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The Value of Zero-Sum Stopping Games in Continuous Time

Rida Laraki, Eilon Solan
<span title="">2005</span> <i title="Society for Industrial &amp; Applied Mathematics (SIAM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/pibbixsrufc7di3xuiggusoggm" style="color: black;">SIAM Journal of Control and Optimization</a> </i> &nbsp;
We study two-player zero-sum stopping games in continuous time and infinite horizon. We prove that the value in randomized stopping times exists as soon as the payoff processes are right-continuous.  ...  In particular, as opposed to existing literature, we do not assume any conditions on the relations between the payoff processes.  ...  We thank the anonymous referee, whose comments improved the presentation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/s0363012903429025">doi:10.1137/s0363012903429025</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sou4q3dzbrc53cy66esysx25ja">fatcat:sou4q3dzbrc53cy66esysx25ja</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922002922/http://www.math.tau.ac.il/%7Eeilons/continuous7.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/0f/55/0f55eecf267f1984f43713286c017f6ad2737013.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/s0363012903429025"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Page 3707 of Mathematical Reviews Vol. , Issue 2002E [page]

<span title="">2002</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
It is focused on two-person zero-sum games, namely, the stopping game for continuous-time models, which is studied by applying the ideas of continuous-time dynamic fuzzy systems.  ...  [Yoshida, Yuji] A zero-sum stopping game in a continuous-time dynamic fuzzy system. (English summary) Math. Comput. Modelling 34 (2001), no. 5-6, 603-614.  ... 
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Equilibrium in Two-Player Non-Zero-Sum Dynkin Games in Continuous Time [article]

Rida Laraki, Eilon Solan
<span title="2010-09-28">2010</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We prove that every two-player non-zero-sum Dynkin game in continuous time admits an epsilon-equilibrium in randomized stopping times.  ...  We provide a condition that ensures the existence of an epsilon-equilibrium in non-randomized stopping times.  ...  The existence of an εequilibrium in randomized strategies in non-zero-sum games has been proven for two-player games in discrete time (Shmaya and Solan, 2004) , and for games in continuous time under  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1009.5627v1">arXiv:1009.5627v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3tstzbc5bfgx3lamhkh7nnrg4q">fatcat:3tstzbc5bfgx3lamhkh7nnrg4q</a> </span>
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Equilibrium in two-player non-zero-sum Dynkin games in continuous time

Rida Laraki, Eilon Solan
<span title="2012-10-09">2012</span> <i title="Informa UK Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tniydh5x6nhxjjdxxqynszrpru" style="color: black;">Stochastics: An International Journal of Probability and Stochastic Processes</a> </i> &nbsp;
We prove that every two-player nonzero-sum Dynkin game in continuous time admits an ε-equilibrium in randomized stopping times.  ...  We provide a condition that ensures the existence of an ε-equilibrium in nonrandomized stopping times.  ...  The next lemma, which is proved in , states that v 1 (t) (resp. v 2 (t)) is in fact the value of the zero-sum games Γ 1 (t) (resp. Γ 2 (t)).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/17442508.2012.726222">doi:10.1080/17442508.2012.726222</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/624z6ldb4reqhhujudfz5owk4y">fatcat:624z6ldb4reqhhujudfz5owk4y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170926203038/https://hal.archives-ouvertes.fr/hal-00753508/document" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a3/cc/a3cc0c244af3f277200c6c87e4060369b6ac2cee.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/17442508.2012.726222"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> tandfonline.com </button> </a>

Non-zero-sum stopping games in continuous time [article]

