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Playing for Susan Read chapter Read first chapter

2020 | OriginalPaper | Chapter

11. More Than Two Players

Authors : Manfred J. Holler, Barbara Klose-Ullmann

Published in: Scissors and Rock

Publisher: Springer International Publishing

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Abstract

If there are more than two players in a game, then there is a potential for forming coalitions. The Core is the most prominent solution concept in this case. It assigns payoff vectors to the players. However, the Core of an n-person game can be empty or contain an infinite number of possible outcome vectors. In this chapter, applying the Core to a network game illustrates this problem. As a consequence, alternative solution concepts are briefly discussed: the Stable Set concept, proposed by von Neumannand Morgenstern, as the Solution; Bargaining Sets that are based on objections and (successful) counterobjections; the Kernel and the Nucleolus. Results are confronted with the problem of competition and cooperation in the triad.

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previous chapter Mixed Strategies and Expected Utility
next chapter Bargaining and Bargaining Games
Footnotes
1
If the game between S and N\S cannot be reduced to a zero-sum game, we differentiate between value \(v_{\upalpha} \left(\text{S} \right)\) that S may secure against resistance of coalition N\S, and value \(v_{\upbeta} \left(\text{S} \right)\) for S that coalition N\S cannot prevent, thus defining the \(\upalpha\)- and \(\upbeta\)-characteristic function.
 
2
Max Weber (1948 [1924]: 180) suggests that “…we understand by ‘power’ the chance of a man or of a number of men to realize their own will in a communal action even against the resistance of others who are participating in the action.”
 
3
Faulhaber (1995) writes on network effects in supplying water, while Holler (1991), referring to Faulhaber’s contribution, discusses the model with respect to “fair and efficient public pricing” in sewage farming.
 
4
Anyone wanting to see the details, please turn the book such that (0, 1000, 0) and thereafter (0, 0, 1000) is on top. The parallel restriction lines regarding the fees of communities 2 and 3 are easily recognized.
 
5
The English translation “The Prince” reduces Machiavelli’s use of “Il Principe” to a certain extent; he calls the institution holding the power in the state “Principe,” irrespective of whether it is a monarchy, a tyranny or a republic. This becomes clear in his second main work: the “Discorsi.” It refers to the Roman Republic. Its subtitle is “Thoughts about Politics and Governing.” However, the following quotations are taken from “Il Principe.”
 
Literature
Faulhaber, G. R. (1995). Cross-subsidization. Pricing in public enterprises. American Economic Review,65, 966–977.
Follesdal, A. (2015). Machiavelli at 500: From cynic to vigilant supporter of international law. Ratio Juris,28, 242–251.CrossRef
Gabel, D. (1994). Competition in the network industry: The telephone industry, 1894–1910. Journal of Economic History,54, 543–572.CrossRef
Hildenbrand, W., & Kirman, A. P. (1976). Introduction to equilibrium analysis. Amsterdam: North-Holland.
Holler, M. J. (1991). Fair and efficient public pricing: An application to sewage farming. Journal of Regional Policy,11, 543–554.
Holler, M. J. (2003). On the regulation of telecommunications markets. In EURAS Yearbook of Standardization (Vol. 4) (Homo Oeconomicus 20). München: Accedo-Verlag.
Holler, M. J., & Widgrén, M. (1999). The value of a coalition is power. Homo Oeconomicus,15, 497–511.
Knieps, G. (1983). Is technological revolution a sufficient reason for changing the system of regulation? The case of telecommunications. Zeitschrift für die gesamte Staatswissenschaft (Journal of Institutional and Theoretical Economics),13, 578–597.
Machiavelli, N. (1882 [1532]). The Prince. The historical, political, and diplomatic writings of Niccolò Machiavelli (Vol. 4) (C. E. Detmold, Trans.). Boston: James R. Osgood and Co.
von Neumann, J., & Morgenstern, O. (1944). The theory of games and economic behavior. Princeton: Princeton University Press.
Owen, G. (1995). Game theory (3rd ed.). San Diego: Academic Press.
Sonnino, P. (Ed.). (1982 [1740]). Frederick of Prussia: The refutation of Machiavelli’s Prince or Anti-Machiavel, Athens, OH: Ohio University Press.
Weber, M. (1948 [1924]). Class, status and party. In H. H. Gerth & C. W. Mills (Eds.), Essays from Max Weber, London: Routledge and Kegan Paul.
Metadata
Title
More Than Two Players
Authors
Manfred J. Holler
Barbara Klose-Ullmann
Copyright Year
2020
Publisher
Springer International Publishing
Book
Scissors and Rock

Print ISBN: 978-3-030-44822-6

Electronic ISBN: 978-3-030-44823-3

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-44823-3_11

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