January  2014, 1(1): 1-15. doi: 10.3934/jdg.2014.1.1

Bio-inspired paradigms in network engineering games

1. 

INRIA Sophia-Antipolis, 2004 Route des Lucioles, 06906, Sophia-Antipolis, France

Received  April 2012 Revised  June 2012 Published  June 2013

Network Engineering Games (NEGs) is an emerging branch of game theory developed in Electrical Engineering Departments. It concerns games that arise in all levels of telecommunication networks. There has been a growing interest among researchers in this community in bio-inspired methodologies in recent years due to two reasons. First, many problems in networking have much in common with problems in biology. Examples are (i) propagation of information in networks, that has similar dynamics as propagation of epidemics; (ii) energy management issues in wireless networks and competition over resources are often similar to issues by biologists; (iii) both equilibria concepts as well as replicator dynamics that arise in evolutionary games are quite relevant to NEGs. In this paper we present an overview of applications and tools used in network engineering games, we then describe in more depth bio-inspired tools used in or relevant to network engineering. We present finally an example of a stochastic epidemic game arising in wireless networks that involves competition over the relaying of information.
Citation: Eitan Altman. Bio-inspired paradigms in network engineering games. Journal of Dynamics and Games, 2014, 1 (1) : 1-15. doi: 10.3934/jdg.2014.1.1
References:
[1]

T. Alpcan and T. Başar, "Network Security. A Decision and Game-Theoretic Approach," Cambridge University Press, Cambridge, 2011.

[2]

E. Altman, "Constrained Markov Decision Processes. Stochastic Modeling," Chapman & Hall/CRC, Boca Raton, FL, 1999.

[3]

E. Altman, R. El Azouzi and V. Abramov, Non-cooperative routing in loss networks, Performance Evaluation, 49 (2002), 257-272. doi: 10.1016/S0166-5316(02)00112-8.

[4]

E. Altman, T. Boulogne, R. El-Azouzi, T. Jiménez and L. Wynter, A survey on networking games in telecommunications, Computers and Operations Research, 33 (2006), 286-311. doi: 10.1016/j.cor.2004.06.005.

[5]

E. Altman and R. El-Azouzi, La théorie des jeux non-coopératifs appliquée aux réseaux de télécommunication, (in French) Annales des Télécommunications, (2007).

[6]

E. Altman and L. Wynter, Equilibrium, games, and pricing in transportation and telecommunications networks, Networks and Spatial Economics, 4 (2004), 7-21. doi: 10.1023/B:NETS.0000015653.52983.61.

[7]

Eitan Altman, A stochastic game approach for competition over popularity in social networks, Dynamic Games and Applications, online publication, (2012). Available from: http://hal.inria.fr/hal-00681959. doi: 10.1007/s13235-012-0057-4.

[8]

Eitan Altman and Yezekael Hayel, Markov decision evolutionary games, IEEE Transactions on Automatic Control, 55 (2010), 1560-1569. doi: 10.1109/TAC.2010.2042230.

[9]

J. Aspnes, K. Chang and A. Yampolskiy, Inoculation strategies for victims of viruses and the sum-of-squares partition problem, J. Comput. Syst. Sci., 72 (2006), 1077-1093. doi: 10.1016/j.jcss.2006.02.003.

[10]

J. Aspnes, N. Rustagi and J. Saia, Worm versus alert: Who wins in a battle for control of a large-scale network?, Lecture Notes in Computer Science, 4878 (2007), 443-456. doi: 10.1007/978-3-540-77096-1_32.

[11]

C. T. Bauch, Imitation dynamics predict vaccinating behavior, Proc. of The Royal Society, (2005). doi: 10.1098/rspb.2005.3153.

[12]

C. T. Bauch and D. J. D. Earn, Vaccination and the theory of games, Proceedings of the National Academy of Science, 101 (2004), 13391-13394. doi: 10.1073/pnas.0403823101.

[13]

N. G. Beans, F. P. Kelly and P. G. Taylor, Braess's paradox in a loss network, J. Appl. Prob., 34 (1997), 155-159. doi: 10.2307/3215183.

