Entropic risk for turn-based stochastic games

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Contributors

Abstract

Entropic risk (ERisk) is an established risk measure in finance, quantifying risk by an exponential re-weighting of rewards. We study ERisk for the first time in the context of turn-based stochastic games with the total reward objective. This gives rise to an objective function that demands the control of systems in a risk-averse manner. We show that the resulting games are determined and, in particular, admit optimal memoryless deterministic strategies. This contrasts risk measures that previously have been considered in the special case of Markov decision processes and that require randomization and/or memory. We provide several results on the decidability and the computational complexity of the threshold problem, i.e. whether the optimal value of ERisk exceeds a given threshold. Furthermore, an approximation algorithm for the optimal value of ERisk is provided.

Details

Original languageEnglish
Article number105214
JournalInformation and computation
Volume301(2024)
Issue numberPart A
Early online dateAug 2024
Publication statusPublished - Dec 2024
Peer-reviewedYes

External IDs

ORCID /0000-0002-5321-9343/work/167215174
ORCID /0000-0003-4829-0476/work/167216986