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 2164-6066

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Volume 5, 2018

Volume 4, 2017

Volume 3, 2016

Volume 2, 2015

Volume 1, 2014

The Journal of Dynamics and Games (JDG) is an applied mathematicsjournal that publishes high quality peer-review and expository papersin all research areas of expertise of its editors. The main focus ofJDG is in the interface of Dynamical Systems and Game Theory. Click here for more information

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“At this time of the passing of Professor Martin Shubik—one of Yale SOM’s most accomplished faculty members and a superbly accomplished contributor to the fields of mathematics and economics—we offer our deepest sympathies to his family and large numbers of friends and colleagues,” said Dean Edward A. Snyder.

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On the stability of an adaptive learning dynamics in traffic games
Miguel A. Dumett and Roberto Cominetti
2018, 5(4) : 265-282 doi: 10.3934/jdg.2018017 +[Abstract](278) +[HTML](217) +[PDF](604.97KB)
Abstract:

This paper investigates the dynamic stability of an adaptive learning procedure in a traffic game. Using the Routh-Hurwitz criterion we study the stability of the rest points of the corresponding mean field dynamics. In the special case with two routes and two players we provide a full description of the number and nature of these rest points as well as the global asymptotic behavior of the dynamics. Depending on the parameters of the model, we find that there are either one, two or three equilibria and we show that in all cases the mean field trajectories converge towards a rest point for almost all initial conditions.

Long-run analysis of the stochastic replicator dynamics in the presence of random jumps
Andrew Vlasic
2018, 5(4) : 283-309 doi: 10.3934/jdg.2018018 +[Abstract](228) +[HTML](189) +[PDF](455.63KB)
Abstract:

The effect of anomalous events on the replicator dynamics with aggregate shocks is considered. The anomalous events are described by a Poisson integral, where this stochastic forcing term is added to the fitness of each agent. Contrary to previous models, this noise is assumed to be correlated across the population. A formula to calculate a closed form solution of the long run behavior of a two strategy game will be derived. To assist with the analysis of a two strategy game, the stochastic Lyapunov method will be applied. For a population with a general number of strategies, the time averages of the dynamics will be shown to converge to the Nash equilibria of a relevant modified game. In the context of the modified game, the almost sure extinction of a dominated pure strategy will be derived. As the dynamic is quite complex, with respect to the original game a pure strict Nash equilibrium and an interior evolutionary stable strategy will be considered. Respectively, conditions for stochastically stability and the positive recurrent property will be derived. This work extends previous results on the replicator dynamics with aggregate shocks.

Delegation principle for multi-agency games under ex post equilibrium
Yu Chen
2018, 5(4) : 311-329 doi: 10.3934/jdg.2018019 +[Abstract](136) +[HTML](133) +[PDF](418.43KB)
Abstract:

We explore the strategic equivalence between the delegated menu contracting procedure and the centralized mechanism contracting procedure in general pure strategy multi-agency games under ex post equilibrium. We allow information externalities, contract externality, correlated types, and primitive constraints across the contracts for different agents. Our delegation principle identifies that even under this general setting ex post menu design is strategically equivalent to bilateral ex post mechanism design, which simplifies collective ex post mechanism design by ignoring relative information reference. Moreover, one can restrict attention to product menu design problems out of general menu design problems if the contract constraint sets have product structures. We provide conditions for when the principal can do strictly better by using the collective mechanism. Our results still hold if we include individual rationality or any degenerated form of our general model.

A non-iterative algorithm for generalized pig games
Fabián Crocce and Ernesto Mordecki
2018, 5(4) : 331-341 doi: 10.3934/jdg.2018020 +[Abstract](139) +[HTML](104) +[PDF](338.82KB)
Abstract:

We provide a polynomial algorithm to find the value and an optimal strategy for a generalization of the Pig game. Modeled as a competitive Markov decision process, the corresponding Bellman equations can be decoupled leading to systems of two non-linear equations with two unknowns. In this way we avoid the classical iterative approaches. A simple complexity analysis reveals that the algorithm requires \begin{document}$O(\mathbf{s}\log\mathbf{s})$\end{document} steps, where \begin{document}$\mathbf{s}$\end{document} is the number of states of the game. The classical Pig and the Piglet (a simple variant of the Pig played with a coin) are examined in detail.

Technology transfer: Barriers and opportunities
Luis C. Corchón and Clara Eugenia García
2018, 5(4) : 343-355 doi: 10.3934/jdg.2018021 +[Abstract](23) +[HTML](16) +[PDF](364.19KB)
Abstract:

In this paper we study technology transfer in a duopoly model with heterogeneous goods under quantity and price competition. We obtain three conclusions: Firstly, under product heterogeneity, technology transfer can take any form. Secondly, the properties found in the homogeneous case generalize to the heterogeneous case with various degrees of generality. Finally, if demand is not symmetric we may find full technology transfer between firms with different sizes and that firms with similar technology do not engage in technology transfer. We find evidence of the latter in the market for antidepressants.

