Problem Set Econ

Experimental Economics

Problem Set #8                                        

Chapter 12. Ultimatum Bargaining

1. In the ultimatum bargaining game proposer tend to offer something on the order of half of the pie to responders. Further, responders typically reject offers of 30% or less.  Some investigators hypothesized that the abstract context of the game motivates the unusually egalitarian behavior.

1. What is the ‘selfish’ Nash equilibrium prediction for this game?

1. Identify three environmental variations we discussed in class that affect play in the game.

1. Cultural differences may also affect performance. What sorts of cultural differences tend to most prominently affect behavior in the ultimatum game.

1. The dictator game is a simplification of the ultimatum game that isolates the altruistic tendencies of players.

1. How is the dictator game played? What is the Nash prediction for the game?  

1. Does switching from the ultimatum to the dictator format affect proposer behavior?

1. What environmental alterations affect behavior in the dictator game?

1. Sometimes it is said that the person who makes the first move in a game has a strategic advantage, and this is the case for a simple ultimatum gam. What game covered in this chapter does not necessarily provide a strategic advantage to the first mover?  Explain

1. Consider a two-stage alternating offer game with a pie of size $3 in the first stage which shrinks to $2 in the second stage. Find the equilibrium first stage offer and explain whether it will be accepted under the assumption that people are perfectly selfish and rational.

1. Consider a legislature composed of five voters, A, B, C, D. and E. There is a pot of money, $30 to be split, and if there is no agreement, most of this money is lost since the earnings in the event of no agreement are $5 for A, $4 for B, $3 for C, $2 for D and $1 for E.  Voter A is exogenously selected to make a single proposal for the division of h $30, which will then be considered in a vote, where each person votes yes or no. If at least three yes votes are obtained, then the proposed split is enacted, and if not, then the default payments are received. No amendments or further motions are allowed. What should voter A propose on the assumption that all voters are selfish and perfectly rational?  After reading about the ultimatum game, would you advise voter A to propose something else?  Explain.

1. A “disadvantageous counteroffer” is said to happen in a two-stage bargaining game when a person rejects an initial offer of $X and the pie then shrinks so that that person’s counteroffer provides less money than the amount they just rejected.  Given an example of this outcome using specific numbers (make up your own game and the numbers for the initial offer and the counter offers).  Would the Fehr-Schmidt utility function explained in Section 12.4 (with 1>α>β>0) be capable of explaining disadvantageous counteroffers?