the course of the week. Management and unions assess these risks and their consequences differently.

This example assumes that to the union, $ 1 today is worth $ 1.01 a week. For management, however, $ 1 today is worth $ 1.02 a week. The “interest rates” for management and the union are thus different. The management is therefore twice as impatient as the union. This difference in impatience between the two sides has dramatic consequences for the deal. The profit shares of the two sides are exactly in inverse proportion to their interest rates. So the union gets two-thirds ($ 2 million a week) and management gets one-third ($ 1 million a week).

In this context, those with the lower costs of waiting can "allow themselves" more patience in the negotiation process and thus receive a larger piece of the pie. So the one with the higher cost of waiting is more impatient. He therefore prefers a quicker agreement than his counterpart. In principle, an immediate agreement, without losing the money, is always an advantage and therefore preferable on all sides. It only gets complicated when the cost of waiting for the other person is unknown. But that's another problem.

supporting documents

  1. ↑ patience. In: The Free Dictionary.
  2. ↑ AK Dixit, BJ Nalebuff (ed.): Game theory for beginners. 1995, p. 46 ff.
  3. ↑ AK Dixit, BJ Nalebuff (ed.): Game theory for beginners. 1995, p. 47.
  4. ↑ AK Dixit, BJ Nalebuff (ed.): Game theory for beginners. 1995, p. 291.
  5. ↑ AK Dixit, BJ Nalebuff (ed.): Game theory for beginners. 1995, p. 291ff.

See also

literature

  • Avinash K. Dixit, Barry J. Nalebuff (Eds.): Game Theory for Beginners - Strategic Know-How for Winners. Schäffer-Poeschel Verlag, Stuttgart 1995, ISBN 3-7910-0913-3 .
  • Avinash K. Dixit, Susan Skeath (Eds.): Games of Strategy. 2nd Edition. WW Norton & Company, 2004, ISBN 0-393-92499-8 .
  • Manfred J. Holler, Gerhard Illing: Introduction to game theory. Springer-Verlag, Berlin 2006, ISBN 3-540-27880-X .
  • Thomas Riechmann: Game Theory. Vahlens short textbooks, Munich 2008, ISBN 978-3-8006-3505-4 .
  • Martin J. Osborne, Ariel Rubinstein: Bargaining and Markets. Academic Press, San Diego 1990, ISBN 0-12-528632-5 .