Selection of a correlated equilibrium in Markov stopping games

Ramsey, David; Szajowski, Krzysztof

doi:10.1016/j.ejor.2006.10.050

Cited by 10 publications

(10 citation statements)

References 41 publications

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“…This occurs because the correlation law is applied stage-wise and optimizes a local criterion; there is no guarantee that the corresponding global criterion is respected. A similar phenomenon was observed in [35,Section 5.4].…”

Section: Numerical Examplessupporting

confidence: 84%

“…Let γ be an Fadapted stochastic process taking values in ∆ 4 . Following [35] we interpret γ(t) as a weak (stepwise) communication device, with γ ij (t) specifying the probability that player 1 takes action i ∈ {0, 1} and player 2 applies action j ∈ {0, 1},…”

Section: 3mentioning

confidence: 99%

“…We begin with analyzing the single-agent objective. Next, in Section 3.2 we move on to the one-shot non-zero-sum stopping game that is built iteratively from the one-period 2 × 2 games, following the methods of [35]. Finally, in Section 3.3 we describe the sequential stopping game that in the limit is shown in Section 3 to coincide with our original model in (3). 3.1.…”

Section: Sequential Stopping Gamementioning

confidence: 99%

See 2 more Smart Citations

Stochastic Switching Games and Duopolistic Competition in Emissions Markets

Ludkovski¹

2011

SIAM J. Finan. Math.

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We study optimal behavior of energy producers under a CO2 emission abatement program. We focus on a two-player discrete-time model where each producer is sequentially optimizing her emission and production schedules. The game-theoretic aspect is captured through a reducedform price-impact model for the CO2 allowance price. Such duopolistic competition results in a new type of a non-zero-sum stochastic switching game on finite horizon. Existence of game Nash equilibria is established through generalization to randomized switching strategies. No uniqueness is possible and we therefore consider a variety of correlated equilibrium mechanisms. We prove existence of correlated equilibrium points in switching games and give a recursive description of equilibrium game values. A simulation-based algorithm to solve for the game values is constructed and a numerical example is presented.2000 Mathematics Subject Classification. 91A15, 60G40, 93E20, 91B76.

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Section: Numerical Examplessupporting

confidence: 84%

Section: 3mentioning

confidence: 99%

Section: Sequential Stopping Gamementioning

confidence: 99%

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Stochastic Switching Games and Duopolistic Competition in Emissions Markets

Ludkovski¹

2011

SIAM J. Finan. Math.

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“…Concerning the dice race problem it would be interesting to know whether the optimal strategy for two players approaching both the target ends up to solve the problem of selection of a correlated equilibrium in Markov stopping games as studied by Ramsey and Szajowski [14]. Lacking experience in this field, we have not pursued this question in more depth.…”

Section: Target N the Mean Number Of Roundsmentioning

confidence: 99%

Recent studies on the Dice Race Problem and its connections

Louchard

2016

MathAppl

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The following type of dice games has been mentioned and/or studied in the literature. Players take turns in rolling a fair die successively, each player accumulating his or her scores as long as the outcome 1 does not occur. If the result 1 turns up, the accumulated score is wiped out, and the turn ends, that is the player gives the die to the next player. At any stage after a roll, the player (she, say) can choose to end her turn and bank her accumulated score. The winner is the first player to reach some fixed target n ∈ N. We present some new results on optimal strategies and winning probability in a one or two players game. For just one player there is no competition of course, and in this case we suppose that the player simply wants to minimize her total expected number of tosses over all possible banking strategies.

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“…A game with continuous time where players have possibility to stop more than once was presented in Laraki and Solan (2005). An extensive bibliography on games can be found in Ekström and Peskir (2008), Nowak and Szajowski (1999), , Ramsey and Szajowski (2008) and Solan and Vieille (2003).…”

Section: Introductionmentioning

confidence: 99%

Construction of Nash equilibrium based on multiple stopping problem in multi-person game

Krasnosielska-Kobos

2015

Math Meth Oper Res

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We consider a multi-person stopping game with players' priorities and multiple stopping. Players observe sequential offers at random or fixed times. Each accepted offer results in a reward. Each player can obtain fixed number of rewards. If more than one player wants to accept an offer, then the player with the highest priority among them obtains it. The aim of each player is to maximize the expected total reward. For the game defined this way, we construct a Nash equilibrium. The construction is based on the solution of an optimal multiple stopping problem. We show the connections between expected rewards and stopping times of the players in Nash equilibrium in the game and the optimal expected rewards and optimal stopping times in the multiple stopping problem. A Pareto optimum of the game is given. It is also proved that the presented Nash equilibrium is a sub-game perfect Nash equilibrium. Moreover, the Nash equilibrium payoffs are unique. We also present new results related to multiple stopping problem.

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Selection of a correlated equilibrium in Markov stopping games

Cited by 10 publications

References 41 publications

Stochastic Switching Games and Duopolistic Competition in Emissions Markets

Stochastic Switching Games and Duopolistic Competition in Emissions Markets

Recent studies on the Dice Race Problem and its connections

Construction of Nash equilibrium based on multiple stopping problem in multi-person game

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