**Biographical
information and web pages**:

- CV
- Duke web page
- Choice theory
course web site
- Forecasting
course web site
- RegressIt Excel add-in
web site

**Published papers:**

- Risk
Neutral Equilibria of Noncooperative Games (forthcoming in
*Theory and Decision*) - Imprecise
Probabilities in Noncooperative Games (Electronic
proceedings of the Seventh International Symposium on Imprecise
Probability: Theories and Applications, 2011) Powerpoint
slides
- A
Theorem for Bayesian Group Decisions (with Ralph Keeney;
*Journal of Risk and Uncertainty*, v. 43, no. 1, 2011) - Risk,
Ambiguity, and State-Preference Theory (
*Economic Theory*, v. 49, no. 1, 2011) - 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)

Edited volume:

**
Older working papers**:

- Bayesianism
Without Priors, Acts Without Consequences (September 2005)
- Coherent
Assessment of Subjective Probability (1981)

Edited volume:

**Other web pages:**

- Risk,
Uncertainty, and Decision (RUD 2009) Conference, June 18-21
- Decision
Analysis Society
- A
Tutorial on the Game of Baseball

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 gray saddle is the set of
independently randomized strategies. The green hexahedron 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.