Exploiting Behavioral Biases to Win Nearly Every Round in a Symmetric Zero-Sum Game Without Observing Payoffs

Core Concepts

Even without knowing the game matrix or observing any payoffs, it is possible to exploit a wide variety of deterministic behavioral biases exhibited by an opponent to win nearly every round in a symmetric zero-sum game.

Abstract

The paper considers symmetric, repeated, two-player, zero-sum games where the player does not know the game matrix or observe any payoffs, but can observe the opponent's actions. It models several deterministic, behaviorally-biased opponents and shows how to exploit each bias to win nearly every round.
Key highlights:

For the Myopic Best Responder opponent, the player can learn best responses to each action and then predict and play the best response to the opponent's predicted action to win every round after the first n+1 rounds.
For the Gambler's Fallacy opponent, the player can learn best responses to the opponent's "most overdue" action and then force the opponent to play that action to win every round after the first 3n rounds.
For the Win-Stay Lose-Shift opponent (with variants for how ties are treated), the player can learn the opponent's action ordering and best responses to win all but a bounded number of rounds.
For the Follow-the-Leader opponent, the player can use the ellipsoid algorithm to estimate the game matrix and then play best responses to the predicted actions to win all but a bounded number of rounds.
The paper also provides a partial characterization of the kinds of behavioral strategies that can be exploited to win nearly every round, and shows that in some cases, the player can win nearly every round against a biased opponent even if they do not know which behavioral strategy the opponent is using.

Stats

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Quotes

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Key Insights Distilled From

Winning Without Observing Payoffs

by Avrim Blum,M... at arxiv.org 04-02-2024

https://arxiv.org/pdf/2404.00150.pdf

Deeper Inquiries

How can the techniques presented be extended to handle probabilistic behavioral strategies rather than deterministic ones

To extend the techniques presented to handle probabilistic behavioral strategies, we would need to adapt the prediction and learning algorithms to account for the uncertainty introduced by the probabilistic nature of the opponent's behavior. Instead of predicting a single deterministic action, we would need to predict a distribution over possible actions based on the opponent's strategy. This could involve using probabilistic models or Bayesian inference to update our beliefs about the opponent's behavior over time. Additionally, the learning algorithms would need to incorporate this uncertainty when determining best responses, potentially by exploring a range of possible actions and their expected payoffs under different probabilistic scenarios.

What are the implications of these results for the design of real-world competitive systems involving human participants with known behavioral biases

The implications of these results for the design of real-world competitive systems involving human participants with known behavioral biases are significant. By understanding and exploiting these biases, designers can create more engaging and balanced gameplay experiences. For example, in online gaming platforms, incorporating mechanisms to counteract common biases like loss aversion or confirmation bias can lead to fairer and more enjoyable gameplay for all participants. Moreover, by leveraging insights from behavioral game theory, developers can design systems that encourage more strategic and rational decision-making among players, ultimately enhancing the overall gaming experience.

Are there any connections between the types of behavioral biases that can be exploited and the underlying game-theoretic properties of the game being played

There are indeed connections between the types of behavioral biases that can be exploited and the underlying game-theoretic properties of the game being played. For instance, biases like the Gambler's Fallacy or Win-Stay Lose-Shift are more exploitable in games where there is a clear pattern or structure to the payoffs and actions. In games with complex or random payoffs, these biases may be less effective. Understanding the interplay between behavioral biases and game structures can help in designing games that are both challenging and engaging, while also providing opportunities for players to learn and adapt their strategies based on their opponents' biases.