[14]

M. Beckmann, C. B. McGuire and C. B. Winsten, "Studies in the Economics of Transportation," Yale Univ. Press, New Haven, 1956.

[15]

T. Berger, The source coding game, IEEE Trans. on Inform. Theory, IT-17 (1971), 71-76.

[16]

N. M. Blachman, Communication as a game, in "I.R.E. WESCON Convention Record Part 2" (August 1957), 61-66.

[17]

D. Braess, Über ein Paradoxien aus der Verkehrsplanung, (German) Unternehmensforschung, 12 (1968), 258-268.

[18]

Mung Chiang, Chee Wei Tan, Prashanth Hande and Tian Lan, Power control in wireless cellular networks, Foundations and Trends in Networking, 2 (2007), 381-533. doi: 10.1561/1300000009.

[19]

S. Coraluppi and S. I. Marcus, Risk-sensitive queueing, in "Proc. 35th Annual Allerton Conf. on Communication, Control, and Computing," Urbana, IL, USA, September 28-October 1, 1997.

[20]

Merouane Debbah and Samson Lasaulce, "Game Theory for Wireless Networks: From Fundamentals to Practice," Elsevier Science & Technology, 2011.

[21]

C. Douligeris, "Optimal Flow Control and Fairness in Communication Networks: A Game Theoretic Perspective," Ph.D. Dissertation, Electrical Engineering, Columbia University, 1989.

[22]

T. Ericson, The noncooperative binary adder channel, IEEE Trans. on Inform. Theory, 32 (1986), 365-374. doi: 10.1109/TIT.1986.1057190.

[23]

D. Falomari, N. Mandayam and D. Goodman, A new framework for power control in wireless data networks: Games utility and pricing, in "Proc. Allerton Conference on Communication, Control and Computing," Champaign, Illinois, USA, (1998), 546-555.

[24]

C. Frenzel, H. Sanneck and S. Hamalainen, "LTE Self-Organising Networks (Son): Network Management Automation for Operational Efficiency," John Wiley & Sons, 2011.

[25]

A. Haurie and P. Marcotte, On the relationship between Nash-Cournot and Wardrop equilibria, Networks, 15 (1985), 295-308. doi: 10.1002/net.3230150303.

[26]

M. T. Hsiao and A. A. Lazar, A game theoretic approach to decentralized flow control of Markovian queueing networks, in "Performance '87" (Brussels, 1987), North-Holland, Amsterdam, (1988), 55-73.

[27]

M. T. Hsiao and A. A. Lazar, Optimal decentralized flow control of Markovian queueing networks with multiple controllers, Performance Evaluation, 13 (1991), 181-204. doi: 10.1016/0166-5316(91)90054-7.

[28]

M. H. R. Khouzani, Saswati Sarkar and Eitan Altman, Saddle-point strategies in malware attack, IEEE Journal on Selected Areas in Communications, 30 (2012), 31-43. doi: 10.1109/JSAC.2012.120104.

[29]

Man-Tung Tony Hsiao, "Optimal Decentralized Flow Control in Computer Communication Networks," Ph.D. Thesis, EE, Columbia Univ, October, 1986.

[30]

Anna Jaśkiewicz, A note on negative dynamic programming for risk-sensitive control, Operations Research Letters, 36 (2008), 531-534. doi: 10.1016/j.orl.2008.03.003.

[31]

Hongbin Ji and Ching-Yao Huang, Non-cooperative uplink power control in cellular radio systems, Wireless Networks, 4 (1998), 233-240.

[32]

B. Jovanovic and R. W. Rosenthal, Anonymous sequential games, Journal of Mathematical Economics, 17 (1988), 77-87. doi: 10.1016/0304-4068(88)90029-8.

[33]

S. Lasaulce and H. Tembine, "Game Theory and Learning for Wireless Networks," Fundamentals and Applications, Academic Press, 2011.

[34]

S. A. Lippman, Applying a new device in the optimization of exponential queueing systems, Operations Research, 23 (1975), 687-710. doi: 10.1287/opre.23.4.687.

