Skip to main content
SpringerLink
Log in

Conditions for Cooperation and Trading in Value-Cost Dynamic Games

  • Chapter
  • First Online:
Advances in Dynamic Games

Part of the book series: Annals of the International Society of Dynamic Games ((AISDG,volume 13))

  • 1110 Accesses

Abstract

In value-cost dynamic games multiple agents adjust the flow and allocation of investments to action pathways that affect the value of other agents. This article determines conditions for cooperation among agents who invest to gain value from each other. These conditions are specified in a game-theoretic setting for agents that invest to realize cooperative benefits and value targets. The dynamic interaction of allocation priorities and the stability of equilibrium concepts is analyzed. One focus is to determine solutions concepts based on cost-exchange ratios and benefit-exchange ratios that represent trade-offs between the agents, as a function of the action and interaction effects of the respective action pathways. The general approach is applied to the trading between buyers and sellers of goods to determine conditions for mutually beneficial market exchange, the price of goods, and the specialization between consumers and producers.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    Capital and investment can be expressed in terms of financial units (money) but other capital resources could also be considered, such as time, labor, energy, and natural resources. The unit chosen is specific to the respective application area.

  2. 2.

    In the following the benefits of both agents are assumed to have the same units. In case of different units conversion factors apply.

References

  • Allen B, Hellwig M (1986) Bertrand-Edgeworth oligopoly in large markets. Rev Econ Stud 53:175–204

    Article  MathSciNet  MATH  Google Scholar 

  • Axelrod R (1984) The evolution of cooperation. Basic Publ., New York

    Google Scholar 

  • Başar T, Olsder G (1982) Dynamic noncooperative game theory. Academic Press, London/New York

    MATH  Google Scholar 

  • Başar T, Zhu Q (2011) Prices of anarchy, information, and cooperation in differential games. Dyn Games Appl 1:50–73

    Article  MathSciNet  MATH  Google Scholar 

  • Bresnehan T (1981) Duopoly models with consistent conjectures. Am Econ Rev 71:934–945

    Google Scholar 

  • Bressan A, Shen W (2004) Semi-cooperative strategies for differential games. Int J Game Theory 32:561–593

    Article  MathSciNet  MATH  Google Scholar 

  • Cao L, Ohtsuki H, Wang B, Aihara K (2011) Evolution of cooperation on adaptively weighted networks. J Theor Biol 272(1):8–15

    Article  MathSciNet  Google Scholar 

  • Chasparis G, Shamma J (2012) Distributed dynamic reinforcement of efficient outcomes in multiagent coordination and network formation. Dyn Games Appl 2:18–50

    Article  MathSciNet  MATH  Google Scholar 

  • Dixon H (1992) The perfectly competitive outcome as the equilibrium in an Edgeworthian price-quantity game. Econ J 102:301–309

    Article  Google Scholar 

  • Dockner E, Jorgensen S, Van Long N, Sorger G (2000) Differential games in economics and management science. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Du F, Fu F (2011) Partner selection shapes the strategic and topological evolution of cooperation: The power of reputation transitivity. Dyn Games Appl 1:354–369

    Article  MathSciNet  MATH  Google Scholar 

  • Engwerda J (2010) Necessary and sufficient conditions for pareto optimal solutions of cooperative differential games. SIAM J Control Optim 48(6):3859–3881

    Article  MathSciNet  MATH  Google Scholar 

  • Epstein J, Axtell R (1997) Growing artificial societies. Bradford Book, Cambridge

    Google Scholar 

  • Figuières C, Jean-Marie A, Quérou N, Tidball M (2004) Theory of conjectural variations. World Scientific, Singapore

    Book  MATH  Google Scholar 

  • Gao J, Li Z, Cong R, Wang L (2012) Tolerance-based punishment in continuous public goods game. Physica 391(16):4111–4120

    Article  Google Scholar 

  • Gerber A (2000) Coalition formation in general NTU games. Rev Econ Des 5(2):149–175

    Google Scholar 

  • Gomez Portillo I (2012) Cooperation and its evolution in growing systems with cultural reproduction. Eur Phys J B 85(12):409

    Article  Google Scholar 

  • Hahn M (2012) An evolutionary analysis of varians model of sales. Dyn Games Appl 2:71–96

    Article  MathSciNet  MATH  Google Scholar 

  • Helbing D, Johansson A (2010) Cooperation, norms, and revolutions: A unified game-theoretical approach. PLoS ONE 5(10):e12530

    Article  Google Scholar 

  • Hofbauer J, Sigmund K (1998) Evolutionary games and population dynamics. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Isakov A, Rand D (2012) The evolution of coercive institutional punishment. Dyn Games Appl 2:97–109

    Article  MathSciNet  MATH  Google Scholar 

  • Louge F, Riedel F (2012) Evolutionary stability in first price auctions. Dyn Games Appl 2(1): 110–128

    Article  MathSciNet  MATH  Google Scholar 

  • Miao X, Zhou X, Wu H (2012) A cooperative differential game model based on network throughput and energy efficiency in wireless networks. Optim Lett 6(1):55–68

    Article  MathSciNet  MATH  Google Scholar 

  • Nemeth A, Takacs K (2010) The paradox of cooperation benefits. J Theor Biol 264(2):301–311

