Payoffs-Beliefs Duality and the Value of Information

In decision problems under incomplete information, payoff vectors (indexed by states of nature) and beliefs are naturally paired by bilinear duality. We exploit this duality to analyze the value of information using convex analysis. We then derive global estimates of the value of information of any information structure from local properties of the value function and of the set of optimal actions taken at the prior belief only, and apply our results to the marginal value of information.

[1]  K. Ball.  CONVEX BODIES: THE BRUNN–MINKOWSKI THEORY , 1994 .

[2]  E. Lehmann.  Comparing Location Experiments , 1988 .

[3]  R. Tyrrell Rockafellar,et al.  Convex Analysis , 1970, Princeton Landmarks in Mathematics and Physics.

[4]  Yuliy Sannikov,et al.  Reputation in Continuous‐Time Games , 2011 .

[5]  H. F. Bohnenblust,et al.  Reconnaissance in Game Theory , 1949 .

[6]  Ehud Lehrer,et al.  The Value of a Stochastic Information Structure , 2008, Games Econ. Behav..

[7]  Olivier Gossner,et al.  A normalized value for information purchases , 2017, J. Econ. Theory.

[8]  J. Hirshleifer.  The Private and Social Value of Information and the Reward to Inventive Activity , 1971 .

[9]  Ehud Lehrer,et al.  The value of information - An axiomatic approach☆ , 1991 .

[10]  D. McFadden.  Conditional logit analysis of qualitative choice behavior , 1972 .

[11]  Sven Rady,et al.  Optimal Experimentation in a Changing Environment , 1997 .

[12]  Daniel McFadden,et al.  Modelling the Choice of Residential Location , 1977 .

[13]  A. Cabrales,et al.  Entropy and the Value of Information for Investors , 2010 .

[14]  D. Blackwell.  Equivalent Comparisons of Experiments , 1953 .

[15]  Patrick Bolton,et al.  Strategic Experimentation: A Revision , 1995 .

[16]  Hector Chade,et al.  Another Look at the Radner-Stiglitz Nonconcavity in the Value of Information , 2001, J. Econ. Theory.

[17]  Michel De Lara,et al.  A tight sufficient condition for Radner-Stiglitz nonconcavity in the value of information , 2007, J. Econ. Theory.

[18]  M. Cripps,et al.  Strategic Experimentation with Exponential Bandits , 2003 .

[19]  Massimo Marinacci,et al.  Complete Monotone Quasiconcave Duality , 2011, Math. Oper. Res..

[20]  J. Hiriart-Urruty,et al.  Convex analysis and minimization algorithms , 1993 .

[21]  Robert J. Aumann,et al.  Repeated Games with Incomplete Information , 1995 .

[22]  Tapen Sinha.  Economic and Financial Decisions under Risk , 2006 .

[23]  A. Rustichini,et al.  Ambiguity Aversion, Robustness, and the Variational Representation of Preferences , 2006 .

[24]  M. Shubik,et al.  COWLES FOUNDATION FOR RESEARCH IN ECONOMICS , 1991 .

[25]  Darinka Dentcheva,et al.  Common Mathematical Foundations of Expected Utility and Dual Utility Theories , 2012, SIAM J. Optim..

[26]  N. Persico.  Information acquisition in auctions , 2000 .

[27]  Susan Athey,et al.  The Value of Information in Monotone Decision Problems , 1998 .

[28]  G. Brier.  VERIFICATION OF FORECASTS EXPRESSED IN TERMS OF PROBABILITY , 1950 .

[29]  D. Blackwell.  Comparison of Experiments , 1951 .

[30]  I. Gilboa,et al.  Maxmin Expected Utility with Non-Unique Prior , 1989 .

[31]  Massimo Marinacci,et al.  AMBIGUITY AVERSION, ROBUSTNESS, AND THE VARIATIONAL , 2006 .