[35]

Allen Mackenzie and Luiz DaSilva, "Game Theory for Wireless Engineers," Synthesis Lectures on Communications, Morgan & Claypool Publishers, 2006. doi: 10.2200/S00014ED1V01Y200508COM001.

[36]

R. Mazumdar, L. G. Mason and C. Douligeris, Fairness in network optimal flow control: Optimality of product forms, IEEE Trans. on Comm., 39 (1991), 775-782. doi: 10.1109/26.87140.

[37]

I. Menache and A. Ozdaglar, "Network Games: Theory, Models, and Dynamics," Synthesis Lectures on Communication Networks, Morgan & Claypool Publishers, 2011. doi: 10.2200/S00330ED1V01Y201101CNT009.

[38]

I. Milchtaich, Congestion games with player-specific payoff functions, Games and Economic Behavior, 13 (1996), 111-124. doi: 10.1006/game.1996.0027.

[39]

W. Murrey, The application of epidemiology to computer viruses, Comp. Security, 7 (1988), 139-150.

[40]

Noam Nisan, Tim Roughgarden, Éva Tardos and Vijay V. Vazirani, eds., "Algorithmic Game Theory," Cambridge University Press, Cambridge, 2007. doi: 10.1017/CBO9780511800481.

[41]

A. Orda, R. Rom and N. Shimkin, Competitive routing in multi-user communication networks, in "INFOCOM '93. Proceedings. Twelfth Annual Joint Conference of the IEEE Computer and Communications Societies. Networking: Foundation for the Future" (San Francisco, CA), IEEE, (1993), 964-971. doi: 10.1109/INFCOM.1993.253270.

[42]

M. Patriksson, "The Traffic Assignment Problem: Models and Methods," VSP BV, P.O. Box 346, 3700 AH Zeist, The Netherlands, 1994.

[43]

R. W. Rosenthal, A class of games possessing pure strategy Nash equilibria, Int. J. Game Theory, 2 (1973), 65-67. doi: 10.1007/BF01737559.

[44]

R. W. Rosenthal, The network equilibrium problem in integers, Networks, 3 (1973), 53-59. doi: 10.1002/net.3230030104.

[45]

William H. Sandholm, "Population Games and Evolutionary Dynamics," Economic Learning and Social Evolution, MIT Press, Cambridge, MA, 2010.

[46]

J. Maynard Smith, Game theory and the evolution of fighting, in "On Evolution" (J. Maynard Smith), Edinburgh University Press, Edinburgh, (1972), 8-28.

[47]

Hamidou Tembine, Eitan Altman, Rachid El-Azouzi and Yezekael Hayel, Evolutionary games in wireless networks, IEEE Transactions on Systems, Man, and Cybernetics, Part B, 40 (2010), 634-646. doi: 10.1109/TSMCB.2009.2034631.

[48]

Hamidou Tembine, Eitan Altman, Rachid El-Azouzi and Yezekael Hayel, Bio-inspired delayed evolutionary game dynamics with networking applications, Telecommunication Systems, 47 (2011), 137-152. doi: 10.1007/s11235-010-9307-1.

[49]

D. C. Trimble, "A Game-Theoretic Approach to Signal and Receiver Design," Ph.D. Thesis, Nov. 1972. doi: 10.1109/TIT.1972.1054913.

[50]

T. L. Vincent and J. S. Brown, "Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics," Cambridge Univ Press, 2005.

[51]

J. G. Wardrop, Some theoretical aspects of road traffic research communication networks, Proc. Inst. Civ. Eng., Part 2, 1 (1952), 325-378.

[52]

Y. Zhang and M. Guizani, "Game Theory for Wireless Commun. and Networking," CRC, 2011.

[53]

Yan Zhang and Mohsen Guizani, "Game Theory for Wireless Communications and Networking," Taylor and Francis, 2010.

[54]

I. Ziedins, A paradox in a queueing network with state-dependent routing and loss, Journal of Applied Mathematics and Decision Sciences, 2007 (2007), Article ID 68280, 10 pp. doi: 10.1155/2007/68280.

show all references

References:
[1]

T. Alpcan and T. Başar, "Network Security. A Decision and Game-Theoretic Approach," Cambridge University Press, Cambridge, 2011.

