The ultimatum game

Hi everyone, today we’re going to talk about the Ultimatum Game. We played this game in the beginning of the semester. 

1 - Presentation of the game

The Ultimatum Game was proposed by Güth, Schwittberger and Schwarze in 1982 based on a real experiment. 

Suppose that there’s 2 players who don’t know each other. In our case, nobody knew each other at the beginning of the year and most of all we played anonymously. They participate in the following experiment. A first player is given a specific amount of money to share with a second player. If the second player accepts the deal, the money is split according to the proposal. But the second player can also choose to refuse the proposition. In this case, none of them earn money. 

 For example, if the player #1 offers 1$ if the player 2 accepts this sum he obtains 1$ and the player 1 keeps his 9$. However, if he rejects this proposition they both get 0$. 

Another example : if player #1 proposes 5$

• A first scenario where the second player accepts : they both get  5$.
• A second scenario would be that the player #2 refuses the split : both of them get 0$.

It’s important to mention that the experiment is originally done once, so there's no reciprocity principle. Moreover, we can see that it’s the second player who has a dominant position because he has the choice between accepting the share or refusing it, thus impacting the first player’s situation.  It’s the opposite of the dictature game since it’s the player 1 who has power: he offers a quantity of money to the second player who is forced to accept. 

2 -  Theoretical predictions

From a purely rational economic perspective, the responder should  accept any positive amount offered as the alternative is no money at all. Indeed, neoclassical theory predicts that, rationally, the responder is expected to accept for example 1$ if the player 1 offers that amount because 1 is better than 0.

For most people, a fair even split emerge as a favoured strategy ( 50/50)

Halselhunl &Mellers  in 2005 said that there is an equilibrium where both receive the most possible without anyone being short-changed.

The Nash equilibrium is (9,1) , the first player wants to keep as much money as possible and to share the least as possible. The player 2 is expected to accept the amount because if not he will get 0 ( 1 is better than 0).

3 - Empirical evidence

⇒ Schimpanzés , how do they play the game?

However, in reality the game is played very differently than the theory. 

Let’s take the following example : a group of children play the Ultimatum Game where players #1 have to split (or not) 10 chocolate coins. 

Every player wants to maximise their own satisfaction, which is getting the most chocolate possible.

As a matter of fact, players #1 propose a smaller and unfair share to players #2. In response, almost every player #2 rejects this split, preferring to have nothing at all. One of them even says: « I don’t care, it’s already too little ». 

At first, this may seem a bit strange. Indeed, it is a way from the second player to « punish » the first one for his/her selfishness. They both failed at playing the game as none of them gets chocolate.

However, when the game is repeated with changing pairs, we notice that the first players tend to modify their strategy. Their goal is still to maximize the number of chocolate coins but they are scared of the reaction of players #2. They play in a more altruist way by proposing a more equal distribution. These fairer splits are most of the time accepted. 

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