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Evolutionary dynamics and equitable core selection in assignment games

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  • Heinrich Nax
  • Bary Pradelski

Abstract

We study evolutionary dynamics in assignment games where many agents interact anonymously at virtually no cost. The process is decentralized, very little information is available and trade takes place at many different prices simultaneously. We propose a completely uncoupled learning process that selects a subset of the core of the game with a natural equity interpretation. This happens even though agents have no knowledge of other agents’ strategies, payoffs, or the structure of the game, and there is no central authority with such knowledge either. In our model, agents randomly encounter other agents, make bids and offers for potential partnerships and match if the partnerships are profitable. Equity is favored by our dynamics because it is more stable, not because of any ex ante fairness criterion. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Heinrich Nax & Bary Pradelski, 2015. "Evolutionary dynamics and equitable core selection in assignment games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 903-932, November.
  • Handle: RePEc:spr:jogath:v:44:y:2015:i:4:p:903-932
    DOI: 10.1007/s00182-014-0459-1
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    1. Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2010. "Stochastic stability for roommate markets," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2218-2240, November.
    2. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November.
    3. Newton, Jonathan & Sawa, Ryoji, 2015. "A one-shot deviation principle for stability in matching problems," Journal of Economic Theory, Elsevier, vol. 157(C), pages 1-27.
    4. E. Inarra & C. Larrea & E. Molis, 2008. "Random paths to P-stability in the roommate problem," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 461-471, March.
    5. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    6. Agastya, Murali, 1999. "Perturbed Adaptive Dynamics in Coalition Form Games," Journal of Economic Theory, Elsevier, vol. 89(2), pages 207-233, December.
    7. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-450, March.
    8. Klaus, Bettina & Klijn, Flip, 2007. "Paths to stability for matching markets with couples," Games and Economic Behavior, Elsevier, vol. 58(1), pages 154-171, January.
    9. Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, vol. 53(4), pages 873-888, July.
    10. Sergiu Hart & Andreu Mas-Colell, 2013. "Stochastic Uncoupled Dynamics And Nash Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 8, pages 165-189, World Scientific Publishing Co. Pte. Ltd..
    11. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    12. Rochford, Sharon C., 1984. "Symmetrically pairwise-bargained allocations in an assignment market," Journal of Economic Theory, Elsevier, vol. 34(2), pages 262-281, December.
    13. Peter Biro & Matthijs Bomhoff & Walter Kern & Petr A. Golovach & Daniel Paulusma, 2012. "Solutions for the Stable Roommates Problem with Payments," CERS-IE WORKING PAPERS 1211, Institute of Economics, Centre for Economic and Regional Studies.
    14. Selten, Reinhard & Stoecker, Rolf, 1986. "End behavior in sequences of finite Prisoner's Dilemma supergames A learning theory approach," Journal of Economic Behavior & Organization, Elsevier, vol. 7(1), pages 47-70, March.
    15. Roth, Alvin E. & Erev, Ido, 1995. "Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term," Games and Economic Behavior, Elsevier, vol. 8(1), pages 164-212.
    16. Diamantoudi, Effrosyni & Miyagawa, Eiichi & Xue, Licun, 2004. "Random paths to stability in the roommate problem," Games and Economic Behavior, Elsevier, vol. 48(1), pages 18-28, July.
    17. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    18. Pradelski, Bary S.R. & Young, H. Peyton, 2012. "Learning efficient Nash equilibria in distributed systems," Games and Economic Behavior, Elsevier, vol. 75(2), pages 882-897.
    19. Bo Chen & Satoru Fujishige & Zaifu Yang, 2010. "Decentralized Market Processes to Stable Job Matchings with Competitive Salaries," KIER Working Papers 749, Kyoto University, Institute of Economic Research.
    20. Rozen, Kareen, 2013. "Conflict leads to cooperation in demand bargaining," Journal of Economic Behavior & Organization, Elsevier, vol. 87(C), pages 35-42.
    21. Demange, Gabrielle & Gale, David & Sotomayor, Marilda, 1986. "Multi-Item Auctions," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 863-872, August.
    22. Murali Agastya, 1997. "Adaptive Play in Multiplayer Bargaining Situations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(3), pages 411-426.
    23. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    24. Germano, Fabrizio & Lugosi, Gabor, 2007. "Global Nash convergence of Foster and Young's regret testing," Games and Economic Behavior, Elsevier, vol. 60(1), pages 135-154, July.
    25. Francesc Llerena & Marina Nunez, 2011. "A geometric characterization of the nucleolus of the assignment game," Economics Bulletin, AccessEcon, vol. 31(4), pages 3275-3285.
    26. Solymosi, Tamas & Raghavan, Tirukkannamangai E S, 1994. "An Algorithm for Finding the Nucleolus of Asignment Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(2), pages 119-143.
    27. Theo S. H. Driessen, 1998. "A note on the inclusion of the kernel in the core of the bilateral assignment game," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(2), pages 301-303.
    28. Sotomayor, Marilda, 2003. "Some further remark on the core structure of the assignment game," Mathematical Social Sciences, Elsevier, vol. 46(3), pages 261-265, December.
    29. Bettina Klaus & Frédéric Payot, 2013. "Paths to Stability in the Assignment Problem," Cahiers de Recherches Economiques du Département d'économie 13.14, Université de Lausanne, Faculté des HEC, Département d’économie.
    30. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    31. Young, H. Peyton, 2009. "Learning by trial and error," Games and Economic Behavior, Elsevier, vol. 65(2), pages 626-643, March.