[2]

E. Altman, "Constrained Markov Decision Processes. Stochastic Modeling," Chapman & Hall/CRC, Boca Raton, FL, 1999.

[3]

E. Altman, R. El Azouzi and V. Abramov, Non-cooperative routing in loss networks, Performance Evaluation, 49 (2002), 257-272. doi: 10.1016/S0166-5316(02)00112-8.

[4]

E. Altman, T. Boulogne, R. El-Azouzi, T. Jiménez and L. Wynter, A survey on networking games in telecommunications, Computers and Operations Research, 33 (2006), 286-311. doi: 10.1016/j.cor.2004.06.005.

[5]

E. Altman and R. El-Azouzi, La théorie des jeux non-coopératifs appliquée aux réseaux de télécommunication, (in French) Annales des Télécommunications, (2007).

[6]

E. Altman and L. Wynter, Equilibrium, games, and pricing in transportation and telecommunications networks, Networks and Spatial Economics, 4 (2004), 7-21. doi: 10.1023/B:NETS.0000015653.52983.61.

[7]

Eitan Altman, A stochastic game approach for competition over popularity in social networks, Dynamic Games and Applications, online publication, (2012). Available from: http://hal.inria.fr/hal-00681959. doi: 10.1007/s13235-012-0057-4.

[8]

Eitan Altman and Yezekael Hayel, Markov decision evolutionary games, IEEE Transactions on Automatic Control, 55 (2010), 1560-1569. doi: 10.1109/TAC.2010.2042230.

[9]

J. Aspnes, K. Chang and A. Yampolskiy, Inoculation strategies for victims of viruses and the sum-of-squares partition problem, J. Comput. Syst. Sci., 72 (2006), 1077-1093. doi: 10.1016/j.jcss.2006.02.003.

[10]

J. Aspnes, N. Rustagi and J. Saia, Worm versus alert: Who wins in a battle for control of a large-scale network?, Lecture Notes in Computer Science, 4878 (2007), 443-456. doi: 10.1007/978-3-540-77096-1_32.

[11]

C. T. Bauch, Imitation dynamics predict vaccinating behavior, Proc. of The Royal Society, (2005). doi: 10.1098/rspb.2005.3153.

[12]

C. T. Bauch and D. J. D. Earn, Vaccination and the theory of games, Proceedings of the National Academy of Science, 101 (2004), 13391-13394. doi: 10.1073/pnas.0403823101.

[13]

N. G. Beans, F. P. Kelly and P. G. Taylor, Braess's paradox in a loss network, J. Appl. Prob., 34 (1997), 155-159. doi: 10.2307/3215183.

[14]

M. Beckmann, C. B. McGuire and C. B. Winsten, "Studies in the Economics of Transportation," Yale Univ. Press, New Haven, 1956.

[15]

T. Berger, The source coding game, IEEE Trans. on Inform. Theory, IT-17 (1971), 71-76.

[16]

N. M. Blachman, Communication as a game, in "I.R.E. WESCON Convention Record Part 2" (August 1957), 61-66.

[17]

D. Braess, Über ein Paradoxien aus der Verkehrsplanung, (German) Unternehmensforschung, 12 (1968), 258-268.

[18]

Mung Chiang, Chee Wei Tan, Prashanth Hande and Tian Lan, Power control in wireless cellular networks, Foundations and Trends in Networking, 2 (2007), 381-533. doi: 10.1561/1300000009.

[19]

S. Coraluppi and S. I. Marcus, Risk-sensitive queueing, in "Proc. 35th Annual Allerton Conf. on Communication, Control, and Computing," Urbana, IL, USA, September 28-October 1, 1997.

[20]

Merouane Debbah and Samson Lasaulce, "Game Theory for Wireless Networks: From Fundamentals to Practice," Elsevier Science & Technology, 2011.

[21]

C. Douligeris, "Optimal Flow Control and Fairness in Communication Networks: A Game Theoretic Perspective," Ph.D. Dissertation, Electrical Engineering, Columbia University, 1989.

