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Rock-Paper-Scissors Play: Beyond the Win-Stay/Lose-Change Strategy

Author

Listed:
  • Hanshu Zhang

    (School of Psychology, Central China Normal University, Wuhan 430079, China
    Department of Social and Decision Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA)

  • Frederic Moisan

    (EM Lyon Business School, GATE UMR 5824, F-69130 Ecully, France)

  • Cleotilde Gonzalez

    (Department of Social and Decision Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA)

Abstract

This research studied the strategies that players use in sequential adversarial games. We took the Rock-Paper-Scissors (RPS) game as an example and ran players in two experiments. The first experiment involved two humans, who played the RPS together for 100 times. Importantly, our payoff design in the RPS allowed us to differentiate between participants who used a random strategy from those who used a Nash strategy. We found that participants did not play in agreement with the Nash strategy, but rather, their behavior was closer to random. Moreover, the analyses of the participants’ sequential actions indicated heterogeneous cycle-based behaviors: some participants’ actions were independent of their past outcomes, some followed a well-known win-stay/lose-change strategy, and others exhibited the win-change/lose-stay behavior. To understand the sequential patterns of outcome-dependent actions, we designed probabilistic computer algorithms involving specific change actions (i.e., to downgrade or upgrade according to the immediate past outcome): the Win-Downgrade/Lose-Stay (WDLS) or Win-Stay/Lose-Upgrade (WSLU) strategies. Experiment 2 used these strategies against a human player. Our findings show that participants followed a win-stay strategy against the WDLS algorithm and a lose-change strategy against the WSLU algorithm, while they had difficulty in using an upgrade/downgrade direction, suggesting humans’ limited ability to detect and counter the actions of the algorithm. Taken together, our two experiments showed a large diversity of sequential strategies, where the win-stay/lose-change strategy did not describe the majority of human players’ dynamic behaviors in this adversarial situation.

Suggested Citation

  • Hanshu Zhang & Frederic Moisan & Cleotilde Gonzalez, 2021. "Rock-Paper-Scissors Play: Beyond the Win-Stay/Lose-Change Strategy," Games, MDPI, vol. 12(3), pages 1-15, June.
    • Handle: RePEc:gam:jgames:v:12:y:2021:i:3:p:52-:d:579711
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    References listed on IDEAS

    as
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    3. de Weerd Harmen & Diepgrond Denny & Verbrugge Rineke, 2018. "Estimating the Use of Higher-Order Theory of Mind Using Computational Agents," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 18(2), pages 1-12, July.
    4. Colin F. Camerer & Teck-Hua Ho & Juin-Kuan Chong, 2004. "A Cognitive Hierarchy Model of Games," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(3), pages 861-898.
    5. Dimitris Batzilis & Sonia Jaffe & Steven Levitt & John A. List & Jeffrey Picel, 2019. "Behavior in Strategic Settings: Evidence from a Million Rock-Paper-Scissors Games," Games, MDPI, vol. 10(2), pages 1-34, April.
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