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

2025/04/01 by Franziska Lesigang, Christian Hilbe, Nikoleta E. Glynatsi · 1 voice · 2 citations
Social Sciences · Decision Sciences · #Evolutionary Game Theory and Cooperation #Game Theory and Applications #Experimental Behavioral Economics Studies

paper · doi:10.1016/j.econlet.2025.112300

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. • We study repeated additive games among two players with finite memory (finite recall). • Suppose one player reacts to the opponent’s actions during the last n rounds. • We prove the opponent has a best response that only depends on the last n-1 rounds.

Cited by

• Payoff equivalence and complete strategy spaces of direct reciprocity
• Expectation-enforcing strategies for repeated games

Discussions

• How valuable is memory? In my very first paper, now published in Economics Letters, together with @chilbe.bsky.social and @nikoletaglyn.bsky.social, we give sufficient conditions under which a player [bsky, 38 points, 4 comments]

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