1)

Consider the following bargaining game: players 1 and 2 have 5 dollars to share. Player 2

can make an offer ofx(between 0 dollars and 5 dollars) to player 1, which player 1 observes

and chooses to accept or reject. If player 1 accepts, player 1 gets x dollars and player 2 gets

5 - x dollars. If player 1 rejects the offer, both players get 0. What is the SPNE of this game?

2)

Consider a two step version of this game, where the players are bargaining over 200 dollars.

First, player 1 makes an offer of ybetween 0 and 200, which player 2 can accept or reject.

If player 2 accepts, player 1 receives 200 - y and player 2 receives y. If player 2 rejects, then

player 2 gets to make an offer x such that 0

x

100. The payoffs are 100 - xto player 2

and xto player 1 if player 1 accepts this offer, or zero to both players if player 1 rejects this

offer.

1. What is the SPNE of this game?
2. Suppose a researcher ran an experiment and found that 50% of the pairs offered y=100 in Round 1 and this was accepted. The researches then declared game theory a success! How would you respond to these researchers? That is, is there another hypothesis for this result and what test do the researchers need to run to make sure that game theory did indeed succeed?