Roland Dürre
Monday November 15th, 2010

Game Theory – The Ultimatum Game

The ultimatum game (Ultimatumspiel) is a practical application of the game theory (Spieltheorie) for business and behavioural research.

Here are the rules:

The recipient E gets a certain amount of money z from a donator S. He has to share the money with a pre-determined partner P. E has to divide the money at his own discretion between himself x and the recipient y. The division is fixed only from E.

The following criteria must be met:

  1. x + y = z
  2. E cannot make P more than one ultimate offer.
  3. In this offer, E must inform the P in an open and standardized way about the division rate.
  4. P can only accept or deny.
  5. If P accepts, E and P may keep the money according to the division rate determined by E.
  6. If P denies, the division is not happening and the money will irrevocably go back to S.
  7. Negotiations are not permitted. They will again cause an irrevocable return of all the money to S.

Basically, it is a simple game. It might be helpful to think in terms of the model.

But are the results of the experiments and the deduced and proven theories really suitable for finally arriving at definite statements or even mathematically describable theories about humans?

How is anybody supposed to scientifically and objectively collect statements about a “moving target” like a person in a society?

How strong is the influence of culture, religion and the media? What role does the social imprint play? How would the ancient Greeks, the ancient Romans, the people living in the various phases of medieval times, the people living during WW2 or directly after have decided?

How would your contemporaries living in the Arctic, in Africa, China, Europe, India, Japan, Russia or the USA decide? How will people decide in 20 or 50 years, who will again have a totally different social background and imprint?

What role does the test person’s age and life situation play?

Besides, it is not possible to set up an objective experiment. I keep making the experience that quite a few test persons intellectually do not understand the rules. You need test persons who do not yet know the topic. The test must render a result at the first run. If you leave time for reflexion or discussion, the result will be considerably altered.

How can you ever get a reasonable mix of test persons with respect to their needs and structures? What amount of money will you have to put at stake in order to generate really serious reactions and get reliable results? How can you make sure that false results caused by intellectual and emotional communication/interaction between the test persons will not take place? How does the way someone is feeling on the day of testing, or even an experience from his recent past or just a whim influence the decision of test persons?

And then we are still saddled with the main problem

How to pay for such an experiment?

🙂 Well, let me assure you that I would gladly volunteer as a test person.

🙂 And I would write down that I am not familiar with the ultimatum game. Ethically, I have no problem with this, because the money would be a donation, anyway.    
Or is there some small print which says you have to hand the money back if you lie?

(Translated by EG)

🙂 This article is one of several in which I grumble about the game theory.

2 Kommentare zu “Game Theory – The Ultimatum Game”

  1. Chris Wood (Tuesday November 16th, 2010)

    It is an interesting variation on this game to permit some negotiation. In the game as described, I guess E would offer P 20% or so. 30% would be cautious, 10% risky.
    With negotiation, as P, I would say “It must be 50-50, only that is fair”. I would refuse to accept less.
    Can we draw conclusions from this?

  2. rd (Tuesday November 16th, 2010)

    Die einzige Schlussfolgerung könnte sein, dass Menschen irrational handeln, weil z.B. ihr Stolz verletzt ist.
    Oder positiv gesagt: Es gibt Menschen, denen Emotionen mehr wert sind, als Geld.

    Siehe auch die (wahre?) Legende, der Lakota-Indianer, die angeblich die Millionen an Entschädigung für Mount Rushmore nicht annehmen, obwohl sie das Geld so dringend brauchen könnten.

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