General limit value in dynamic programming
Jérôme Renault
2014, 1(3) : 471-484 doi: 10.3934/jdg.2014.1.471 +[Abstract](760) +[PDF](385.9KB) Cited By(8)
Pure and Random strategies in differential game with incomplete informations
Pierre Cardaliaguet, Chloé Jimenez and Marc Quincampoix
2014, 1(3) : 363-375 doi: 10.3934/jdg.2014.1.363 +[Abstract](866) +[PDF](386.0KB) Cited By(6)
Existence of the uniform value in zero-sum repeated games with a more informed controller
Fabien Gensbittel, Miquel Oliu-Barton and Xavier Venel
2014, 1(3) : 411-445 doi: 10.3934/jdg.2014.1.411 +[Abstract](746) +[PDF](550.1KB) Cited By(6)
Discrete time dynamic oligopolies with adjustment constraints
Chrystie Burr, Laura Gardini and Ferenc Szidarovszky
2015, 2(1) : 65-87 doi: 10.3934/jdg.2015.2.65 +[Abstract](727) +[PDF](535.9KB) Cited By(4)
Reversibility and oscillations in zero-sum discounted stochastic games
Sylvain Sorin and Guillaume Vigeral
2015, 2(1) : 103-115 doi: 10.3934/jdg.2015.2.103 +[Abstract](728) +[PDF](364.9KB) Cited By(4)
Approachability, regret and calibration: Implications and equivalences
Vianney Perchet
2014, 1(2) : 181-254 doi: 10.3934/jdg.2014.1.181 +[Abstract](903) +[PDF](897.5KB) Cited By(4)
Nonzero-sum stochastic differential games with additive structure and average payoffs
Beatris Adriana Escobedo-Trujillo and José Daniel López-Barrientos
2014, 1(4) : 555-578 doi: 10.3934/jdg.2014.1.555 +[Abstract](917) +[PDF](527.0KB) Cited By(4)
Paths to stability in the assignment problem
Bettina Klaus and Frédéric Payot
2015, 2(3&4) : 257-287 doi: 10.3934/jdg.2015004 +[Abstract](855) +[PDF](538.5KB) Cited By(3)
Optimal strategies for operating energy storage in an arbitrage or smoothing market
Lisa C Flatley, Robert S MacKay and Michael Waterson
2016, 3(4) : 371-398 doi: 10.3934/jdg.2016020 +[Abstract](995) +[PDF](831.3KB) Cited By(3)
Dynamics of human decisions
Renato Soeiro, Abdelrahim Mousa, Tânia R. Oliveira and Alberto A. Pinto
2014, 1(1) : 121-151 doi: 10.3934/jdg.2014.1.121 +[Abstract](936) +[PDF](2417.1KB) Cited By(3)
Critical transitions and Early Warning Signals in repeated Cooperation Games
Christian Hofer, Georg Jäger and Manfred Füllsack
2018, 5(3) : 223-230 doi: 10.3934/jdg.2018014 +[Abstract](588) +[HTML](385) +[PDF](384.4KB) PDF Downloads(85)
Robust portfolio decisions for financial institutions
Ioannis Baltas, Anastasios Xepapadeas and Athanasios N. Yannacopoulos
2018, 5(2) : 61-94 doi: 10.3934/jdg.2018006 +[Abstract](955) +[HTML](397) +[PDF](721.98KB) PDF Downloads(72)
Hyperopic topologies on $l^{∞}$
Paulo Klinger Monteiro, Jaime Orrillo and Rudy José Rosas Bazán
2018, 5(1) : 1-7 doi: 10.3934/jdg.2018001 +[Abstract](1128) +[HTML](319) +[PDF](346.6KB) PDF Downloads(58)
Equivalences between two matching models: Stability
Paola B. Manasero
2018, 5(3) : 203-221 doi: 10.3934/jdg.2018013 +[Abstract](458) +[HTML](346) +[PDF](442.62KB) PDF Downloads(55)
On the linearity property for allocation problems and bankruptcy problems
Joss Sánchez-Pérez
2018, 5(1) : 9-20 doi: 10.3934/jdg.2018002 +[Abstract](749) +[HTML](288) +[PDF](333.3KB) PDF Downloads(42)
Imperfectly competitive markets, trade unions and inflation: Do imperfectly competitive markets transmit more inflation than perfectly competitive ones? A theoretical appraisal
Luis C. Corchón
2018, 5(3) : 189-201 doi: 10.3934/jdg.2018012 +[Abstract](431) +[HTML](287) +[PDF](458.0KB) PDF Downloads(40)
Constrained stochastic differential games with additive structure: Average and discount payoffs
Beatris Adriana Escobedo-Trujillo, Alejandro Alaffita-Hernández and Raquiel López-Martínez
2018, 5(2) : 109-141 doi: 10.3934/jdg.2018008 +[Abstract](791) +[HTML](270) +[PDF](599.26KB) PDF Downloads(37)
Transitional dynamics, externalities, optimal subsidy, and growth
Enrique R. Casares, Lucia A. Ruiz-Galindo and María Guadalupe García-Salazar
2018, 5(1) : 41-59 doi: 10.3934/jdg.2018005 +[Abstract](758) +[HTML](415) +[PDF](485.2KB) PDF Downloads(34)
Games with nested constraints given by a level structure
Francisco Sánchez-Sánchez and Miguel Vargas-Valencia
2018, 5(2) : 95-107 doi: 10.3934/jdg.2018007 +[Abstract](804) +[HTML](258) +[PDF](386.75KB) PDF Downloads(32)
Strategic delegation effects on Cournot and Stackelberg competition
Nickolas J. Michelacakis
2018, 5(3) : 231-242 doi: 10.3934/jdg.2018015 +[Abstract](300) +[HTML](184) +[PDF](304.41KB) PDF Downloads(31)

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