[Photo of Dov Samet]
Dov Samet

Home page on the web site of The Leon Recanati Graduate School of Business Administration

Faculty of Management
Tel Aviv University
Tel Aviv, 69978

Before publication

[New] Agreeing to agree and Dutch books
(with J. Yi-Chun Chen, Ehud Lehrer, Jiang Li, and Eran Shmaya)

We say that agreeing to agree is possible for an event E if there exist posterior beliefs of the agents, with a common prior, such that it is common knowledge that the agents’ posteriors for E coincide. We propose a notion called Dutch book which is a profile of interim contracts between an outsider and the agents based on the occurrence of E, such that the outsider makes positive profit in all states. We show that in a finite state space, when the agents cannot tell whether E occurred or not, agreeing to agree is possible for E if and only if there is no Dutch book on E. This characterization also holds in countable state spaces with two agents. We weaken the notion of Dutch book to characterize agreeing to agree in a countable state space with multiple agents, when each set in each agent’s information partition is finite.

[New] Belief consistency and trade consistency (Last version: June, 2012)
(with E. Lehrer)

Interpersonal consistency can be described in epistemic terms as a property of beliefs, or in economic terms as the impossibility of certain trades. The existence of a common prior from which all agents' beliefs are derived is of the first kind. The nonexistence of an agreeable bet, that is a contingent zero-sum trade which is always favorable to all agents is of the second kind. It is well established that these two notions of consistency are equivalent for finite type spaces but not for countable ones. We present three equivalences of epistemic consistency and economic consistency conditions for countable type spaces, defining in this way three levels of consistency of type spaces: weak consistency, consistency, and strong consistency. These three levels coincide in the finite case. We fully analyze the level of consistency of type spaces based on the knowledge structure of Rubinstein's email game. The new notion of belief consistency introduced here helps to justify the requirement of boundedness of payoff functions in countable type spaces by showing that in a large class of spaces there exists an agreeable unbounded bet even when a common prior exists.

The table below summarizes the three equivalence theorems. The conditions on the left column are economic and on the right, epistemic. Equivalence holds in each row. The two notions in red were proved in previous works to be equivalent in finite spaces. In this case all the implications in the columns are equivalences.

Three equivalence theorems
weak trade consistency      ⇔     weak belief consistency
no agreeable bet* uniformly existence of common
bounded away from 0 ε-priors** for all ε > 0
trade consistency belief consistency
no agreeable bet* the common ε-priors** of some type
vanish infinitely more slowly than ε
strong trade consistency      ⇔     strong belief consistency
for some state and agent, the gains existence of a common prior
in ε-agreeable bets*** vanish with ε

A glossary
* A bet is a contingent zero-sum trade.
A bet is agreeable if the expected gains of all agents are always positive.
** An ε-prior of an agent is a probability distribution ε-close to a prior of the agent.
A common ε-prior is a probability distribution which is an ε-prior of all agents.
*** An ε-agreeable bet is a bet such the expected loss of each agents is at most ε.

[New] Conditional belief types (September, 2011)
(with A. Di Tillio and J. Halpern)

Decision making requires that agents have beliefs about what happens given events that are believed or known not to happen. Such beliefs can be modeled by conditional probability functions which allow conditioning on unconditionally null events. Players with such beliefs must have conditional beliefs about conditional beliefs. We model this using a type space where a player's type at a state is a conditional probability on the space. We axiomatize type spaces using conditional belief operators, and examine additional three axioms of increasing strength: introspection, that requires that the agent is unconditionally certain of her beliefs; echo, according to which the unconditional beliefs that are implied by the condition must be held given the condition; anddetermination, which says that the conditional beliefs are the unconditional beliefs that are conditionally certain. The echo axiom implies that conditioning events must be unconditionally certain. Thus, conditioning on an event is conditioning on the agent being certain of the event. This formalizes the meaning frequently given to conditioning in probability theory. The echo axiom also implies that the probability given an event is a prior of the unconditional probability. Type spaces are closely related to the sphere models of counterfactual conditionals and to models of hypothetical knowledge.

[New] On the dispensable role of time in games of perfect information (July, 2011)

Time present and time past
Are both perhaps present in time future,
And time future contained in time past.

T. S. Eliot, Burnt Norton—the Four Quartets

In two papers on rationality in games with perfect information, Aumann (1995) and Aumann (1998), time is assumed implicitly in the description of games of perfect information, and it is part of the epistemic distinction between ex-ante and ex-post knowledge. We show that ex-post knowledge can be expressed by ex-ante knowledge and therefore epistemically, time is irrelevant to the analysis. Furthermore, we show that material rationality by weak dominance and by expectation can be expressed in the timeless language of the strategic form of the game.

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).

Matching of like rank and the size of the core in the marriage problem (last version, September, 2013)

When men and women are objectively ranked in a marriage problem, say by beauty, then pairing individuals of equal rank is the only stable matching. We generalize this observation by providing bounds on the size of the rank gap between mates in a stable matchings in terms of the size of the ranking sets. Using a metric on the set of matchings, we provide bounds on the diameter of the core---the set of stable matchings---in terms of the size of the ranking sets and in terms of the size of the rank gap. We conclude that when the set of rankings is small, so are the core and the rank gap in stable matchings.

The sure thing principle and independence of irrelevant knowledge (2008)

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 simple models of knowledge, we examine the sure thing principle, presenting two ways to capture it. One is in terms of the union of future events, for which we reserve the original name — the sure thing principle; the other is in terms of the intersection of kens — bodies of agents' knowledge — which we call independence of irrelevant knowledge. We show that the two principles are equivalent and that the only property of knowledge required for this equivalence is the axiom of truth--the requirement that whatever is known is true. We present a symmetric version of the independence of irrelevant knowledge which is equivalent to the impossibility of agreeing to disagree on the decision made by agents, namely the impossibility of agents making different decisions being common knowledge

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.