Dividing da Pie

What is the ultimatum game? Give an example using £100

-A simple two-person one-shot game

-Two anonymous players split £100. The Proposer offers any share to the Responder, who accepts or rejects it. If accepted, both get their share. If rejected, both get nothing. This is the take-it-or-leave-it offer

Why is the take-it-or-leave-it game concerned with sharing economic rents and opportunity costs?

-The proposer is given the pie to divide. If such negotiation succeeds with the responder, both receive a rent.

-Their next best alternative is to get nothing

-So if the proposer divides the £100 by giving the responder £20, the Responder has a cost of saying no: £20. Therefore, we can say that £20 is the opportunity cost of rejecting such an offer

Why does this game showcase a sequential game?

-Why does the difference matter?

-A game in which not all players choose their strategies at the same time. The players who choose later can see the strategies already chosen by the other players.

-This means the proposer needs to imagine how the responder will respond to their offer. You only have one try, and you can’t YOLO it.

What does the minimum acceptable offer entail in this game?

-The smallest offer that is proposed, which will not be rejected by the responder. The least favourable offer that would be accepted.

-Where it lies depends on the relationship between the two players, social norms, fairness, insulting…

-Where the satisfaction the responder gets from rejecting the offer and getting 0 money equates the pleasure of getting the money

In theory, when would an offer here be accepted? Start with a fairness norm of 50-50

-If a fairness norm of 50-50 exists, then if an offer below £50 was offered, the responder may punish.

-But being offered £45 compared to £0 invokes completely different levels of anger.

-So the responder’s satisfaction from rejecting an offer comes from a responder’s private reciprocity motive R and the gain from accepting the offer y. The larger the number, the more intense each force is.

-So we can say that the satisfaction at rejecting a low offer is R(50-y), and the satisfaction at gaining the offer is just y

-Therefore, an equation of the form such that if:

y < R(50-y), she will reject the offer. Thus to find the minimum acceptable offer, rearrange in terms of y < and: