# Iterated Prisoner's Dilemma with Partial Imitation in Noisy Environments

### Andre Amend, Degang Wu, Kwok Yip Szeto

#### Abstract

Players with one-step memory in an iterated Prisoner's Dilemma game can adaptively change their strategies after playing some games with their opponent. The probability of change of strategies depends on noise levels, the players’ patience (or reaction time), and initial strategies. Players perform partial imitation, since, realistically, they can only imitate what they observe. Patience determines the frequency of a player's possible strategies changes. In this paper, we focus on the evolution of strategies between two major categories of players whose innate characters belong either to cheaters (traitors) or nice (benevolent) players. We consider them as agents whose characters are fixed, but their detailed genetic makeup can still vary among several types, so that, for example, the cheaters can evolve among different types of cheaters. We observe their evolutions by means of their degree of cooperation, where the variables are initial strategies, noise, and patience. Here, noise is incorporated in a sigmoid function that accounts for errors in learning. The numerical results show interesting features that we can explain heuristically: in the iterated games between an adaptive cheater against a patient nice player in a noisy environment, we observe a minimum degree of cooperation at a specific noise level.

#### References

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#### Paper Citation

#### in Harvard Style

Amend A., Wu D. and Szeto K. (2014). **Iterated Prisoner's Dilemma with Partial Imitation in Noisy Environments** . In *Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: ECTA, (IJCCI 2014)* ISBN 978-989-758-052-9, pages 228-235. DOI: 10.5220/0005075402280235

#### in Bibtex Style

@conference{ecta14,

author={Andre Amend and Degang Wu and Kwok Yip Szeto},

title={Iterated Prisoner's Dilemma with Partial Imitation in Noisy Environments},

booktitle={Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: ECTA, (IJCCI 2014)},

year={2014},

pages={228-235},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005075402280235},

isbn={978-989-758-052-9},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Evolutionary Computation Theory and Applications - Volume 1: ECTA, (IJCCI 2014)

TI - Iterated Prisoner's Dilemma with Partial Imitation in Noisy Environments

SN - 978-989-758-052-9

AU - Amend A.

AU - Wu D.

AU - Szeto K.

PY - 2014

SP - 228

EP - 235

DO - 10.5220/0005075402280235