Tadelis 11.4 Consider a two player alternating bargaining game where instead of
ID: 1124837 • Letter: T
Question
Tadelis 11.4
Consider a two player alternating bargaining game where instead of the pie shrinking by a discount factor < 1, the players each pay a cost ci > 0, i {1, 2} to advance from one period to another. So, if player i receives a share of the pie that gives him a value of xi in period t then his payoff is vi = xi (t 1)ci . If the game has T periods then a sequence of rejections results in each player receiving vi = (T 1)ci .
(a) Assume that T = 2. Find the subgame-perfect equilibrium of the game and show in which way it depends on the values of c1 and c2.
(b) Are there Nash equilibria in the two period game that are not subgameperfect?
(c) Assume that T = 3. Find the subgame perfect equilibrium of the game and show in which way it depends on the values of c1 and c2.
Explanation / Answer
A Rubinstein bargaining model refers to a class of bargaining games that feature alternating offers through an infinite time horizon. The original proof is due to Ariel Rubinstein in a 1982 paper.[1] For a long time, the solution to this type of game was a mystery; thus, Rubinstein's solution is one of the most influential findings in game theory.
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