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Strategies to Exploit Myopic and Gambler’s Fallacy Opponentsby@algorithmicbias

Strategies to Exploit Myopic and Gambler’s Fallacy Opponents

by Algorithmic Bias (dot tech)
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Algorithmic Bias (dot tech)

@algorithmicbias

Explore the intersection of AI, game theory, and behavioral strategies....

January 24th, 2025
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This section introduces algorithms to exploit the Myopic Best Responder and Gambler's Fallacy opponents in zero-sum games. For the Myopic Best Responder, Algorithm 2 guarantees wins after recording best responses in initial rounds. Against Gambler’s Fallacy, Algorithm 3 uses patterns of overdue actions to predict and counter the opponent, ensuring consistent wins after the initial rounds.
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STORY’S CREDIBILITY

Academic Research Paper

Academic Research Paper

Part of HackerNoon's growing list of open-source research papers, promoting free access to academic material.

Authors:

(1) Avrim Blum, Toyota Technological Institute at Chicago, IL, USA;

(2) Melissa Dutz, Toyota Technological Institute at Chicago, IL, USA.

Abstract and 1 Introduction

2 Setting and 2.1 Models of behaviorally-biased opponents

3 Preliminaries and Intuition

4.1 Myopic Best Responder and 4.2 Gambler’s Fallacy Opponent

4.3 Win-Stay, Lose-Shift Opponent

4.4 Follow-the-Leader Opponent and 4.5 Highest Average Payoff Opponent

5 Generalizing

5.1 Other Behaviorally-Biased Strategies

5.2 Exploiting an Unknown Strategy from a Known Set of Strategies

6 Future Work and References

A Appendix

A.1 Win-Stay Lose-Shift Variant: Tie-Stay

A.2 Follow-the-Leader Variant: Limited History

A.3 Ellipsoid Mistake Bounds

A.4 Highest Average Payoff Opponent


4. Strategies for Beating Behaviorally Biased Opponents

4.1 Myopic Best Responder


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▶ Theorem 3. Playing Algorithm 2 against the Myopic Best Responder in a permissible game (Definition 1) results in winning every round after the first n + 1 rounds.


Proof. The Myopic Best Responder plays a best response to our previous action, so we record a correct best response to each action during the first n + 1 rounds. The Myopic Best Responder always plays the same best response (the first one in its action ordering) following any given action, so we correctly predict the action it will play from round n + 2 onward. Therefore we win every round from round n + 2 onward, since we correctly predict the opponent’s action and play a valid best response to it.


4.2 Gambler’s Fallacy Opponent

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▶ Theorem 4. Playing Algorithm 3 against the Gambler’s Fallacy opponent in a permissible game (Definition 1) results in winning every round from round 3n onward.


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This paper is available on arxiv under CC BY 4.0 DEED license.


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Algorithmic Bias (dot tech)@algorithmicbias
Explore the intersection of AI, game theory, and behavioral strategies.

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