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A model of state aggregation

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In this paper, due to limited attention and lack of focus, an agent has tendency toward framing of available information that drives her to see the state space as a collection of the events or “small worlds” related to a particular ambience, which we call a state aggregation. This work axiomatizes the model of state aggregation, shows how to recover the structure of the “small worlds” together with beliefs and utility from the individual demand for assets, and provides comparative statics and revealed preference restrictions.

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References

  • Afriat, S.: The construction of utility functions from expenditure data. Int. Econ. Rev. 8(1), 67–77 (1967)

    Article  Google Scholar 

  • Ahn, D., Ergin, H.: Framing contingencies. Econometrica 78(2), 655–695 (2010)

    Article  Google Scholar 

  • Balbus, L.: On recursive utilities with non-affine aggregator and conditional certainty equivalent. Econ. Theor. 70, 551–577 (2020). https://doi.org/10.1007/s00199-019-01221-8

    Article  Google Scholar 

  • Bordalo, P., Gennaioli, N., Shleifer, A.: Competition for attention. Rev. Econ. Stud. 83(2), 481–513 (2016)

    Article  Google Scholar 

  • Carvajal, A., Riascos, A.: Identification of individual demands from market data under uncertainty. BE J. Theor. Econ. 8(1), (2008)

  • Chambers, C., Liu, C., Martinez, S.K.: A test for risk-averse expected utility. J. Econ. Theory 163, 775–785 (2016)

    Article  Google Scholar 

  • Chew, S., Sagi, J.: Small worlds: modeling attitudes toward sources of uncertainty. J. Econ. Theory 139, 1–24 (2008)

    Article  Google Scholar 

  • Cosaert, S., Demuynck, T.: Revealed preference theory for finite choice sets. Econ. Theor. 59, 169–200 (2015). https://doi.org/10.1007/s00199-014-0813-3

    Article  Google Scholar 

  • Diewert, W.: Afriat’s theorem and some extensions to choice under uncertainty. Econ. J. 122(560), 305–331 (2012)

    Article  Google Scholar 

  • Dreber, A., Ellingsen, T., Johannesson, M., Rand, D.G.: Do people care about social context? Framing effects in dictator games. Exp. Econ. 16(3), 349–371 (2013)

    Article  Google Scholar 

  • Echenique, F., Saito, K.: Savage in the market. Econometrica 83(4), 1467–1495 (2015)

    Article  Google Scholar 

  • Eliaz, K., Spiegler, R.: Consideration sets and competitive marketing. Rev. Econ. Stud. 78(1), 235–262 (2011)

    Article  Google Scholar 

  • Epstein, L., Zhang, J.: Subjective probabilities on subjectively unambiguous events. Econometrica 69(2), 265–306 (2001)

    Article  Google Scholar 

  • Epstein, L., Marinacci, M., Seo, K.: Coarse contingencies and ambiguity. Theor. Econ. 2(4), 355–394 (2007)

    Google Scholar 

  • Ergin, H., Gul, F.: A theory of subjective compound lotteries. J. Econ. Theory 144, 899–929 (2009)

    Article  Google Scholar 

  • Geanakoplos, J.: Afriat from maxmin. Econ. Theory 54, 443–448 (2013). https://doi.org/10.1007/s00199-013-0783-x

    Article  Google Scholar 

  • Geanakoplos, J., Polemarchakis, H.: Observability and optimality. J. Math. Econ. 19(1–2), 153–165 (1990)

    Article  Google Scholar 

  • Green, H.A.J.: Aggregation in Economic Analysis. Princeton University Press, Princeton (1964)

    Book  Google Scholar 

  • Green, R.C., Srivastava, S.: Expected utility maximization and demand behavior. J. Econ. Theory 38(2), 313–323 (1986)

    Article  Google Scholar 

  • Hammond, P.: Consequentialist foundations for expected utility. Theor. Decis. 25(1), 25–78 (1988)

    Article  Google Scholar 

  • Hens, T.: A note on Savage’s theorem with a finite number of states. J. Risk Uncertain. 5, 63–71 (1992)

    Article  Google Scholar 

  • Karni, E., Viero, M.L.: Am. Econ. Rev. 103(7), 2790–2810 (2013)

    Article  Google Scholar 

  • Klibanoff, P., Marinacci, M., Mukerji, S.: A smooth model of decision making under ambiguity. Econometrica 73(6), 1849–1892 (2005)