[22]

T. Ericson, The noncooperative binary adder channel, IEEE Trans. on Inform. Theory, 32 (1986), 365-374. doi: 10.1109/TIT.1986.1057190.

[23]

D. Falomari, N. Mandayam and D. Goodman, A new framework for power control in wireless data networks: Games utility and pricing, in "Proc. Allerton Conference on Communication, Control and Computing," Champaign, Illinois, USA, (1998), 546-555.

[24]

C. Frenzel, H. Sanneck and S. Hamalainen, "LTE Self-Organising Networks (Son): Network Management Automation for Operational Efficiency," John Wiley & Sons, 2011.

[25]

A. Haurie and P. Marcotte, On the relationship between Nash-Cournot and Wardrop equilibria, Networks, 15 (1985), 295-308. doi: 10.1002/net.3230150303.

[26]

M. T. Hsiao and A. A. Lazar, A game theoretic approach to decentralized flow control of Markovian queueing networks, in "Performance '87" (Brussels, 1987), North-Holland, Amsterdam, (1988), 55-73.

[27]

M. T. Hsiao and A. A. Lazar, Optimal decentralized flow control of Markovian queueing networks with multiple controllers, Performance Evaluation, 13 (1991), 181-204. doi: 10.1016/0166-5316(91)90054-7.

[28]

M. H. R. Khouzani, Saswati Sarkar and Eitan Altman, Saddle-point strategies in malware attack, IEEE Journal on Selected Areas in Communications, 30 (2012), 31-43. doi: 10.1109/JSAC.2012.120104.

[29]

Man-Tung Tony Hsiao, "Optimal Decentralized Flow Control in Computer Communication Networks," Ph.D. Thesis, EE, Columbia Univ, October, 1986.

[30]

Anna Jaśkiewicz, A note on negative dynamic programming for risk-sensitive control, Operations Research Letters, 36 (2008), 531-534. doi: 10.1016/j.orl.2008.03.003.

[31]

Hongbin Ji and Ching-Yao Huang, Non-cooperative uplink power control in cellular radio systems, Wireless Networks, 4 (1998), 233-240.

[32]

B. Jovanovic and R. W. Rosenthal, Anonymous sequential games, Journal of Mathematical Economics, 17 (1988), 77-87. doi: 10.1016/0304-4068(88)90029-8.

[33]

S. Lasaulce and H. Tembine, "Game Theory and Learning for Wireless Networks," Fundamentals and Applications, Academic Press, 2011.

[34]

S. A. Lippman, Applying a new device in the optimization of exponential queueing systems, Operations Research, 23 (1975), 687-710. doi: 10.1287/opre.23.4.687.

[35]

Allen Mackenzie and Luiz DaSilva, "Game Theory for Wireless Engineers," Synthesis Lectures on Communications, Morgan & Claypool Publishers, 2006. doi: 10.2200/S00014ED1V01Y200508COM001.

[36]

R. Mazumdar, L. G. Mason and C. Douligeris, Fairness in network optimal flow control: Optimality of product forms, IEEE Trans. on Comm., 39 (1991), 775-782. doi: 10.1109/26.87140.

[37]

I. Menache and A. Ozdaglar, "Network Games: Theory, Models, and Dynamics," Synthesis Lectures on Communication Networks, Morgan & Claypool Publishers, 2011. doi: 10.2200/S00330ED1V01Y201101CNT009.

[38]

I. Milchtaich, Congestion games with player-specific payoff functions, Games and Economic Behavior, 13 (1996), 111-124. doi: 10.1006/game.1996.0027.

[39]

W. Murrey, The application of epidemiology to computer viruses, Comp. Security, 7 (1988), 139-150.

[40]

Noam Nisan, Tim Roughgarden, Éva Tardos and Vijay V. Vazirani, eds., "Algorithmic Game Theory," Cambridge University Press, Cambridge, 2007. doi: 10.1017/CBO9780511800481.