    32. Fuhito Kojima & M. Ünver, 2008. "Random paths to pairwise stability in many-to-many matching problems: a study on market equilibration," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 473-488, March.
    33. Sawa, Ryoji, 2014. "Coalitional stochastic stability in games, networks and markets," Games and Economic Behavior, Elsevier, vol. 88(C), pages 90-111.
    34. M. L. Balinski, 1965. "Integer Programming: Methods, Uses, Computations," Management Science, INFORMS, vol. 12(3), pages 253-313, November.
    35. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    36. Iñarra, E. & Larrea, C. & Molis, E., 2013. "Absorbing sets in roommate problems," Games and Economic Behavior, Elsevier, vol. 81(C), pages 165-178.
    37. , P. & , Peyton, 2006. "Regret testing: learning to play Nash equilibrium without knowing you have an opponent," Theoretical Economics, Econometric Society, vol. 1(3), pages 341-367, September.
    38. Sergiu Hart & Andreu Mas-Colell, 2013. "Uncoupled Dynamics Do Not Lead To Nash Equilibrium," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 7, pages 153-163, World Scientific Publishing Co. Pte. Ltd..
    39. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-1480, November.
    40. M. Maschler & B. Peleg & L. S. Shapley, 1979. "Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 303-338, November.
    41. Jackson, Matthew O. & Watts, Alison, 2002. "The Evolution of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 106(2), pages 265-295, October.
    42. Arnold, Tone & Schwalbe, Ulrich, 2002. "Dynamic coalition formation and the core," Journal of Economic Behavior & Organization, Elsevier, vol. 49(3), pages 363-380, November.
    43. Newton, Jonathan, 2012. "Recontracting and stochastic stability in cooperative games," Journal of Economic Theory, Elsevier, vol. 147(1), pages 364-381.
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    3. Maria Montero & Alex Possajennikov, 2021. "An Adaptive Model of Demand Adjustment in Weighted Majority Games," Games, MDPI, vol. 13(1), pages 1-17, December.
    4. Kononovicius, Aleksejus & Ruseckas, Julius, 2019. "Order book model with herd behavior exhibiting long-range memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 171-191.
    5. Nax, Heinrich H., 2015. "Equity dynamics in bargaining without information exchange," LSE Research Online Documents on Economics 65426, London School of Economics and Political Science, LSE Library.
    6. Ennio Bilancini & Leonardo Boncinelli, 2020. "The evolution of conventions under condition-dependent mistakes," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 497-521, March.
    7. Hwang, Sung-Ha & Lim, Wooyoung & Neary, Philip & Newton, Jonathan, 2018. "Conventional contracts, intentional behavior and logit choice: Equality without symmetry," Games and Economic Behavior, Elsevier, vol. 110(C), pages 273-294.
    8. Satoru Fujishige & Zaifu Yang, 2017. "On a spontaneous decentralized market process," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 2(1), pages 1-37, December.
    9. Bolle Friedel & Otto Philipp E., 2016. "Matching as a Stochastic Process," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 236(3), pages 323-348, May.
    10. Bary S. R. Pradelski & Heinrich H. Nax, 2020. "Market sentiments and convergence dynamics in decentralized assignment economies," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 275-298, March.
    11. Casajus, André & Kramm, Michael & Wiese, Harald, 2020. "Asymptotic stability in the Lovász-Shapley replicator dynamic for cooperative games," Journal of Economic Theory, Elsevier, vol. 186(C).
    12. Klaus, Bettina & Newton, Jonathan, 2016. "Stochastic stability in assignment problems," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 62-74.
    13. Bilancini, Ennio & Boncinelli, Leonardo & Newton, Jonathan, 2020. "Evolution and Rawlsian social choice in matching," Games and Economic Behavior, Elsevier, vol. 123(C), pages 68-80.
    14. Bando, Keisuke & Kawasaki, Ryo, 2021. "Stability properties of the core in a generalized assignment problem," Games and Economic Behavior, Elsevier, vol. 130(C), pages 211-223.
    15. Ratul Lahkar, 2020. "Convergence to Walrasian equilibrium with minimal information," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 15(3), pages 553-578, July.
    16. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    17. Arthur Dolgopolov & Cesar Martinelli, 2021. "Learning and Acyclicity in the Market Game," Working Papers 1084, George Mason University, Interdisciplinary Center for Economic Science.
    18. Alós-Ferrer, Carlos & Buckenmaier, Johannes, 2017. "Trader matching and the selection of market institutions," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 118-127.
    19. Arnaud Zlatko Dragicevic, 2022. "Exchange Networks with Stochastic Matching," Games, MDPI, vol. 14(1), pages 1-18, December.
    20. Leshno, Jacob D. & Pradelski, Bary S.R., 2021. "The importance of memory for price discovery in decentralized markets," Games and Economic Behavior, Elsevier, vol. 125(C), pages 62-78.
    21. Heinrich H. Nax & Bary S. R. Pradelski, 2016. "Core Stability and Core Selection in a Decentralized Labor Matching Market," Games, MDPI, vol. 7(2), pages 1-16, March.
    22. Sawa, Ryoji, 2019. "Stochastic stability under logit choice in coalitional bargaining problems," Games and Economic Behavior, Elsevier, vol. 113(C), pages 633-650.
    23. Heinrich Nax, 2015. "Equity dynamics in bargaining without information exchange," Journal of Evolutionary Economics, Springer, vol. 25(5), pages 1011-1026, November.
    24. Maria Montero & Alex Possajennikov, 2022. ""Greedy" Demand Adjustment in Cooperative Games," Discussion Papers 2022-05, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.

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    More about this item

    Keywords

    Assignment games; Cooperative games; Core; Equity; Evolutionary game theory; Learning; Matching markets; Stochastic stability; C71; C73; C78; D83;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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