Rubenstein bargaining

Definition

Two players agree to share a pie of size $1$. Player 1 proposes sharing rule $(x,1-x)$ in periods $0, 2, 4$ etc. that player 2 can accept or reject. Game ends if a player accepts. If player 2 rejects player 1's offer in period $2k$, in period $2k+1$ can propose sharing rule $(x,1-x)$ that player 1 can accept or reject.

This is an infinite-horizon game of perfect information.

Subgame perfect equilibrium

There is a subgame perfect equilibrium in this model when

#incomplete

Notes

• is a class of bargaining games

References

1. Rubinstein, A. (1982). Perfect equilibrium in a bargaining model. Econometrica: Journal of the Econometric Society, 97-109. https://doi.org/10.2307/1912531
2. Ståhl, I. (1973). Bargaining theory (Doctoral dissertation, Stockholm School of Economics). https://research.hhs.se/esploro/outputs/doctoral/Bargaining-theory/991001480620406056
3. Shaked, A., & Sutton, J. (1984). Involuntary unemployment as a perfect equilibrium in a bargaining model. Econometrica: Journal of the Econometric Society, 1351-1364. https://doi.org/10.2307/1913509
4. Fudenberg and Tirole, Game theory. MIT press; 1991, pp. 113-114.
5. M. Maschler, E. Solan, and Shmuel Zamir, Game Theory, Cambridge University Press, 2013, pp. 622-635.
6. Wu, Young. "CS540 Lecture 20 Rubinstein Bargaining"; 2019. https://www.youtube.com/watch?v=377p9MJrgU8
7. Ozyurt, Selcuk. "(AGT3E7) [Game Theory] Solving Rubinstein's Alternating Offer Bargaining Game: Two-Period Version"; 2021. https://www.youtube.com/watch?v=oZDDEKVN280
8. Ozyurt, Selcuk. "(AGT3E8) [Game Theory] Solving Rubinstein's Infinite Horizon Alternating Offer Bargaining Game"; 2021. https://www.youtube.com/watch?v=4T8tOI034QA
9. https://web.stanford.edu/~jdlevin/Econ 203/RepeatedGames.pdf