 Combined Games with Randomly Delayed BeginningsF. Thomas Bruss
Mathematics, 2021, vol. 9, issue 5, 1-16 Abstract: This paper presents two-person games involving optimal stopping. As far as we are aware, the type of problems we study are new. We confine our interest to such games in discrete time. Two players are to chose, with randomised choice-priority, between two games G 1 and G 2 . Each game consists of two parts with well-defined targets. Each part consists of a sequence of random variables which determines when the decisive part of the game will begin. In each game, the horizon is bounded, and if the two parts are not finished within the horizon, the game is lost by definition. Otherwise the decisive part begins, on which each player is entitled to apply their or her strategy to reach the second target. If only one player achieves the two targets, this player is the winner. If both win or both lose, the outcome is seen as “deuce”. We motivate the interest of such problems in the context of real-world problems. A few representative problems are solved in detail. The main objective of this article is to serve as a preliminary manual to guide through possible approaches and to discuss under which circumstances we can obtain solutions, or approximate solutions. Keywords: two-person game; optimal stopping; patterns; occurrence time; renewal process; li-algorithm; odds-algorithm; plug-in odds-algorithm; business plans; competition (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:5:p:534-:d:510067 Access Statistics for this article Mathematics is currently edited by Ms. Emma He More articles in Mathematics from MDPI |
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