Abstract
Peter Vanderschraaf’s Strategic Justice provides a defense of the egalitarian bargaining solution. Vanderschraaf’s discussion of the egalitarian solution invokes three arguments typically given to support the Nash bargaining solution. Overall, we reinforce Vanderschraaf’s criticism of arguments in favor of the Nash solution and point to potential weaknesses in Vanderschraaf’s positive case for the egalitarian solution.
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Notes
In particular, they show that there always exists an equilibrium where both make demands compatible with the KS solution and that the KS solution is unique in this respect.
Binmore (1993) offers such a defense, although it is worth noting that Binmore takes aim at procedures that involve an arbitrator. For instance, Moulin (1984) and Bossert and Tan (1995) show how different arbitration methods can lead to the KS and egalitarian solutions, respectively. Since the procedure discussed by Anbarci and Boyd (2011) does not involve an arbitrator, Binmore’s critique does not apply.
This assumes the hare-hunting equilibrium is risk-dominant
The difference between these models is that Young (1993a) investigates the Nash demand game (where bargainers simply issue claims and compatible claims are rewarded) while Young (1998) looks at a “contract” game where agents bargain over terms of a contract and in the end must agree to the same contract (see Young 1998: 783 for a discussion of the differences). In this section we consider a model that is closer to Young (1993a). It would be interesting to see whether similar results can be attained if we modify our model to make it more in-line with Young (1998).
See, however, Bruner (2020).
Some speculation as to why philosophers haven’t turned their attention to the asymmetric bargaining problem: for one, the analysis is cumbersome and can involve simulations that move at a snail’s pace. Second, philosophers for the most part seemed satisfied with Young’s stochastic stability analysis. Finally, it is unclear how one should go about generating asymmetric bargaining problems. We consider one method in this section, and point to the need for more work in this area.
It is worth noting that Vanderschraaf is well aware that his evolutionary analysis of the bargaining problem is suggestive (and not definitive). For this reason, Vanderschraaf places more weight on the consistency argument he provides for egalitarianism in Chapter 8 of Strategic Justice (discussed in Sect. 3 of this paper).
In many cases, it simply is impossible for the results of our simulation to perfectly match a bargaining solution since the claim precision of our simulation is only 1/100.
It is worth noting that this means it is possible for a simulation to “count” for two or even three bargaining solutions despite the fact that the bargaining solutions do not coincide.
When r is instead r = 0.02 the average size of the basin of attraction for the Nash, KS and egalitarian solutions are 0.472, 0.244 and 0.086, respectively.
Ties occurred in cases where solutions either coincide or were extremely close to each other.
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Acknowledgements
Many thanks to Peter V. (as he likes to be called) for detailed discussion of all things bargaining. I also thank the participants of the Grundlegung Group at the University of Groningen for comments on an earlier draft as well as participants of the Author Meets Critic Session at the 3rd PPE Society Meeting and the Vanderschraaf Workshop at Chapman University.
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Bruner, J.P. Convention, correlation and consistency. Philos Stud 178, 1707–1718 (2021). https://doi.org/10.1007/s11098-020-01499-8
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DOI: https://doi.org/10.1007/s11098-020-01499-8