[Photo of Dov Samet]
Dov Samet

Faculty of Management
Tel Aviv University
Tel Aviv, 69978

Before publication

[New] Desirability relations in Savage's model of decision making (May, 2018)
(with D. Schmeidler)

The subjective probability of a decision maker is a numerical representation of a qualitative probability which is a binary relation on events that satisfies certain axioms. We show that a similar relation between numerical measures and qualitative relations on events exists also in Savage's model. A decision maker in this model is equipped with a unique pair of probability on the state space and cardinal utility on consequences, which represents her preferences on acts. We show that the numerical pair probability-utility is a representation of a family of desirability relations on events that satisfy certain axioms. We first present axioms on a desirability relation defined in the interim stage, that is, after an act has been chosen. These axioms guarantee that the desirability relation is represented by a pair of probability and utility by taking for each event conditional expected utility. We characterize the set of representing pairs by measuring the optimism of probabilities on consequences and the content of utility functions. We next present axioms on the way desirability relations are associated ex ante with various acts. These axioms determine the unique pair of probability and utility in Savage's model.

Weak and strict dominance: A unified approach (Last revision: April, 2018)
(with J. Hillas)

[teacher and student]

Strict-dominance rationality is a non-Bayesian notion of rationality which means that players do not choose strategies they know to be strictly dominated. Similarly, weak-dominance rationality means that players do not choose strategies that they know to be weakly dominated. Iterative elimination of strictly dominated strategies can be intuitively and formally justified by players having common knowledge of strict-dominance rationality. In contrast, common knowledge of weak-dominance rationality fails to justify iterative elimination of weakly dominated strategies.

Examining the reasons for this failure leads to a characterization of the strategy profiles played when weak-dominance rationality is commonly known. These are profiles that survive a process of iterative elimination of profiles called weak flaws that was introduced by Stalnaker to characterize certain Bayesian models of games. We define, analogously, strict flaws, and show that the iterative elimination of either weak or strict flaws is order independent. Our main result is that the case of weak dominance and strict dominance are completely analogous: Common knowledge of weak-dominance or strict-dominance rationality is characterized by iterative elimination of weak or strict flaws correspondingly. Our results hold equally for domination by pure and mixed strategies, which distinguish them from characterizations in Bayesian models that hold only for mixed domination.

[New] Is common knowledge of rationality sluggish? (November, 2015)

Or else, why does it lag behind the iterative elimination of strongly dominated strategies?

The sure-thing principle in epistemic terms (Last revision: April, 2015)

Savage (1954) introduced the sure thing principle in terms of the dependence of decisions on knowledge, but gave up on formalizing it in epistemic terms for lack of a formal definition of knowledge. Using a standard model of knowledge, we examine the sure thing principle, presenting two ways to capture it. One is in terms of of knowledge operators, which we call the principle of follow the knowledgeable; the other is in terms of kens---bodies of agents' knowledge---which we call independence of irrelevant knowledge. We show that the two principles are equivalent. We present a stronger version of the independence of irrelevant knowledge and show that it is equivalent to the impossibility of agreeing to disagree on the decision made by agents, namely the impossibility of different decisions made by agents being common knowledge.

Non-probabilistic correlated equilibrium as an expression of non-Bayesian rationality (May, 2014)
(with J. Hillas)

We define weak and strong rationality of players in terms of dominance rather than expectation with respect to probabilistic beliefs. We also define certain subsets of strategy profiles as weak or strong non-probabilistic correlated equilibrium, analogously to correlated equilibrium. It is shown that the set of profiles played when there is common knowledge of weak or strong rationality is a weak or strong non-probabilistic correlated equilibrium, correspondingly. The largest weak non-probabilistic correlated equilibrium is the set of profiles that survive iterated elimination of strictly dominated strategies. Rationality can be strengthened for games with perfect information by considering rationality in subgames. A player is substantively rational if she is rational in all subgames, and materially rational if she rational in subgames at vertices that are reached. Aumann (1995, 1998) introduced and studied these two notions for the case of weak rationality. We characterize the weak and the strong versions of these notions of rationality in terms of non-probabilistic correlated equilibria. We show that non-probabilistic correlated equilibria can be also characterized in terms of non-probabilistic belief rather than knowledge.