[41]

A. Orda, R. Rom and N. Shimkin, Competitive routing in multi-user communication networks, in "INFOCOM '93. Proceedings. Twelfth Annual Joint Conference of the IEEE Computer and Communications Societies. Networking: Foundation for the Future" (San Francisco, CA), IEEE, (1993), 964-971. doi: 10.1109/INFCOM.1993.253270.

[42]

M. Patriksson, "The Traffic Assignment Problem: Models and Methods," VSP BV, P.O. Box 346, 3700 AH Zeist, The Netherlands, 1994.

[43]

R. W. Rosenthal, A class of games possessing pure strategy Nash equilibria, Int. J. Game Theory, 2 (1973), 65-67. doi: 10.1007/BF01737559.

[44]

R. W. Rosenthal, The network equilibrium problem in integers, Networks, 3 (1973), 53-59. doi: 10.1002/net.3230030104.

[45]

William H. Sandholm, "Population Games and Evolutionary Dynamics," Economic Learning and Social Evolution, MIT Press, Cambridge, MA, 2010.

[46]

J. Maynard Smith, Game theory and the evolution of fighting, in "On Evolution" (J. Maynard Smith), Edinburgh University Press, Edinburgh, (1972), 8-28.

[47]

Hamidou Tembine, Eitan Altman, Rachid El-Azouzi and Yezekael Hayel, Evolutionary games in wireless networks, IEEE Transactions on Systems, Man, and Cybernetics, Part B, 40 (2010), 634-646. doi: 10.1109/TSMCB.2009.2034631.

[48]

Hamidou Tembine, Eitan Altman, Rachid El-Azouzi and Yezekael Hayel, Bio-inspired delayed evolutionary game dynamics with networking applications, Telecommunication Systems, 47 (2011), 137-152. doi: 10.1007/s11235-010-9307-1.

[49]

D. C. Trimble, "A Game-Theoretic Approach to Signal and Receiver Design," Ph.D. Thesis, Nov. 1972. doi: 10.1109/TIT.1972.1054913.

[50]

T. L. Vincent and J. S. Brown, "Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics," Cambridge Univ Press, 2005.

[51]

J. G. Wardrop, Some theoretical aspects of road traffic research communication networks, Proc. Inst. Civ. Eng., Part 2, 1 (1952), 325-378.

[52]

Y. Zhang and M. Guizani, "Game Theory for Wireless Commun. and Networking," CRC, 2011.

[53]

Yan Zhang and Mohsen Guizani, "Game Theory for Wireless Communications and Networking," Taylor and Francis, 2010.

[54]

I. Ziedins, A paradox in a queueing network with state-dependent routing and loss, Journal of Applied Mathematics and Decision Sciences, 2007 (2007), Article ID 68280, 10 pp. doi: 10.1155/2007/68280.

[1]

Andrew P. Sage. Risk in system of systems engineering and management. Journal of Industrial and Management Optimization, 2008, 4 (3) : 477-487. doi: 10.3934/jimo.2008.4.477

[2]

Maide Bucolo, Federica Di Grazia, Luigi Fortuna, Mattia Frasca, Francesca Sapuppo. An environment for complex behaviour detection in bio-potential experiments. Mathematical Biosciences & Engineering, 2008, 5 (2) : 261-276. doi: 10.3934/mbe.2008.5.261

[3]

Caixia Gao, Enmin Feng, Zongtao Wang, Zhilong Xiu. Nonlinear dynamical systems of bio-dissimilation of glycerol to 1,3-propanediol and their optimal controls. Journal of Industrial and Management Optimization, 2005, 1 (3) : 377-388. doi: 10.3934/jimo.2005.1.377

[4]

Aniello Buonocore, Antonio Di Crescenzo, Alan Hastings. Preface for the special issue of Mathematical Biosciences and Engineering, BIOCOMP 2012. Mathematical Biosciences & Engineering, 2014, 11 (2) : i-ii. doi: 10.3934/mbe.2014.11.2i

[5]

Mohamed A. Tawhid, Ahmed F. Ali. An effective hybrid firefly algorithm with the cuckoo search for engineering optimization problems. Mathematical Foundations of Computing, 2018, 1 (4) : 349-368. doi: 10.3934/mfc.2018017