Zhou Zhou
<span title="2015-08-17">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Unlike the Dynkin game, here we assume that U(s,t) is F_s∨ t-measurable. Assuming the continuity of U^i in (s,t), we show that there exists an ϵ-Nash equilibrium for any ϵ>0.  ...  On a filtered probability space (Ω ,F, (F_t)_t∈[0,∞], P), we consider the two-player non-zero-sum stopping game u^i := E[U^i(ρ,τ)], i=1,2, where the first player choose a stopping strategy ρ to maximize  ...  Let T be the set of stopping times taking values in [0, ∞]. For any σ ∈ T , denote T σ (resp. T σ+ ) as the set of stopping times that is no less (resp. strictly greater) than σ.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1508.03921v1">arXiv:1508.03921v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pg47xppz2fgbthepf24aurncs4">fatcat:pg47xppz2fgbthepf24aurncs4</a> </span>
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Page 722 of Mathematical Reviews Vol. 55, Issue 2 [page]

<span title="">1978</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Juskevié (Moscow) Mertens, Jean-Francois; Zamir, Shmuel 5217 The value of two-person zero-sum repeated games with lack of information on both sides. Internat. J. Game Theory 1 (1971/72), 39-64.  ...  Arms Control and Disarmament Agency, Washington, D.C., 1967; “Repeated games of incomplete information: the zero-sum extensive case”, Rep. No. ACDA/ST-143, pp. 37-116, U.S.  ... 
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Page 568 of Mathematical Reviews Vol. 43, Issue 2 [page]

<span title="">1972</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
The following two person zero-sum game is considered. Player 1[2] may stop the process (2;),<7 at those times ¢ for which ¢,=1 [y¥,=1].  ...  Optimal stopping rules in games with continuous time. (Russian) Uspehi Mat. Nauk 25 (1970), no. 3 (153), 271-272.  ... 
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Zero-Sum Stopping Game Associated with Threshold Probability [chapter]

Yoshio Ohtsubo
<span title="2010-08-17">2010</span> <i title="Sciyo"> Stochastic Control </i> &nbsp;
We consider a zero-sum stopping game (Dynkin's game) with a threshold probability criterion in discrete time stochastic processes.  ...  We first obtain fundamental characterization of value function of the game and optimal stopping times for both players as the result of the classical Dynkin's game, but the value function of the game and  ...  For each n ∈ N, we denote by Γ n the class of (F n )-stopping times τ such that τ ≥ n a. s.. We consider the following zero-sum stopping game.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5772/9731">doi:10.5772/9731</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dri2xp2irvab7pdito7ehzpqhy">fatcat:dri2xp2irvab7pdito7ehzpqhy</a> </span>
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Dynkin games with heterogeneous beliefs

Erik Ekström, Kristoffer Glover, Marta Leniec
<span title="">2017</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3zvvh7mxurewtffxuh4aa4rccq" style="color: black;">Journal of Applied Probability</a> </i> &nbsp;
We study zero-sum optimal stopping games (Dynkin games) between two players who disagree about the underlying model.  ...  As an example, we provide a thorough study of the game version of the American call option under heterogeneous beliefs. Finally, we also study equilibria in randomized stopping times.  ...  Other more recent contributions study various modifications of the zero-sum optimal stopping game.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/jpr.2016.97">doi:10.1017/jpr.2016.97</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wua57x22lre3heuzs7wdnpfkiq">fatcat:wua57x22lre3heuzs7wdnpfkiq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180723045802/https://opus.lib.uts.edu.au/bitstream/10453/119801/1/asymmetric_games.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/8c/81/8c813e211c7b1deed0bd62ae1870612d0a0e0bb2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/jpr.2016.97"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> cambridge.org </button> </a>

Zero-sum dynamic games and a stochastic variation of Ramsey's theorem

Eran Shmaya, Eilon Solan
<span title="">2004</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/oeoum6frfvactev64cas33x6ta" style="color: black;">Stochastic Processes and their Applications</a> </i> &nbsp;
We show how a stochastic variation of a Ramsey's theorem can be used to prove the existence of the value, and to construct -optimal strategies, in two-player zero-sum dynamic games that have certain properties  ...  applied to prove the existence of an equilibrium in two-player non-zero-sum stopping games in discrete time (see Shmaya and Solan, 2002) .  ...  Here we present another tool for proving the existence of the value in inÿnite-stage competitive interactions, or two-player zero-sum dynamic games.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.spa.2004.03.001">doi:10.1016/j.spa.2004.03.001</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tjmpn4lgqjduzpc2hyjajiro2e">fatcat:tjmpn4lgqjduzpc2hyjajiro2e</a> </span>
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On Dynkin Games with Unordered Payoff Processes [article]

