Random Perfect Information Games

János Flesch (), Arkadi Predtetchinski () and Ville Suomala ()
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János Flesch: Department of Quantitative Economics, Maastricht University, 6200 MD Maastricht, Netherlands
Arkadi Predtetchinski: Department of Economics, Maastricht University, 6200 MD Maastricht, Netherlands
Ville Suomala: Department of Mathematical sciences, University of Oulu, FI–90014 Oulu, Finland

Mathematics of Operations Research, 2023, vol. 48, issue 2, 708-727

Abstract: 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.

Keywords: Primary: 91A70; 91A25; 91A18; secondary: 60J85; zero-sum game; perfect information; value; Galton–Watson measure; branching process (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:48:y:2023:i:2:p:708-727

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