Markov stopping games with random priority

Szajowski, Krzysztof

doi:10.1007/bf01440735

Cited by 19 publications

(31 citation statements)

References 11 publications

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“…Similarly as in consideration by Szajowski (1994) and Neumann et al (2002) the other Nash equilibria can be constructed. There are similarities between the considered model and the asymptotic behavior of Nash equilibria for the non-zero sum game version of the SP with number of objects tending to infinity.…”

Section: Resultsmentioning

confidence: 99%

“…Two decision maker model of stopping the Markov process can be applied to investigate the competitive SP. A non-zero sum discrete time game approach considered by Szajowski (1994) gives model for the following situation. At each moment n = 1, 2, .…”

Section: Introductionmentioning

confidence: 99%

“…In this paper the game considered in Szajowski (1994) is generalized to the continuous-time version of the SP problem investigated in Bruss (1987). The mathematical model will be presented and equilibria for each α defining priority will be derived in Section 4 where also interesting properties of some solutions are point out (see also conclusion in Section 5).…”

Section: Introductionmentioning

confidence: 99%

“…The aim of each player is to choose a realization which maximizes his expected utility. The problem considered by Fushimi (1981) was a trigger for the consideration of Szajowski (1994). In fact, the problem will be formulated as a two person non-zero sum game with the concept of the Nash equilibrium as the solution.…”

Section: Introductionmentioning

confidence: 99%

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A game version of the Cowan–Zabczyk–Bruss’ problem

Szajowski¹

2007

Statistics & Probability Letters

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To cite this version:Krzysztof Szajowski. A game version of the Cowan-Zabczyk-Bruss' problem. Statistics and Probability Letters, Elsevier, 2009, 77 (17) This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. A c c e p t e d m a n u s c r i p t AbstractThe paper deal with the continuous-time two person non-zero sum game extension of the no information secretary problem. The objects appear according to the compound Poisson process and each player can choose only one applicant. If both players would like to select the same one, then the priority is assigned randomly. The aim of the players is to choose the best candidate. A construction of Nash equilibria for such game is presented. The extension of the game with randomized stopping times is taken into account. The Nash values for such extension is obtained. Analysis of the solutions for different priority defining lotteries are given.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A game version of the Cowan–Zabczyk–Bruss’ problem

Szajowski¹

2007

Statistics & Probability Letters

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“…Szajowski [36] extended this model to permit random priority. Ramsey and Szajowski [22,24] considered a mathematical model of competitive selection with random priority and random acceptance of the offer (uncertain employment) by candidates.…”

Section: Introductionmentioning

confidence: 99%

Correlated equilibria in competitive staff selection problem

Ramsey

Szajowski

2006

Game Theory and Mathematical Economics

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Abstract. This paper deals with an extension of the concept of correlated strategies to Markov stopping games. The Nash equilibrium approach to solving nonzero-sum stopping games may give multiple solutions. An arbitrator can suggest to each player the decision to be applied at each stage based on a joint distribution over the players' decisions. This is a form of equilibrium selection. Examples of correlated equilibria in nonzero-sum games related to the staff selection competition in the case of two departments are given. Utilitarian, egalitarian, republican and libertarian concepts of correlated equilibria selection are used.

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On multilateral incomplete information decision models

Szajowski

Skarupski

2019

High Frequency

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This paper treats the decision problem related to theobservation of a Markov process by decision makers. The informationdelivered to the players is based on the aggregation of thehigh‐frequency data by some functions. Admissible strategies arestopping moments related to the available information. The paymentsare defined by the state at the time of stopping. The players' decision to stop has various effects which depend on the decisionmakers' type. The type β player's stopping decision assignsthe state of the process with chance β, and it offers thisstate to the opponent with probability 1-β. The knowledgeabout the type of the players is not public and in this way, thepayers have also different information. The details of thedescription allow to formulate the problem as a Bayesian game withsets of strategies based on the stopping times. It is an extensionof Dynkin's game related to the observation of a Markov process withthe random assignment mechanism of states to the players. Some examples related to the best choice problem (BCP) are analyzed. MSC (2000) Primary: 90D15; Secondary: 93C30.

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Markov stopping games with random priority

Cited by 19 publications

References 11 publications

A game version of the Cowan–Zabczyk–Bruss’ problem

A game version of the Cowan–Zabczyk–Bruss’ problem

Correlated equilibria in competitive staff selection problem

On multilateral incomplete information decision models

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