Abstract
We consider dominant strategy implementation in a large population aggregative game. The model has strategic complementarities which generates multiple Nash equilibria. Moreover, externalities are positive due to which, all equilibria are socially inefficient. The planner, therefore, constructs a direct mechanism and assigns efficient strategies and transfer levels to agents. Truthful revelation then becomes strictly dominant, which implements efficiency. In our new evolutionary approach to this mechanism, the reported type distribution evolves under dynamics satisfying monotone percentage growth. Such dynamics eliminate dominated strategies thereby ensuring convergence to truthful revelation by all agents. Dominant strategy implementation is, therefore, robust under such evolutionary dynamics. Our evolutionary approach differs from existing models of evolutionary implementation based on potential games. That approach may fail to implement efficiency under strategic complementarities as a Pareto inferior Nash equilibrium can remain asymptotically stable under evolutionary dynamics. Our evolutionary approach is effective even under such strategic complementarities.
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References
Arrow, K.: The property rights doctrine and demand revelation under incomplete information. In: Boskin, M. (ed.) Economics and Human Welfare. Academic Press, New York (1979)
Cheung, M.W.: Pairwise comparison dynamics for games with continuous strategy space. J. Econ. Theory 153, 344–375 (2014)
Cheung, M.W.: Imitative dynamics for games with continuous strategy space. Games Econ. Behav. 99, 206–223 (2016)
Cheung, M.W., Lahkar, R.: Nonatomic potential games: the continuous strategy case. Games Econ. Behav. 108, 341–362 (2018)
Clarke, E.: Multi-part pricing of public goods. Public Choice 11, 17–23 (1971)
Cooper, R.J.: Coordination Games: Complementarities and Macroeconomics. Cambridge University Press, Cambridge (1999)
Corchón, L.: Comparative statics for aggregative games the strong concavity case. Math. Soc. Sci. 28, 151–165 (1994)
d’Aspremont, C., Gérard-Varet, L.-A.: Incentives and incomplete information. J. Public Econ. 11, 25–45 (1979)
Gilboa, I., Matsui, A.: Social stability and equilibrium. Econometrica 59, 859–867 (1991)
Green, J., Laffont, J.-J.: Incentives in Public Decision-Making. Elsevier, North-Holland (1979)
Groves, T.: Incentives in teams. Econometrica 41, 617–631 (1973)
Güth, W.: An evolutionary approach to explaining cooperative behavior by reciprocal incentives. Int. J. Game Theory 24, 323–344 (1995)
Güth, W., Yaari, M.: Explaining reciprocal behavior in simple strategic games: an evolutionary approach. In: Witt, U. (ed.) Explaining Forces and Change: Approaches to Evolutionary Economics, pp. 23–34. University of Michigan Press, Ann Arbor (1992)
Heifetz, A., Shannon, C., Spiegel, Y.: The dynamic evolution of preferences. Econ. Theory 32, 251–286 (2007). https://doi.org/10.1007/s00199-006-0121-7
Hofbauer, J.: From Nash and Brown to Maynard Smith: equilibria, dynamics, and ESS. Selection 1, 81–88 (2000)
Hofbauer, J., Sandholm, W.H.: Evolution in games with randomly disturbed payoffs. J. Econ. Theory 132, 47–69 (2007)
Hofbauer, J., Sandholm, W.H.: Survival of dominated strategies under evolutionary dynamics. Theor. Econ. 6, 341–377 (2011)
Hofbauer, J., Oechssler, J., Riedel, F.: Brown–von Neumann–Nash dynamics: the continuous strategy case. Games Econ. Behav. 65, 406–429 (2009)
Katz, M.L., Shapiro, C.: Technology adoption in the presence of network externalities. J. Polit. Econ. 94, 822–841 (1986)
