Three-player impartial games
Past efforts to classify impartial three-player combinatorial games (the theories of Li (Internat. J. Game Theory 7 (1978) 31-36) and Straffin (College J. Math. 16 (1985) 386-394)) have made various restrictive assumptions about the rationality of one's opponents and the formation and behavior of coalitions. One may instead adopt an agnostic attitude towards such issues, and seek only to understand in what circumstances one player has a winning strategy against the combined forces of the other two. By limiting ourselves to this more modest theoretical objective, and by regarding two games as being equivalent if they are interchangeable in all disjunctive sums as far as single-player winnability is concerned, we can obtain an interesting analogue of Grundy values for three-player impartial games. (C) 2000 Elsevier Science B.V. All rights reserved.
game coalition disjunctive sum multi-player nim