What if Achilles and the tortoise were to bargain?
An argument against interim agreements?
(January, 2010. Last version, April, 2010)

[Picture of Achilles and the tortoise]

Engaging in a dynamic process of interim agreements guarantees that agreement will never be reached. Arguments of Zeno, Aristotle, von Neumann, Nash, Raiffa, and C. Northcote Parkinson lead to this grim conclusion. Is the everlasting Israeli-Palestinian peace process a case in point?

(In the picture, Achilles and the tortoise bargain on the splitting of a drachma).

PowerPoint Presentations

Publications available in e-journals

The Determination of Marginal Cost Prices Under a Set of Axioms

(with Y. Tauman) Econometrica, Vol. 50, No. 4, 1982.

An Application of the Aumann--Shapley Prices for Cost Allocation in Transportation Problems

(with Y. Tauman and I. Zang), Math. of Oper.Res., Vol. 9, No. 1, 1984.

An Axiomatic Approach to the Allocation of a Fixed Cost Through Prices

(with L. Mirman and Y. Tauman), The Bell Journal of Economics, Vol. 14, No. 1, 1983.

Vector Measures are Open Maps

Math. of Oper. Res., Vol. 9, No. 3, 1984.

On the Core and Dual Set of Linear Programming Games

(with E. Zemel), Math. of Oper. Res., Vol. 9, No. 2, 1984.

Persistent Equilibria in Strategic Games

(with E. Kalai), International Journal of Game Theory, Vol. 13, No. 3, 1984.

Monotonic Solutions to General Cooperative Games

(with E. Kalai), Econometrica, Vol. 53, No. 2, 1985.

An Axiomatic Characterization of the Egalitarian Solution for Cooperative Games

Mathematical Social Sciences, No. 9, 1985.

Unanimity Games and Pareto Optimality

(with E. Kalai), International Journal of Game Theory, Vol. 14, No. 1, 1985.

Dissipation of Contestable Rents by Small Numbers of Contenders

(with A. Hillman), Public Choice, Vol. 54, 1987.

Continuous Selections for Vector Measures

Math.of Oper. Res., Vol. 12, No. 3, 1987.

On Weighted Shapley Values

(with E. Kalai), International Journal of Game Theory, Vol. 16, No. 3, 1987.

A Note on Reactive Equilibria in the Discounted Prisoners' Dilemma and Associated Games

(with E. Kalai and W. Stanford), Games and Economic Behavior, Vol. 13, No. 3, 1988.

Approximating Common Knowledge with Common Beliefs

(with D. Monderer), Games and Economic Behavior, Vol. 1, No. 2, 1989.

Bounded Versus Unbounded Rationality: The Tyranny of the Weak

(with I. Gilboa), Games and Economic Behavior, Vol. 1, No. 3, 1989.

Bertrand Competition with Subcontracting

(with M. Kamien and L. Li), The Rand Journal of Economics, Vol. 20, No. 4, 1989.

Ignoring Ignorance and Agreeing to Disagree

J. of Economic Theory, Vol. 52, No. 1, 1990.

Agreeing to Disagree in Infinite Information Structures

Games and Economic Behavior, Vol. 21, No. 3, 1992.

Weighted Values and the Core

(with D. Monderer and L. Shapley), International Journal of Game Theory, Vol. 21, 1992.

Stochastic Common Learning

(with D. Monderer), Games and Economic Behavior, Vol. 9, No. 2, 1995.

`Knowing Whether', `Knowing That' and the Cardinality of State Spaces

(with S. Hart and A. Heifetz), Journal of Economic Theory, Vol. 70, No. 1, 1996.

Proximity of Information Structures

(with D. Monderer), Math. of Oper. Res., Vol. 21, No. 3, 1996.

Hypothetical Knowledge and Games with Perfect Information

Games and Economic Behavior, Vol. 17, No. 2, 1996.

Belief Affirming in Learning Processes

(with D. Monderer and A. Sela), Journal of Economic Theory, Vol. 73, No.2, 1997.

