Cross Dominance: A Shared-Interest Parallel to Strict Dominance

Kudo, Shiko (2025): Cross Dominance: A Shared-Interest Parallel to Strict Dominance.

Abstract

We describe cross dominance, a bilateral strengthening of weak dominance: switching B->A is never worse for either player. Cross dominance is strictly stronger than weak dominance yet orthogonal to strict dominance; within the Pareto-monotone slice we have SD => CD => WD. This yields a shared-interest ladder (weak -> cross -> strict-cross) that runs in parallel to the classical self-interest ladder (weak -> strict), offering a simple, outcome-agnostic rationale for pruning strategies like B in the motivating 2x2 game.

• Item Type: MPRA Paper
• Language: English
• Keywords: game theory; weak dominance; strict dominance; cross dominance; Pareto-monotone; strategy elimination
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C70 - General; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games

References

Selten, R. (1975). Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games. International Journal of Game Theory, 4, 25–55. https://doi.org/10.1007/BF01766400

Osborne, M. J., & Rubinstein, A. (1994). A Course in Game Theory. MIT Press.