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Can I afford to remember less than you? Best responses in repeated additive games

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  • Lesigang, Franziska
  • Hilbe, Christian
  • Glynatsi, Nikoleta E.

Abstract

In this paper, we study best responses in repeated additive games among two players. A stage game is additive if each player’s payoff is the sum of two components, and each component only depends on the action of a single player. We suppose one player’s strategy depends on the co-player’s last n actions. Then we prove that the other player has a best response that only depends on their own n−1 actions. That is, for an important sub-class of games and strategies, players can achieve maximum payoffs even with less memory than their opponent.

Suggested Citation

  • Lesigang, Franziska & Hilbe, Christian & Glynatsi, Nikoleta E., 2025. "Can I afford to remember less than you? Best responses in repeated additive games," Economics Letters, Elsevier, vol. 250(C).
    • Handle: RePEc:eee:ecolet:v:250:y:2025:i:c:s0165176525001375
    DOI: 10.1016/j.econlet.2025.112300
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    References listed on IDEAS

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    1. Mailath, George J. & Olszewski, Wojciech, 2011. "Folk theorems with bounded recall under (almost) perfect monitoring," Games and Economic Behavior, Elsevier, vol. 71(1), pages 174-192, January.
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    5. Wes Maciejewski & Feng Fu & Christoph Hauert, 2014. "Evolutionary Game Dynamics in Populations with Heterogenous Structures," PLOS Computational Biology, Public Library of Science, vol. 10(4), pages 1-16, April.
    6. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796, Decembrie.
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