    Article  Google Scholar 

  • Kochov, A.: A behavioral definition of unforeseen contingencies. J. Econ. Theory 175, 265–290 (2018)

    Article  Google Scholar 

  • Kopylov, I.: Combinatorial models of subjective states. Working Paper (2018)

  • Kreps, D., Porteus, E.: Temporal resolution of uncertainty and dynamic choice theory. Econometrica 46(1), 185–200 (1978)

    Article  Google Scholar 

  • Kubler, F., Polemarchakis, H.: The identification of beliefs from asset demand. Econometrica 85(4), 1219–1238 (2017)

    Article  Google Scholar 

  • Leontief, W.: A note on the interrelation of subsets of independent variables of a continuous function with continuous first derivatives. Bull. Am. Math. Soc. 53, 343–350 (1947)

    Article  Google Scholar 

  • Li, J.: Preferences for partial information and ambiguity. Theor. Econ. 15(3), 1059–1094 (2020)

    Article  Google Scholar 

  • Machina, M.: Dynamic consistency and non-expected utility models of choice under uncertainty. J. Econ. Lit. 27(4), 1622–1668 (1989)

    Google Scholar 

  • Machina, M., Schmeidler, D.: A more robust definition of subjective probability. Econometrica 60(4), 745–780 (1992)

    Article  Google Scholar 

  • Mas-Colell, A.: The recoverability of consumers’ preferences from market demand behavior. Econometrica 45(6), 1409–1430 (1977)

    Article  Google Scholar 

  • Mas-Colell, A.: The Theory of General Economic Equilibiurm: A Differentiable Approach. Cambridge University Press, Cambridge (1985)

    Book  Google Scholar 

  • Matzkin, R.: Identification of consumer preferences when their choices are unobservable. Econ. Theor. 26(2), 423–443 (2005). https://doi.org/10.1007/3-540-29578-X_10

    Article  Google Scholar 

  • Piccione, M., Spiegler, R.: Price competition under limited comparability. Quart. J. Econ. 127(1), 97–135 (2012)

    Article  Google Scholar 

  • Pivato, M.: Subjective expected utility with a spectral state space. Econ. Theor. 69, 249–313 (2020). https://doi.org/10.1007/s00199-018-01173-5

    Article  Google Scholar 

  • Polemarchakis, H., Selden, L., Song, X.: The identification of ambiguity. Working paper (2019)

  • Polisson, M., Quah, J.K.H., Renou, L.: Revealed preferences over risk and uncertainty. Am. Econ. Rev. 110(6), 1782–1820 (2020)

    Article  Google Scholar 

  • Salant, Y., Rubinstein, A.: \(({A}, f)\): choice with frames. Rev. Econ. Stud. 75(4), 1287–1296 (2008)

    Article  Google Scholar 

  • Salant, Y., Siegel, R.: Contracts with framing. Am. Econ. J.: Microecon. 10(3), 315–346 (2018)

    Google Scholar 

  • Savage, L.J.: The Foundations of Statistics. Wiley, Hoboken (1954)

    Google Scholar 

  • Schipper, B.: Awareness-dependent subjective expected utility. Int. J. Game Theory 42(3), 725–753 (2013)

    Article  Google Scholar 

  • Segal, U.: Two-stage lotteries without the reduction axiom. Econometrica 58(2), 349–377 (1990)

    Article  Google Scholar 

  • Varian, H.: Non-parametric tests of consumer behaviour. Rev. Econ. Stud. 50(1), 99–110 (1983)

    Article  Google Scholar 

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Acknowledgements

This paper is adapted from parts of my PhD dissertation at UCLA. I thank co-editor Mark Machina and anonymous referees for their constructive comments that led to significant improvement of the paper. I am deeply indebted to Murali Agastya, Jay Lu, Rosa Matzkin, and Bill Zame for their guidance and support. I also have benefited from comments by Kadir Atalay, Stefano Fiorin, Itzhak Gilboa, Jian Li, and Marciano Siniscalchi as well as audiences at McGill, UNSW, USyd, UCLA, ITAM, ES NASM 2016, Spring 2016 MWET, ES Latin American Workshop in Economic Theory 2015, and the 10th Annual Economic Graduate Student Conference at WUSTL.

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Correspondence to Anastasia Burkovskaya.

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Burkovskaya, A. A model of state aggregation. Econ Theory 73, 121–149 (2022). https://doi.org/10.1007/s00199-020-01326-5

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