Knowledge Spaces with Arbitrarily High Rank

(with A. Heifetz), Games and Economic Behavior, Vol. 22, No. 2, 1998.

Iterated Expectations and Common Priors

Games and Economic Behavior, Vol. 24, No. 1 1998.

Common Priors and the Separation of Convex Sets

Games and Economic Behavior, Vol. 24, No. 1 1998.

Topology-Free Typology of Belief

(with A. Heifetz), Journal of Economic Theory, Vol. 82, 1998.

Coherent Beliefs are not Always Types

(with A. Heifetz), Journal of Mathematical Economics, Vol. 32, 1999.

Bayesianism without Learning

Research in Economics, Vol. 53, 1999.

Hierarchies of Knowledge: An Unbounded Stairway

(with A. Heifetz), Mathematical Social Sciences, Vol. 38, 1999.

Quantified Beliefs and Believed Quantities

Journal of Economic Theory, Vol. 95, 2000.

Learning to Play Games in Extensive Form by Valuation

(with P. Jehiel), NAJ Economics Vol. 1, 2001. Journal of Economic Theory, Vol. 124, 2005.

Between Liberalism and Democracy

(with D. Schmeidler) Journal of Economic Theory, Vol. 110, 2003.

An Ordinal Solution to Bargaining Problems with Many Players

(with Z. Safra), Games and Economic Behavior, Vol. 46, 2004

One Observation Behind Two Envelope Puzzles

(with I. Samet and D. Schmeidler), American Mathematical Monthly, Vol. 111, 2004.

Bargaining with an agenda

(with B. O'neill, E. Winter, and Z. Wiener) Games and Economic Behavior, Vol. 48, 2004.

Utilitarian Aggregation of Beliefs and Tastes

(with I.Gilboa, and D. Schmeidler) J. of Political Economy, Vol. 112, 2004.

A family of Ordinal Solutions for bargaining problems with Many Players

(with Z. Safra) Games and Economic Behavior, Vol. 50, 2005.

Counterfactuals in wonderland

Games and Economic Behavior, Vol. 51, 2005.

Probabilities as Similarity-Weighted Frequencies

(with A. Billot, I. Gilboa, and D. Schmeidler) Econometric, 73, 2005.

Valuation Equilibrium

(with P. Jehiel), Theoretical Economics, 2, 2007.

On Definability in Multimodal Logic

(with J. Halpern and E. Segev), The Review of Symbolic Logic, 2, 2009, , 451-468.

Defining Knowledge in Terms of Belief: The Modal Logic Perspective

(with J. Halpern and E. Segev), The Review of Symbolic Logic, 2, 2009, 469-487.

S5 knowledge without partitions

Synthese, 172, 2010, 145-155

Agreeing to disagree: The non-probabilistic case

Games and Economic Behavior, Vol. 69, 2010, 169-174.

A commitment folk theorem

(with Adam Tauman Kalai, Ehud Kalai, and Ehud Lehrer) Games and Economic Behavior, 69, 2010.

Agreeing to Agree

(with E. Lehrer) Theoretical Economics, 6, 2011.

Generalized Raiffa solutions

(with A. Diskin and M. Koppel) Games and Economic Behavior, 73, 2011.

How common are common priors?

(with Ziv Hellman) Games and Economic Behavior, 74, 2012.

Common belief of rationality in games of perfect information

Games and Economic Behavior, 79, 2013.

Belief consistency and trade consistency

(with E. Lehrer) Games and Economic Behavior, 83, 2014.

Conditional belief types

(with A. Di Tillio and J. Halpern) Games and Economic Behavior, 87, 2014.

Matching of like rank and the size of the core in the marriage problem

(with R. Holzmna) Games and Economic Behavior, 88, 2014.

Agreeing to agree and Dutch books

(with J. Y. Chen, E. Lehrer, J. Li, and E. Shmaya) Games and Economic Behavior, 93, 2015.

On the dispensable role of time in games of perfect information

Inernational Journal of Game Theory, 45, 2016.

Coalition preferences with independent prospects

(with M. Baucells) Inernational Journal of Game Theory, forthcoming.