Ivan Guo
<span title="2020-08-16">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
A Dynkin game is a zero-sum, stochastic stopping game between two players where either player can stop the game at any time for an observable payoff.  ...  In both discrete and continuous time settings, we provide necessary and sufficient conditions for the existence of pure strategy Nash equilibria and epsilon-optimal stopping times in all possible subgames  ...  Discrete-Time Dynkin Games We first present in Section 2.1 the classic results on discrete-time zero-sum Dynkin games.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2008.06882v1">arXiv:2008.06882v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ep5aqkjagfgavi4t7qvmfxswmm">fatcat:ep5aqkjagfgavi4t7qvmfxswmm</a> </span>
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The Continuous Time Nonzero-Sum Dynkin Game Problem and Application in Game Options

Said Hamadène, Jianfeng Zhang
<span title="">2010</span> <i title="Society for Industrial &amp; Applied Mathematics (SIAM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/pibbixsrufc7di3xuiggusoggm" style="color: black;">SIAM Journal of Control and Optimization</a> </i> &nbsp;
In this paper we study the nonzero-sum Dynkin game in continuous time which is a two player non-cooperative game on stopping times.  ...  As an application, we consider the problem of pricing American game contingent claims by the utility maximization approach. AMS Classification subjects: 91A15; 91A10; 91A30; 60G40; 91A60.  ...  Introduction Dynkin games of zero-sum or nonzero-sum, continuous or discrete time types, are games on stopping times. Since their introduction by E.B.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/080738933">doi:10.1137/080738933</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lrngn7d4knbhpmo3cf6zt4s5x4">fatcat:lrngn7d4knbhpmo3cf6zt4s5x4</a> </span>
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The Continuous Time Nonzero-sum Dynkin Game Problem and Application in Game Options [article]

Said Hamadene, Jianfeng Zhang
<span title="2008-10-31">2008</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper we study the nonzero-sum Dynkin game in continuous time which is a two player non-cooperative game on stopping times.  ...  As an application, we consider the problem of pricing American game contingent claims by the utility maximization approach.  ...  Introduction Dynkin games of zero-sum or nonzero-sum, continuous or discrete time types, are games on stopping times. Since their introduction by E.B.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0810.5698v1">arXiv:0810.5698v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/77ccfx3ezvdwdbvo5lju4xzije">fatcat:77ccfx3ezvdwdbvo5lju4xzije</a> </span>
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Page 4658 of Mathematical Reviews Vol. , Issue 87h [page]

<span title="">1987</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Stopping times which are ¢-optimal for the two players in this zero-sum game are found under conditions which guarantee their existence. John C.  ...  The authors consider a two-person zero-sum stochastic game of stopping with discrete time, infinite horizon, arbitrary state and real action spaces as well as general transition law.  ... 
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Non-zero-sum stopping games in discrete time [article]

Zhou Zhou
<span title="2015-08-25">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We consider two-player non-zero-sum stopping games in discrete time. Unlike Dynkin games, in our games the payoff of each player is revealed after both players stop.  ...  In this case, we show the existence of a Nash equilibrium in pure stopping strategies.  ...  In particular, [1, 2] consider the zero-sum case, and [1] investigates the non-zero-sum case in continuous time. In this paper, given a filtered probability space (Ω, F, (F) t=0,...  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1508.06032v1">arXiv:1508.06032v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mh2gl6j4afgkldti42rff33fyq">fatcat:mh2gl6j4afgkldti42rff33fyq</a> </span>
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