Biographical information for Bob Nau
Published papers:
- Duality Between Maximization of Expected Utility and Minimization of Relative Entropy When Probabilities are Imprecise ( Electronic proceedings of the Sixth International Symposium on Imprecise Probabilities and Their Applications, 2009)
- Sensitivity to Distance and Baseline Distributions in Forecast Evaluation (with Victor Richmond Jose and Bob Winkler, Management Science, v. 55, no. 4, 2009
- Scoring
Rules, Generalized Entropy, and Utility Maximization (with Victor
Richmond Jose and Bob Winkler, Operations
Research, v. 56, no. 4, 2008) Spreadsheet example
Contour
plots
- Extensions
of the Subjective Expected Utility Model, in Advances in Decision Analysis, Cambridge
Univ. Press, 2007, edited
by Edwards, Miles, and von Winterfeldt)
- The
Shape
of Incomplete
Preferences (The Annals of Statistics,
v. 34, no. 5, 2006) Supplement:
mathematical programs for example
- Uncertainty
Aversion
With Second-Order Utilities and Probabilities (Management Science, v. 52, no.1,
2006) Proofs of
theorems Spreadsheet
example
- On
the
Geometry
of Nash Equilibria and Correlated Equilibria (International Journal
of Game Theory, v. 32, no. 4, 2004)
- A
Generalization
Of Pratt-Arrow Measure To Non-Expected-Utility Preferences And
Inseparable
Probability And Utility (Management Science v.49 n.8, 2003)
- The
Aggregation
of Imprecise Probabilities (J. Stat. PIanning & Inference v.
105 n.1, 2002)
- De
Finetti Was Right: Probability Does Not Exist (Theory and
Decision v.
51 n. 2-4, 2001)
- Uncertainty Aversion with Second-Order Probabilities and Utilities (Electronic proceedings of the Second International Symposium on Imprecise Probabilities and Their Applications, 2001)
- Arbitrage,
Incomplete Models,
and Other People's Brains (in Beliefs,
Interactions, and Preferences in Decision Making, Machina &
Munier, eds., Kluwer, 1999)
- Valuing
Risky Projects: Options Pricing Theory and Decision
Analysis (with Jim Smith, Management
Science v. 41 n.5, 1995)
- Coherent
Decision Analysis with Inseparable Probabilities and Utilities (J. Risk and Uncertainty v. 10, 1995)
- The
Incoherence of Agreeing to Disagree (Theory
and Decision v. 39, 1995)
- Indeterminate
Probabilities on Finite Sets (The Annals of Statistics v. 20 n.
4, 1992)
- Joint
Coherence in Games of Incomplete Information (Management Science
v. 38 n. 3, 1992)
- Arbitrage,
Rationality, and Equilibrium (with Kevin McCardle, Theory and Decision v. 31, 1991)
- Coherent
Behavior in Noncooperative Games (with Kevin McCardle, J. Econ. Theory v. 50 n. 2, 1990)
- Decision
Analysis with Indeterminate or Incoherent Probabilities (Annals of Operations Research v.
19, 1989)
- Blau's
Dilemma Revisited (Management Science
v. 33, 1987)
- Should
Scoring Rules Be 'Effective'? (Management
Science v. 31, 1985)
- Adaptive
Filtering Revisited (J. Operational
Research Society v. 30 n. 9, 1979)
Working papers
Edited volume:
Web pages:
What does this figure represent?
If you guessed "battle of the sexes," you are correct. The
figure
illustrates a theorem concerning the geometry of the set of solutions
of
a noncooperative game, as it applies to the 2x2 game known as
battle-of-the-sexes.
(He prefers the boxing match, she prefers the ballet, but they would
like
to go somewhere together rather than separately. What should they
do?) The blue saddle is the set of independently randomized
strategies.
The red hexahedron (with three more faces and one more vertex on the
back
side) is the set of correlated equilibria. Their three points of
intersection
(red dots) are Nash equilibria. The sensible solution is not
a Nash
equilibrium.
For more details see the following
paper.