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Dynamic stochastic dominance in bandit decision problems

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Abstract

The aim of this paper is to study the monotonicity properties with respect to the probability distribution of the state processes, of optimal decisions in bandit decision problems. Orderings of dynamic discrete projects are provided by extending the notion of stochastic dominance to stochastic processes.

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REFERENCES

  • Banks, J.S. and Sundaram, R.K. (1992), Denumerable armed bandit problems, Econometrica 60(5):1071–1096.

    Google Scholar 

  • Berry, D.A. and Fristedt, B. (1985), Bandit Problems: Sequential Allocation of Experiments, London: Chapman and Hall.

    Google Scholar 

  • Berry, D.A. and Kertz, R.P. (1991), Worth of perfect information in Bernoulli bandits, Adv.Appl.Prob.23: 1–23.

    Google Scholar 

  • Bikhchandani, S. and Sharma, S. (1990), Optimal search with learning, Working Paper no. 580, Department of Economics, University of California, Los Angeles.

    Google Scholar 

  • Bikhchandani, S., Segal, U. and Sharma, S. (1992), Stochastic dominance under Bayesian learning, Journal of Economic Theory 56(2):352–377.

    Google Scholar 

  • Billingsley, P. (1986), Probability and Measure, New York: Wiley.

    Google Scholar 

  • Blackwell, D. (1965), Discounted dynamic programming, Ann.Math.Statis.36: 226–35.

    Google Scholar 

  • DeGroot, M.H. (1970), Optimal Statistical Decisions, New York: McGraw-Hill Book.

    Google Scholar 

  • Fishman, A. (1990), Stochastic dominance in multi sampling environments, Journal of Economic Theory51: 77–91.

    Google Scholar 

  • Flinn, C. (1986), Wages and job mobility of young workers, Journal of Political Economy94: S88–S110.

    Google Scholar 

  • Gittins, J.C. (1989), Multi-armed Bandit Allocation Indices, New York: Wiley

    Google Scholar 

  • Gittins, J.C. and Jones, D.M. (1974), A dynamic allocation index for sequential design of experiments, in J. Gani (ed.), Progress in Statistics, Amsterdam: North-Holland, pp. 241–266.

    Google Scholar 

  • Gittins, J.C. and Wang, Y.-G. (1992), The learning component of allocation indices, Annals of Statistics 20(3):1625–1636.

    Google Scholar 

  • Hadar, J. and Russel, W.R. (1969), Rules for ordering uncertain prospects, The American Economic Review59: 25–34.

    Google Scholar 

  • Jovanovic, B. (1979), Job-matching and the theory of turnover, Journal of Political Economy87: 972–990.

    Google Scholar 

  • Kamae, T., Krengel, U. and O'Brien, G.L. (1977), Stochastic inequalities on partially ordered spaces, The Annals of Probability5: 899–912.

    Google Scholar 

  • Milgrom, P.R. and Weber, R.J. (1982), A theory of auctions and competitive bidding, Econometrica50: 1089–1122.

    Google Scholar 

  • Miller, R. (1984), Job matching and occupational choice, Journal of Political Economy92: 1086–1120.

    Google Scholar 

  • Rothschild, M. and Stiglitz, J.E. (1970), Increasing risk, I: A definition, Journal of Economic Theory2: 225–243.

    Google Scholar 

  • Rothschild, M. (1974), A two-armed bandit theory of market pricing, Journal of Economic Theory9: 185–202.

    Google Scholar 

  • Russel, W.R. and Seo, T.K. (1989), Representative sets for stochastic dominance rules, in T.B. Fomby and T.K. Seo (eds.), Studies in the Economics of Uncertainty, Berlin: Springer Verlag.

    Google Scholar 

  • Whittle, P. (1982), Optimization over Time, 2 vols, New York: Wiley.

    Google Scholar 

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Magnac, T., Robin, JM. Dynamic stochastic dominance in bandit decision problems. Theory and Decision 47, 267–295 (1999). https://doi.org/10.1023/A:1005142630173

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