TY - JOUR

T1 - Algorithms may not learn to play a unique Nash equilibrium

AU - Fujiwara-Greve, Takako

AU - Nielsen, Carsten Krabbe

N1 - Funding Information:
The authors are grateful to an anonymous referee for useful comments.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd.

PY - 2021/11

Y1 - 2021/11

N2 - There is a widespread hope that, in the near future, algorithms become so sophisticated that “solutions” to most problems are found by machines. In this note, we throw some doubts on this expectation by showing the following impossibility result: given a set of finite-memory, finite-iteration algorithms, a continuum of games exist, whose unique and strict Nash equilibrium cannot be reached from a large set of initial states. A Nash equilibrium is a social solution to conflicts of interest, and hence finite algorithms should not be always relied upon for social problems. Our result also shows how to construct games to deceive a given set of algorithms to be trapped in a cycle without a Nash equilibrium.

AB - There is a widespread hope that, in the near future, algorithms become so sophisticated that “solutions” to most problems are found by machines. In this note, we throw some doubts on this expectation by showing the following impossibility result: given a set of finite-memory, finite-iteration algorithms, a continuum of games exist, whose unique and strict Nash equilibrium cannot be reached from a large set of initial states. A Nash equilibrium is a social solution to conflicts of interest, and hence finite algorithms should not be always relied upon for social problems. Our result also shows how to construct games to deceive a given set of algorithms to be trapped in a cycle without a Nash equilibrium.

KW - Algorithm

KW - Impossibility

KW - Learning

KW - Nash equilibrium

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U2 - 10.1007/s42001-021-00109-9

DO - 10.1007/s42001-021-00109-9

M3 - Article

AN - SCOPUS:85126046420

VL - 4

SP - 839

EP - 850

JO - Journal of Computational Social Science

JF - Journal of Computational Social Science

SN - 2432-2717

IS - 2

ER -