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Schelling's Game TheoryHow to Make Decisions$
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Robert V. Dodge

Print publication date: 2012

Print ISBN-13: 9780199857203

Published to Oxford Scholarship Online: May 2012

DOI: 10.1093/acprof:oso/9780199857203.001.0001

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The Commons and Fair Division

The Commons and Fair Division

(p.188) Chapter 16 The Commons and Fair Division
Schelling's Game Theory


Oxford University Press

This chapter looks at self-interest and group welfare in society. It introduces Schelling's view of a social contract to restrict self-interest from overcoming the general good, which is followed by an example he uses. The chapter is then concerned with Hardin's “The Tragedy of the Commons” as an explanation for the failure of individual cooperation in society's interest. Hardin described a multi-person prisoner's dilemma where it was in everyone's interest to cooperate but nobody had individual incentive to do so. Overfishing, pollution, and congestion are common problems which illustrate this. The remainder of the chapter is about the idea of fair division. Historical references come from Herodotus and the Bible. The method of “one cuts, the other chooses,” introduces Hugo Steinhaus, who expanded it to encompass “the last diminisher” as a way for physical objects to be distributed among “n” number of players. Steinhaus's method for “adding value” follows, where the total can exceed 100% of what is being divided. This involves the division of objects when claimants place different values on what is to be divided. The use of lottery and auction as methods for fair division are introduced and the chapter concludes with a Schelling problem, “Overbooked Airline Flight.” No solutionis provided; just guidelines to consider in determining what would be fair and what would be seen to be fair.

Keywords:   social contract, Tragedy of the Commons, fair division, Hugo Steinhaus, the last diminisher, lottery, auction

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