Exploring Important Ideas in Game Theory and Fairness Bibliography


Prepared by:
Joseph Malkevitch
Mathematics and Computing Department
York College (CUNY)
Jamaica, New York 11451-0001

Email: malkevitch@york.cuny.edu (for additions, suggestions, and corrections)


This bibliographical list is organized by important "models" and themes. The papers listed are often surveys rather than a paper which originated the ideas, but I have aimed for papers which cover topics in a self-contained way. They differ greatly in length and technicality. Most of the papers are limited to discrete mathematical tools of exposition but some also discuss continuous methods. The items are listed chronologically within categories, article title first. Many of these items can be found on the internet, not behind a "pay wall."

Allocation, bankruptcy and cost sharing

Cost allocation, H. P. Young, Fair Allocation, H. P Young, Editor, American Mathematical Society, Providence, 1985, pp. 69-94.

Equity, equality, proportionality, Chapter 4, H. Peyton Young, Equity: In Theory and Practice, Princeton U. Press, Princeton, 1994.

Introduction to the theory of fair allocation, William Thomson, Chapter 11, Handbook of Computational Social Choice, Editors, F. Brandt, V. Conitzer, U. Endriss, J. Lang, A. Procaccia, Cambridge U. Press, Cambridge, 2016.

Fair allocation of indivisible goods, S. Bouveret, Y. Chevaleyre, and N. Maudet, Chapter 12, Handbook of Computational Social Choice, Editors, F. Brandt, V. Conitzer, U. Endriss, J. Lang, A. Procaccia, Cambridge U. Press, Cambridge, 2016.

Cost Sharing, Chapter 5, H. Peyton Young, Equity: In Theory and Practice, Princeton U. Press, Princeton, 1994.

Cost allocation, H.P. Young, Chapter 34, Handbook of Game Theory, Vol. 2, Editors, R. Aumann and S. Hart, North-Holland, 1994.

Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update, William Thomson, Mathematical Social Sciences, 74 (2015) 41-59.

Apportionment

The apportionment problem, William Lucas, Chapter 14, Political and Related Models, editors, S. Brams, William Lucas, and Philip Straffin, Jr., Volume 2, Modules in Applied Mathematics, editor, William Lucas, Springer-Verlag, New York, 1978.

The apportionment of representation, M. Balinski and H. P. Young, Fair Allocation, H. P Young, Editor, American Mathematical Society, Providence, 1985, pp. 1-29.

Auctions

The lovely but lonely Vickrey Auction, Lawrence Ausbel and Paul Milgrom, Chapter 1, Combinatorial Auctions, Editors, P. Cramton, Y. Shoham, and Richard Steinberg, MIT Press, Cambridge, 2006.

Cake cutting and fair division

Better ways to cut a cake, S. Brams, M. Jones, and C. Klamler, Notices Amer. Math. Soc. 53 (2006) 1314-1321.

Cake cutting: not just child's play, Ariel Procaccia, Communications of the ACM 56 (2013) 78-87.

Cake cutting algorithms, A. Procaccia, Chapter 13, Handbook of Computational Social Choice, Editors, F. Brandt, V. Conitzer, U. Endriss, J. Lang, A. Procaccia, Cambridge U. Press, Cambridge, 2016.

Elections and voting

Voting procedures Chapter 30, Steven Brams, Handbook of Game Theory, Vol. 2, Editors, R. Aumann and S. Hart, North-Holland, 1994. .

Introduction to the theory of voting, William Zwicker, Chapter 2, Handbook of Computational Social Choice, Editors, F. Brandt, V. Conitzer, U. Endriss, J. Lang, A. Procaccia, Cambridge U. Press, Cambridge, 2016.

Gale/Shapley; Two-sided markets

David Gale and L. Shapley, College admissions and the stability of marriage. American Mathematical Monthly 69 (1962) 9-15.

Two-sided matchings, A. Roth and M. Sotomayor, Chapter 16, Handbook of Game Theory, Volume 1, Editors, R. Aumann, S. Hart, North Holland, 1992.

Matching under preferences, B. Klaus, D. Manlove, F. Rossi, Chapter 14, Handbook of Computational Social Choice, Editors, F. Brandt, V. Conitzer, U. Endriss, J. Lang, A. Procaccia, Cambridge U. Press, Cambridge, 2016.

