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Sequential games. (English) Zbl 1002.60082

Various special sequential games have been studied. For recent studies see the authors’ references. For the most part, the games that have been studied fit into the general class of \(n\)-point win-by-\(k\) games between two players engaged in Bernoulli trials. In spite of the number of papers on special games, there have been few systematic studies of sequential games to our knowledge.
This note attempts to address the deficiency, and has the basic parts: 1. The authors give a construction of sequential games with multiple players that is general to encompass the key ideas without being unnecessarily technical. 2. The authors give a general construction of composition, the important way in which sequential games are combined to form new games. 3. The authors study the property of independence between the winner of the game and the number of points played. 4. Also, the authors obtain new properties of the class of win-by-\(k\) games, including the independence property and closure under composition. 5. Finally, new results on the asymptotic efficiency of the \(n\)-point, win-by-\(k\) game are obtained.

MSC:

60K10 Applications of renewal theory (reliability, demand theory, etc.)
62C05 General considerations in statistical decision theory
91A15 Stochastic games, stochastic differential games
60G40 Stopping times; optimal stopping problems; gambling theory
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