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Controlling conditional expectations by Zero-Determinant strategies

Operations Research Forum Volume 3 Page 48-
published_at 2022-09-05
s43069-022-00159-3.pdf
[fulltext] 2.47 MB
Title
Controlling conditional expectations by Zero-Determinant strategies
Abstract
Zero-determinant strategies are memory-one strategies in repeated games which unilaterally enforce linear relations between expected payoffs of players. Recently, the concept of zero-determinant strategies was extended to the class of memory-n strategies with n _ 1, which enables more compli-cated control of payoffs by one player. However, what we can do by memory-n zero-determinant strategies is still not clear. Here, we show that memory-n zero-determinant strategies in repeated games can be used to control condi-tional expectations of payoffs. Equivalently, they can be used to control ex-pected payoffs in biased ensembles, where a history of action pro_les with large value of bias function is more weighted. Controlling conditional expectations of payoffs is useful for strengthening zero-determinant strategies, because play-ers can choose conditions in such a way that only unfavorable action pro_les to one player are contained in the conditions. We provide several examples of memory-n zero-determinant strategies in the repeated prisoner's dilemma game. We also explain that a deformed version of zero-determinant strategies is easily extended to the memory-n case.
Creators Ueda Masahiko
[e_rad]00826571
Affiliate Master Yamaguchi University
[kakenhi]15501 grid.268397.1
Source Identifiers [EISSN] 2662-2556
Creator Keywords
Repeated games Zero-determinant strategies Memory-n strategies
Languages eng
Resource Type journal article
Publishers Springer Nature
Date Issued 2022-09-05
Rights
Creative Commons Attribution 4.0 International(https://creativecommons.org/licenses/by/4.0/)
File Version Version of Record
Access Rights open access
Relations
[isIdenticalTo] https://doi.org/10.1007/s43069-022-00159-3
Funding Refs
Japan Society for the Promotion of Science [crossref_funder]https://doi.org/10.13039/501100001691
Award Economic theory of information markets based on information science 20K19884
Funding Refs
Inamori Foundation
Award 繰り返しゲームにおける利得制御の数理構造の解明