Game theory

Elementary game theory, E. Packel, Chapter 6, The Mathematics of Games and Gambling, MAA, Washington, 1981.

Games in extensive form, Sergiu Hart, Chapter 2, Handbook of Game Theory, Volume 1, Editors, R. Aumann, S. Hart, North Holland, 1992.

Von Neumann-Morgenstern stable sets, William Lucas, Chapter 17, Handbook of Game Theory, Volume 1, Editors, R. Aumann, S. Hart, North Holland, 1992.

Game theory and evolutionary biology, Chapter 28, Peter Hammerstein and Reinhard Selton, Handbook of Game Theory, Vol. 2, Editors, R. Aumann and S. Hart, North-Holland, 1994.

Cooperative models of bargaining, William Thomson, Chapter 35, Handbook of Game Theory, Vol. 2, Editors, R. Aumann and S. Hart, North-Holland, 1994.

Zero-sum two-person games, Chapter 20, T. Raghavan, Handbook of Game Theory, Vol. 2, Editors, R. Aumann and S. Hart, North-Holland, 1994.

Non-zero-sum two-person games, Chapter 44, T. Raghavan, Handbook of Game Theory, Vol. 3, Editors, R. Aumann and S. Hart, North-Holland, 2002.

Basic solution concepts and conceptual issues, E. Tardos and V. Vazirani, Chapter 1, Algorithmic Game Theory, Editors, N. Nisan, T. Roughgarden, E. Tardos, V. Vazirani, Cambridge U. Press, Cambridge, 2007.

Behavioral game theory experiments and modeling, Colin Camererer and Teck-Hua Ho,, Chapter 10, Handbook of Game Theory, Editors, H. Peyton Young and Shmuel Zamir; North Holland, 2014.

Mechanism design

Introduction to mechanism design (for computer scientists), N. Nisan, Chapter 9, Algorithmic Game Theory, Editors, N. Nisan, T. Roughgarden, E. Tardos, V. Vazirani, Cambridge U. Press, Cambridge, 2007.

Mechanism design without money, J. Schummer and R. Vohra, Chapter 10, Algorithmic Game Theory, Editors, N. Nisan, T. Roughgarden, E. Tardos, V. Vazirani, Cambridge U. Press, Cambridge, 2007.

School choice

School choice, a mechanism design approach, Atila Abdulkadirolu and Sonmez Tayfun, American Economic Review, 93 (2003) 729-747.

What really matters in designing school choice mechanisms, Parag Pathak, Advances in Economics and Econometrics 1(2017)176-214.

Social choice

Social Choice, Herve Moulin, Chapter 31, Handbook of Game Theory, Vol. 2, Editors, R. Aumann and S. Hart, North-Holland, 1994.

Judgment aggregation, U. Endriss, Chapter 17, Handbook of Computational Social Choice, Editors, F. Brandt, V. Conitzer, U. Endriss, J. Lang, A. Procaccia, Cambridge U. Press, Cambridge, 2016.

Utility


Utility and subjective probability, Peter Fishburn, Chapter 39, Handbook of Game Theory, Vol. 2, Editors, R. Aumann and S. Hart, North-Holland, 1994.

Voting games and weighted voting

Measuring power in weighted voting games, William Lucas, Chapter 9, Political and Related Models, editors, S. Brams, William Lucas, and Philip Straffin, Jr., Volume 2, Modules in Applied Mathematics, editor, William Lucas, Springer-Verlag, New York, 1978.

Power indices in politics, Philip Straffin, Jr., Chapter 11, Political and Related Models, editors, S. Brams, William Lucas, and Philip Straffin, Jr., Volume 2, Modules in Applied Mathematics, editor, William Lucas, Springer-Verlag, New York, 1978.

Power and stability in politics, Philip Straffin, Jr., Chapter 32, Introduction to the theory of voting, William Zwicker, Chapter 2, Handbook of Computational Social Choice, Editors, F. Brandt, V. Conitzer, U. Endriss, J. Lang, A. Procaccia, Cambridge U. Press, Cambridge, 2016.