University of Oulu

János Flesch, Arkadi Predtetchinski, Ville Suomala (2022) Random Perfect Information Games. Mathematics of Operations Research 48(2):708-727.

Random perfect information games

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Author: Flesch, János1; Predtetchinski, Arkadi2; Suomala, Ville3
Organizations: 1Department of Quantitative Economics, Maastricht University, P.O.Box 616, 6200 MD, The Netherlands
2Department of Economics, Maastricht University, P.O.Box 616, 6200 MD, The Netherlands
3Department of Mathematical sciences, University of Oulu, P.O.Box 8000, FI–90014, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.4 MB)
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Language: English
Published: Institute for Operations Research and the Management Sciences, 2023
Publish Date: 2023-06-16


The paper proposes a natural measure space of zero-sum perfect information games with upper semicontinuous payoffs. Each game is specified by the game tree and by the assignment of the active player and the capacity to each node of the tree. The payoff in a game is defined as the infimum of the capacity over the nodes that have been visited during the play. The active player, the number of children, and the capacity are drawn from a given joint distribution independently across the nodes. We characterize the cumulative distribution function of the value v using the fixed points of the so-called value-generating function. The characterization leads to a necessary and sufficient condition for the event v≥k to occur with positive probability. We also study probabilistic properties of the set of player I’s k-optimal strategies and the corresponding plays.

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Series: Mathematics of operations research
ISSN: 0364-765X
ISSN-E: 1526-5471
ISSN-L: 0364-765X
Volume: 48
Issue: 2
Pages: 708 - 727
DOI: 10.1287/moor.2022.1277
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
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