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FIZIKA B 14 (2005) 2, 235 - 244
 
LETTER TO THE EDITOR
NON-TRANSITIVE QUANTUM GAMES
MICHAEL L. STOHLERa,b and EPHRAIM FISCHBACHb
aPhysics Department, Wabash College, Crawfordsville, IN
47933-0352
bPhysics Department, Purdue University, West Lafayette, IN 47907-2036
Received 7 July 2005; Accepted 26 September 2005
Online 7 December 2005
We present two alternative approaches to constructing 3 ×3 entangled quantum games,
based on different formulations of mixed strategies in a quantum game. Although these
formulations are quite similar in 2 ×2 games (2 players × 2 choices), their
differences become pronounced in the 3 ×3 case. A 3 ×3 classical game is the simplest
platform which allows for non-transitive strategies A, B, C, where A beats B, B beats C,
and C beats A (A > B > C > A). We consider non-transitive strategies in both
formulations of 3 ×3 quantum games, and show that non-transitivity survives in the
quantum versions of the corresponding classical games. Some physical implications of these
results are also considered.
PACS numbers: 02.10.Eb
UDC 530.161
Keywords: entangled quantum games, non-transitivity, physical implications
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