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Related Experiment Video

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The Spatial Memory Game: Testing the Relationship Between Spatial Language, Object Knowledge, and Spatial Cognition

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Published on: February 19, 2018

Zero-determinant strategies under observation errors in repeated games.

Azumi Mamiya¹, Genki Ichinose¹

¹Department of Mathematical and Systems Engineering, Shizuoka University, Hamamatsu 432-8561, Japan.

Physical Review. E

|October 20, 2020

Summary

Zero-determinant (ZD) strategies in the repeated prisoner's dilemma maintain linear payoffs, even with discounting and errors. However, specific ZD subsets like Extortion and Generous strategies do not exist under these conditions.

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Area of Science:

Game Theory
Computational Economics
Evolutionary Game Theory

Background:

Zero-determinant (ZD) strategies enforce linear payoffs in the repeated prisoner's dilemma (RPD).
Real-world interactions often involve discounting and observation errors, which were not initially considered for ZD strategies.

Purpose of the Study:

To analytically investigate ZD strategies in the RPD game with both discounting and observation errors.
To identify all strategies that maintain linear payoff relationships under these generalized conditions.

Main Methods:

Analytical study of strategies enforcing linear payoff relationships in the RPD with discount factors and observation errors.
Numerical derivation of threshold values for the existence of specific ZD strategy subsets.

Main Results:

Payoffs can still be represented by determinants, similar to the original ZD strategy findings.
Only Zero-determinant (ZD) strategies and unconditional strategies satisfy the linear payoff condition with errors and discounting.
Extortion and Generous strategies, subsets of ZD strategies, do not exist under these generalized conditions.

Conclusions:

The study clarifies the conditions under which ZD strategies and their subsets exist in more realistic RPD scenarios.
Findings contribute to a deeper understanding of strategy dynamics in noisy and discounted game-theoretic interactions.