    Article  MathSciNet  Google Scholar 

  • Ohtsuki H (2011) Evolutionary dynamics of the Nash demand game: A diffusion approach. Dyn Games Appl 1:449–461

    Article  MathSciNet  MATH  Google Scholar 

  • Perc M, Szolnoki A (2012) Coevolutionary games—A mini review. Biosystems 99(2):109–125

    Article  Google Scholar 

  • Petrosjan L (1995) The Shapley value for differential games. In: Olsder G (ed) New trends in dynamic games and application. Birkhäuser, Boston, pp 407–417

    Google Scholar 

  • Petrosjan L (2004) Cooperation in games with incomplete information. In: Nonlinear analysis and convex analysis, Yokohama Publ., Yokohama, pp 469–479

    Google Scholar 

  • Requejo R, Camacho J (2012) Analytical models for well-mixed populations of cooperators and defectors under limiting resources. Phys Rev E 85(6):066112

    Article  Google Scholar 

  • Rezaei G, Kirley M (2012) Dynamic social networks facilitate cooperation in the N-player prisoner’s dilemma. Physica 391(23):6199–6211

    Article  Google Scholar 

  • Scheffran J (2001) Stability and control of value-cost dynamic games. Cent Eur J Oper Res 9(7):197–225

    MathSciNet  MATH  Google Scholar 

  • Scheffran J (2006) The formation of adaptive coalitions. In: Haurie A, Muto S, Petrosjan L, Raghavan T (eds) Advances in dynamic games. Birkhäuser, Boston, pp 163–178

    Chapter  Google Scholar 

  • Scheffran J, Bendor T (2009) Bioenergy and land use—A spatial-agent dynamic model of energy crop production in Illinois. Int J Environ Pollut 39(1/2):4–27

    Article  Google Scholar 

  • Scheffran J, Hannon B (2007) From complex conflicts to stable cooperation. Complexity 13(2): 78–91

    Article  MathSciNet  Google Scholar 

  • Selten R, Stoecker R (1986) End behavior in sequences of finite prisoner’s dilemma supergames. J Econ Behav Organ 7:47–70

    Article  Google Scholar 

  • Simaan M, Cruz J (1976) On the Stackelberg strategy in nonzero-sum games. In: Leitmann G (ed) Multicriteria decision making and differential games. Plenum Press, New York, pp 173–195

    Chapter  Google Scholar 

  • Su Y, van der Schaar M (2011) Linearly coupled communication games. IEEE Trans Commun 59(9):2543–2553

    Article  Google Scholar 

  • Szidarovszky F, Li W (2000) A note on the stability of a Cournot-Nash equilibrium: The multiproduct case with adaptive expectations. J Math Econ 33:101–107

    Article  MathSciNet  MATH  Google Scholar 

  • Tanabe S, Masuda N (2012) Evolution of cooperation facilitated by reinforcement learning with adaptive aspiration levels. J Theor Biol 293:151–160

    Article  MathSciNet  Google Scholar 

  • Tolwinski B, Haurie A, Leitmann G (1986) Cooperative equilibria in differential games. J Math Anal Appl 119:182–202

    Article  MathSciNet  MATH  Google Scholar 

  • Tuinstra J (2000) A discrete and symmetric price adjustment process on the simplex. J Econ Dyn Contr 24(5–7):881–907

    Article  MathSciNet  MATH  Google Scholar 

  • Wang R, He J, Wang Y, Shi L, Li YT  2010 (2010) Asymmetric interaction will facilitate the evolution of cooperation. Sci China Life Sci 53(8):1041–1046

    Google Scholar 

  • Weidlich W (2000) Sociodynamics—A systematic approach to mathematical modelling in the social sciences. Harwood Academic Publishers, Amsterdam

    MATH  Google Scholar 

  • Yeung D, Petrosjan L (2006) Cooperative stochastic differential games. Springer, New York

    MATH  Google Scholar 

  • Yeung D, Petrosjan L (2012) Subgame consistent economic optimization: An advanced cooperative dynamic game analysis. Birkhäuser, Boston

    Book  Google Scholar 

  • Zhang A, Zhang Y (1996) Stability of a Cournot–Nash equilibrium: The multi-product case. J Math Econ 26:441–462

    Article  MATH  Google Scholar 

Download references

Acknowledgements

Research for this article was funded in parts by the German Science Foundation (DFG) through the Cluster of Excellence CliSAP (EXC177). The author is grateful to Harry Dankowicz for discussion of some of the issues in an earlier version of this article.

Author information

Authors and Affiliations

  1. Institute of Geography, University of Hamburg, KlimaCampus, 20144, Hamburg, Germany

    Jürgen Scheffran

Authors
  1. Jürgen Scheffran
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jürgen Scheffran .

Editor information

Editors and Affiliations

  1. Institute of Entomology Dept. of Theoretical Ecology, Biology Centre AS CR, České Budějovice, Czech Republic

    Vlastimil Křivan

  2. GERAD, HEC Montréal, Montreal, Québec, Canada

    Georges Zaccour

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Scheffran, J. (2013). Conditions for Cooperation and Trading in Value-Cost Dynamic Games. In: Křivan, V., Zaccour, G. (eds) Advances in Dynamic Games. Annals of the International Society of Dynamic Games, vol 13. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-02690-9_9

Download citation

Publish with us

Policies and ethics

Search

Navigation