Abstract
In this chapter, after specifying the bargaining problem à la Nash (1950), the Rubinstein game and its subgame-perfect Nash equilibrium are presented. The equilibrium is determined (1) by the shrinking of the cake to be distributed among the two players and (2) by how the shrinking is evaluated by the players. If players can make binding agreements, then the self-enforcing power of the equilibrium is no longer needed. The players can jointly decide on feasible payoffs to serve as a bargaining outcome. The Nash solution is the most prominent concept that supports such a decision; it is considered to be fair and reasonable. The Kalai-Smorodinsky solution is an alternative concept briefly discussed in the chapter. The Rubinstein game and the Nash solution “meet” in the Nash program. More generally, the Nash program asks for a non-cooperative game, like the Rubinstein game, to produce outcomes as suggested by a cooperative game of the Nash solution type. Of course, a non-cooperative game can result in cooperation.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
This of course is a reference to Kenneth Boulding’s “The Economy of Love and Fear: A Preface to Grants Economics” of 1973.
- 2.
If ri is the “relevant interest rate” of agent i, then the discount factor equals δi = 1/(1 + ri).
- 3.
That is, the “wings” of the equilateral hyperbola are converging to axes c1 and c2.
- 4.
Again, the real number ai must be positive, otherwise the ranking would change. If ai < 0, what was valued “high” before the transformation, would be valued “low” thereafter and vice versa. Condition ai > 0 assures that the transformation is order-preserving. The real number bi may be positive, negative, or equal to zero.
- 5.
See the next section.
- 6.
It is important that utility frontier H(P) does not “flatten” with increasing u1 which is excluded by payoff space P being a convex set (cf. Sect. 2.3).
- 7.
The education of the youth was also of great importance in the Roman Republic. For this, quite often Greek philosophers were hired by the Romans, not always with satisfying results because of cultural differences.
References
Berz, G. (2015). Game theory, bargaining, and auction strategies(2nd ed.). New York, Houndmills: Palgrave Macmillan.
Bitros, G. C., & Karayannis, A. D. (2010). Morality, institutions and the wealth of nations: Some lessons from ancient Greece. European Journal of Political Economy,26, 68–81.
Hobbes, T. (1996 [1651]). Leviathan. In R. Tuck (Ed.), Revised Student Edition. Cambridge: Cambridge University Press.
Holler, Manfred J. (1986). Two concepts of monotonicity in two-person bargaining theory. Quality & Quantity,20, 431–435.
Kalai, E., & Smorodinsky, M. (1975). Other solutions to Nash’s bargaining problem. Econometrica,43, 513–518.
Nash, J. F. (1950). The bargaining problem. Econometrica,18, 155–162.
Nash, J. F. (1953). Two-person cooperative games. Econometrica,21, 128–140.
Owen, G. (1995). Game theory (3rd ed.). San Diego: Academic.
Roth, A. (1979), Axiomatic models of bargaining. Lecture notes in economics and mathematical systems (Vol. 170). Berlin: Springer.
Rubinstein, A. (1982). Perfect equilibrium in a bargaining model. Econometrica,50, 97–111.
Saner, R. (2005). The expert negotiator (2nd ed.). Leiden, Boston: Martinus Nijhoff Publishers.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Holler, M.J., Klose-Ullmann, B. (2020). Bargaining and Bargaining Games. In: Scissors and Rock. Springer, Cham. https://doi.org/10.1007/978-3-030-44823-3_12
Download citation
DOI: https://doi.org/10.1007/978-3-030-44823-3_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-44822-6
Online ISBN: 978-3-030-44823-3
eBook Packages: Economics and FinanceEconomics and Finance (R0)