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Regularity of pure strategy equilibrium points in a class of bargaining games

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  • Tasos Kalandrakis
Abstract
We develop an index theory for the Stationary Subgame Perfect (SSP) equilibrium set in a class of n-player $(n\ge 2)$ sequential bargaining games with probabilistic recognition rules. For games with oligarchic voting rules (a class that includes unanimity rule), we establish conditions on individual utilities that ensure that for almost all discount factors, the number of SSP equilibria is odd and the equilibrium correspondence lower-hemicontinuous. For games with general, monotonic voting rules, we show generic (in discount factors) determinacy of SSP equilibria under the restriction that the agreement space is of dimension one. For non-oligarchic voting rules and agreement spaces of higher finite dimension, we establish generic determinacy for the subset of SSP equilibria in pure strategies. The analysis also extends to the case of fixed delay costs. Lastly, we provide a sufficient condition for uniqueness of SSP equilibrium in oligarchic games. Copyright Springer-Verlag Berlin/Heidelberg 2006

Suggested Citation

  • Tasos Kalandrakis, 2006. "Regularity of pure strategy equilibrium points in a class of bargaining games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(2), pages 309-329, June.
    • Handle: RePEc:spr:joecth:v:28:y:2006:i:2:p:309-329
    DOI: 10.1007/s00199-005-0620-y
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    Cited by:

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    3. Eraslan, Hülya & McLennan, Andrew, 2013. "Uniqueness of stationary equilibrium payoffs in coalitional bargaining," Journal of Economic Theory, Elsevier, vol. 148(6), pages 2195-2222.
    4. Kalandrakis, Tasos, 2015. "Computation of equilibrium values in the Baron and Ferejohn bargaining model," Games and Economic Behavior, Elsevier, vol. 94(C), pages 29-38.
    5. Herings, P.J.J. & Predtetchinski, A., 2011. "Procedurally fair income taxation schemes," Research Memorandum 035, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    6. Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2011. "On the asymptotic uniqueness of bargaining equilibria," Economics Letters, Elsevier, vol. 111(3), pages 243-246, June.
    7. Jon Eguia, 2013. "On the spatial representation of preference profiles," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 103-128, January.
    8. Herings, P.J.J. & Predtetchinski, A., 2011. "Procedurally fair taxation," Research Memorandum 024, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    9. Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2015. "Bargaining with non-convexities," Games and Economic Behavior, Elsevier, vol. 90(C), pages 151-161.
    10. Kim, Duk Gyoo & Lim, Wooyoung, 2024. "Multilateral bargaining over the division of losses," Games and Economic Behavior, Elsevier, vol. 146(C), pages 59-76.
    11. Herings, P. Jean-Jacques & Meshalkin, Andrey & Predtetchinski, Arkadi, 2017. "A one-period memory folk theorem for multilateral bargaining games," Games and Economic Behavior, Elsevier, vol. 103(C), pages 185-198.
    12. Zapal, Jan, 2020. "Simple Markovian equilibria in dynamic spatial legislative bargaining," European Journal of Political Economy, Elsevier, vol. 63(C).
    13. Can, Burak, 2014. "Weighted distances between preferences," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 109-115.
    14. Herings, P. Jean-Jacques & Predtetchinski, Arkadi, 2010. "One-dimensional bargaining with Markov recognition probabilities," Journal of Economic Theory, Elsevier, vol. 145(1), pages 189-215, January.
    15. Duggan, John & Kalandrakis, Tasos, 2012. "Dynamic legislative policy making," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1653-1688.
    16. Kalandrakis, Tasos, 2004. "Equilibria in sequential bargaining games as solutions to systems of equations," Economics Letters, Elsevier, vol. 84(3), pages 407-411, September.
    17. P. Herings & Arkadi Predtetchinski, 2015. "Procedural fairness and redistributive proportional tax," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(2), pages 333-354, June.
    18. Yves Breitmoser, 2012. "Proto-coalition bargaining and the core," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(3), pages 581-599, November.
    19. Predtetchinski, A., 2007. "One-dimensional bargaining with a general voting rule," Research Memorandum 045, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    20. P. Jean-Jacques Herings & A. Predtetchinski, 2016. "Bargaining under monotonicity constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 221-243, June.
    21. Shunsuke Hanato, 2020. "Equilibrium payoffs and proposal ratios in bargaining models," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(2), pages 463-494, June.
    22. David Baron & Daniel Diermeier & Pohan Fong, 2012. "A dynamic theory of parliamentary democracy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(3), pages 703-738, April.
    23. Predtetchinski, A., 2010. "One-dimensional bargaining: a revision," Research Memorandum 031, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    24. Alós-Ferrer, Carlos & Ritzberger, Klaus, 2021. "Multi-lateral strategic bargaining without stationarity," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    25. Yves Breitmoser, 2011. "Parliamentary bargaining with priority recognition for committee members," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(1), pages 149-169, June.

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