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Misperception influence on zero-determinant strategies in iterated Prisoner's Dilemma
Zhaoyang Cheng1,2, Guanpu Chen1,3, Yiguang Hong4,5
1Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Beijing, 100190, China.
Scientific Reports
|March 26, 2022
Summary
This study examines Zero-determinant strategies in Iterated Prisoner's Dilemma games under misperception. It establishes conditions for these strategies and analyzes utility deviations when one player perceives the other's misperception.
Area of Science:
- Game Theory
- Computational Economics
- Artificial Intelligence
Background:
- Zero-determinant (ZD) strategies offer unilateral control over players' expected utilities in Iterated Prisoner's Dilemma (IPD).
- Misperception is a common factor in real-world IPD scenarios, introducing uncertainty.
- Understanding misperception's impact on ZD strategies is crucial for practical applications.
Purpose of the Study:
- To investigate the influence of misperception on Zero-determinant strategies in IPD.
- To establish conditions for ZD strategies when one player (X) detects and accounts for the other's (Y) misperception.
- To analyze the bounds of utility deviation and potential improvements for player X.
Main Methods:
- Mathematical modeling of IPD with asymmetric cognitive states (misperception).
- Derivation of necessary and sufficient conditions for ZD strategies under misperception.
- Analysis of expected utility deviations and player X's utility optimization.
Main Results:
- A precise condition for the existence of ZD strategies in IPD with misperception was identified.
- A linear relationship between player utilities is maintained within player X's cognition.
- Bounds for the deviation of expected utilities from this linear relationship were determined.
Conclusions:
- ZD strategies can be robust even in the presence of misperception, provided specific conditions are met.
- Player X can leverage the detection of misperception to improve its own utility while maintaining a linear relationship.
- The study provides a theoretical framework for understanding strategic interactions under uncertainty in IPD.
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