Choice from Comparisons: A Survey of Game-Theoretical Methods

We survey several choice correspondences defined for pairwise comparison structures and their relation with the game-theoretical concepts of weak dominance, weak saddle and optimal mixed strategies. These correspondences are the Uncovered set, the Minimal Covering set and the Essential set. We notice that the Uncovered set and the Minimal Covering set make use of ordinal information at the level of the comparison structure. The Essential set uses cardinal comparisons, but it is possible to indirectly define an « Ordinal Essential set ».

[1]  Gerald H. Kramer,et al.  A dynamical model of political equilibrium , 1977 .

[2]  Jennifer Ryan,et al.  Tournament games and positive tournaments , 1995, J. Graph Theory.

[3]  Begoña Subiza,et al.  Condorcet choice correspondences for weak tournaments , 1999 .

[4]  David C. Fisher,et al.  Optimal strategies for a generalized “scissors, paper, and stone” game , 1992 .

[5]  P. Fishburn.  Condorcet Social Choice Functions , 1977 .

[6]  John Duggan,et al.  Dutta's Minimal Covering Set and Shapley's Saddles , 1996 .

[7]  Richard D. McKelvey,et al.  Covering, Dominance, and Institution Free Properties of Social Choice , 1986 .

[8]  M. Breton,et al.  The Bipartisan Set of a Tournament Game , 1993 .

[9]  Nicholas R. Miller.  A New Solution Set for Tournaments and Majority Voting: Further Graph- Theoretical Approaches to the Theory of Voting , 1980 .

[10]  Jean-François Laslier,et al.  A Theorem on Symmetric Two-Player Zero-Sum Games , 1997 .

[11]  L. Shapley.  SOME TOPICS IN TWO-PERSON GAMES , 1963 .

[12]  P. B. Simpson.  On Defining Areas of Voter Choice: Professor Tullock on Stable Voting , 1969 .

[13]  H. Moulin.  Choosing from a tournament , 1986 .

[14]  Jean-François Laslier,et al.  Tournament Solutions And Majority Voting , 1997 .

[15]  Bhaskar Dutta,et al.  Comparison functions and choice correspondences , 1999 .

[16]  Jean-François Laslier,et al.  Condorcet choice correspondences: A set-theoretical comparison , 1995 .

[17]  Jean-François Laslier,et al.  On Regular Composed Tournaments , 1994 .

[18]  Bhaskar Dutta.  Covering sets and a new condorcet choice correspondence , 1988 .

[19]  Jean-François Laslier,et al.  Social-Choice Mediators , 1994 .