Lahkar, R.: Large population aggregative potential games. Dyn. Games Appl. 7, 443–467 (2017)
Lahkar, R.: Elimination of non-individualistic preferences in large population aggregative games. J. Math. Econ. 84, 150–165 (2019)
Lahkar, R.: Convergence to Walrasian equilibrium with minimal information. J. Econ. Interact. Coord. 15, 553–578 (2020)
Lahkar, R., Mukherjee, S.: Evolutionary implementation in a public goods game. J. Econ. Theory 181, 423–460 (2019)
Lahkar, R., Mukherjee, S.: Dominant strategy implementation in a large population public goods game. Econ. Lett. 197, 109616 (2020)
Lahkar, R., Mukherjee, S.: Evolutionary implementation in aggregative games. Math. Soc. Sci. 109, 137–151 (2021)
Lahkar, R., Riedel, F.: The logit dynamic for games with continuous strategy sets. Games Econ. Behav. 91, 268–282 (2015)
Lahkar, R., Sandholm, W.H.: The projection dynamic and the geometry of population games. Games Econ. Behav. 64, 565–590 (2008)
McMahon, W.W.: Education and Development: Measuring the Social Benefits. Oxford University Press, Oxford (1999)
Monderer, D., Shapley, L.: Potential games. Games Econ. Behav. 14, 124–143 (1996)
Norman, T.W.: Evolutionary stability in the generalized second-price auction. Econ. Theory 71, 235–250 (2021). https://doi.org/10.1007/s00199-019-01240-5
Oechssler, J., Riedel, F.: Evolutionary dynamics on infinite strategy spaces. Econ. Theory 17, 141–162 (2001). https://doi.org/10.1007/PL00004092
Oechssler, J., Riedel, F.: On the dynamic foundation of evolutionary stability in continuous models. J. Econ. Theory 107, 223–252 (2002)
Perkins, S., Leslie, D.: Stochastic fictitious play with continuous action sets. J. Econ. Theory 152, 179–213 (2014)
Phelps, S., McBurney, P., Parsons, S.: Evolutionary mechanism design: a review. Auton. Agent Multi-Agent Syst. 21, 237–264 (2010)
Rothkopf, M.H.: Thirteen reasons why the Vickrey–Clarke–Groves process is not practical. Oper. Res. 55, 191–197 (2007)
Rothkopf, M.H., Teisberg, T.J., Kahn, E.P.: Why are Vickrey auctions rare? J. Polit. Econ. 98, 94–109 (1990)
Samuelson, L.: Does evolution eliminate weakly dominated strategies. In: Binmore, K., Kirman, A., Tani, P. (eds.) Frontiers of Game Theory. MIT Press, London (1993)
Samuelson, L., Zhang, J.: Evolutionary stability in asymmetric games. J. Econ. Theory 57, 363–391 (1992)
Sandholm, W.H.: Potential games with continuous player sets. J. Econ. Theory 97, 81–108 (2001)
Sandholm, W.H.: Evolutionary implementation and congestion pricing. Rev. Econ. Stud. 69, 667–689 (2002)
Sandholm, W.H.: Negative externalities and evolutionary implementation. Rev. Econ. Stud. 72, 885–915 (2005)
Sandholm, W.H.: Pigouvian pricing and stochastic evolutionary implementation. J. Econ. Theory 132, 367–382 (2007)
Sandholm, W.H.: Population Games and Evolutionary Dynamics. MIT Press, Cambridge (2010)
Schlag, K.H.: Why imitate, and if so, how? A boundedly rational approach to multi-armed bandits. J. Econ. Theory 78, 130–156 (1998)
Smith, M.J.: The stability of a dynamic model of traffic assignment—an application of a method of Lyapunov. Transp. Sci. 18, 245–252 (1984)
Taylor, P.D., Jonker, L.: Evolutionarily stable strategies and game dynamics. Math. Biosci. 40, 145–156 (1978)
Vickrey, W.: Counterspeculation, auctions, and competitive sealed tenders. J. Finance 16, 8–37 (1961)
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Bandhu, S., Lahkar, R. Evolutionary robustness of dominant strategy implementation. Econ Theory 76, 685–721 (2023). https://doi.org/10.1007/s00199-022-01474-w
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DOI: https://doi.org/10.1007/s00199-022-01474-w