[6]

Burcu Gürbüz. A computational approximation for the solution of retarded functional differential equations and their applications to science and engineering. Journal of Industrial and Management Optimization, 2022, 18 (4) : 2319-2334. doi: 10.3934/jimo.2021069

[7]

Stepan Sorokin, Maxim Staritsyn. Feedback necessary optimality conditions for a class of terminally constrained state-linear variational problems inspired by impulsive control. Numerical Algebra, Control and Optimization, 2017, 7 (2) : 201-210. doi: 10.3934/naco.2017014

[8]

Sen Zhang, Guo Zhou, Yongquan Zhou, Qifang Luo. Quantum-inspired satin bowerbird algorithm with Bloch spherical search for constrained structural optimization. Journal of Industrial and Management Optimization, 2021, 17 (6) : 3509-3523. doi: 10.3934/jimo.2020130

[9]

Adrian Korban, Serap Şahinkaya, Deniz Ustun. A novel genetic search scheme based on nature-inspired evolutionary algorithms for binary self-dual codes. Advances in Mathematics of Communications, 2022  doi: 10.3934/amc.2022033

[10]

Georgios Konstantinidis. A game theoretic analysis of the cops and robber game. Journal of Dynamics and Games, 2014, 1 (4) : 599-619. doi: 10.3934/jdg.2014.1.599

[11]

Yannick Viossat. Game dynamics and Nash equilibria. Journal of Dynamics and Games, 2014, 1 (3) : 537-553. doi: 10.3934/jdg.2014.1.537

[12]

Jiahua Zhang, Shu-Cherng Fang, Yifan Xu, Ziteng Wang. A cooperative game with envy. Journal of Industrial and Management Optimization, 2017, 13 (4) : 2049-2066. doi: 10.3934/jimo.2017031

[13]

Ying Ji, Shaojian Qu, Fuxing Chen. Environmental game modeling with uncertainties. Discrete and Continuous Dynamical Systems - S, 2019, 12 (4&5) : 989-1003. doi: 10.3934/dcdss.2019067

[14]

Harish Garg. Solving structural engineering design optimization problems using an artificial bee colony algorithm. Journal of Industrial and Management Optimization, 2014, 10 (3) : 777-794. doi: 10.3934/jimo.2014.10.777

[15]

Inmaculada Antón, Julián López-Gómez. Global bifurcation diagrams of steady-states for a parabolic model related to a nuclear engineering problem. Conference Publications, 2013, 2013 (special) : 21-30. doi: 10.3934/proc.2013.2013.21

[16]

Ruiheng Cai, Feng-kuang Chiang. A laser-cutting-centered STEM course for improving engineering problem-solving skills of high school students in China. STEM Education, 2021, 1 (3) : 199-224. doi: 10.3934/steme.2021015

[17]

Xin Du, M. Monir Uddin, A. Mostakim Fony, Md. Tanzim Hossain, Md. Nazmul Islam Shuzan. Iterative Rational Krylov Algorithms for model reduction of a class of constrained structural dynamic system with Engineering applications. Numerical Algebra, Control and Optimization, 2022, 12 (3) : 481-493. doi: 10.3934/naco.2021016

[18]

René Aïd, Roxana Dumitrescu, Peter Tankov. The entry and exit game in the electricity markets: A mean-field game approach. Journal of Dynamics and Games, 2021, 8 (4) : 331-358. doi: 10.3934/jdg.2021012

[19]

Abbas Ja'afaru Badakaya, Aminu Sulaiman Halliru, Jamilu Adamu. Game value for a pursuit-evasion differential game problem in a Hilbert space. Journal of Dynamics and Games, 2022, 9 (1) : 1-12. doi: 10.3934/jdg.2021019

[20]

David Cantala, Juan Sebastián Pereyra. Endogenous budget constraints in the assignment game. Journal of Dynamics and Games, 2015, 2 (3&4) : 207-225. doi: 10.3934/jdg.2015002

 Impact Factor: 

Metrics

  • PDF downloads (54)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]