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Asymptotic Behavior of Strategies in the Repeated Prisoner's Dilemma Game in the Presence of Errors

Asymptotic Behavior of Strategies in the Repeated Prisoner's Dilemma Game in the Presence of Errors
Asymptotic Behavior of Strategies in the Repeated Prisoner's Dilemma Game in the Presence of Errors
We examine the asymptotic behavior of a finite, but error-prone population, whose agents can choose one of ALLD (always defect), ALLC (always cooperate), or Pavlov (repeats the previous action if the opponent cooperated and changes action otherwise) to play the repeated Prisoner's Dilemma. A novelty of the study is that it allows for three types of errors that affect agents' strategies in distinct ways: (a) implementation errors, (b) perception errors of one's own action, and (c) perception errors of the opponent's action. We also derive numerical results based on the payoff matrix used in the tournaments of Axelrod (1984). Strategies' payoffs are monitored as the likelihood of committing errors increases from zero to one, which enables us to provide a taxonomy of best response strategies. We find that for some range of error levels, a unique best response (i.e. a dominant strategy) exists. In all other, the population composition can vary based on the proportion of each strategist's type and/or the payoffs of the matrix. Overall, our results indicate that the emergence of cooperation is considerably weak at most error levels.
Prisoner's dilemma, bounded rationality, Markov process, dominant strategies
1927-6974
28-37
Ioannou, Christos A.
753c2afb-918b-4576-ba47-da42502f37c9
Ioannou, Christos A.
753c2afb-918b-4576-ba47-da42502f37c9

Ioannou, Christos A. (2014) Asymptotic Behavior of Strategies in the Repeated Prisoner's Dilemma Game in the Presence of Errors. Artificial Intelligence Research, 3 (4), 28-37. (doi:10.5430/air.v3n4p28).

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Abstract

We examine the asymptotic behavior of a finite, but error-prone population, whose agents can choose one of ALLD (always defect), ALLC (always cooperate), or Pavlov (repeats the previous action if the opponent cooperated and changes action otherwise) to play the repeated Prisoner's Dilemma. A novelty of the study is that it allows for three types of errors that affect agents' strategies in distinct ways: (a) implementation errors, (b) perception errors of one's own action, and (c) perception errors of the opponent's action. We also derive numerical results based on the payoff matrix used in the tournaments of Axelrod (1984). Strategies' payoffs are monitored as the likelihood of committing errors increases from zero to one, which enables us to provide a taxonomy of best response strategies. We find that for some range of error levels, a unique best response (i.e. a dominant strategy) exists. In all other, the population composition can vary based on the proportion of each strategist's type and/or the payoffs of the matrix. Overall, our results indicate that the emergence of cooperation is considerably weak at most error levels.

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Published date: 28 September 2014
Keywords: Prisoner's dilemma, bounded rationality, Markov process, dominant strategies
Organisations: Economics

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Local EPrints ID: 369272
URI: http://eprints.soton.ac.uk/id/eprint/369272
ISSN: 1927-6974
PURE UUID: d58ee936-a0b9-4f88-8816-35ec2f89c237

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Date deposited: 30 Sep 2014 12:39
Last modified: 14 Mar 2024 18:00

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Author: Christos A. Ioannou

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