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A note on asymptotic stability and game blocks

Author

Listed:
  • Ritzberger, Klaus
  • Weibull, Jörgen W.
  • Wikman, Peter

Abstract

This note establishes that if the face spanned by a strategy block in a finite normal-form game is asymptotically stable under any evolutionary selection dynamic in a wide class, then the block is a game block as defined by Ritzberger et al. (2025). That is, the block respects Nash equilibrium components and the index sum of the components with support in the block equals +1. The result extends Theorem 1 of Demichelis and Ritzberger (2003) from equilibrium components to faces of strategy blocks.

Suggested Citation

  • Ritzberger, Klaus & Weibull, Jörgen W. & Wikman, Peter, 2026. "A note on asymptotic stability and game blocks," Economics Letters, Elsevier, vol. 264(C).
    • Handle: RePEc:eee:ecolet:v:264:y:2026:i:c:s0165176526001849
    DOI: 10.1016/j.econlet.2026.112990
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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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