[Photo of Dov Samet]
Dov Samet

Coller School of Management
Tel Aviv University
Tel Aviv, 69978

Most recent

A priori and a posteriori knowledge in epistemic logic (last version Aug 29, 2022)

We study the dichotomy of a priori and a posteriori in multi-agent epistemic logic. A formula is said to be a posteriori discernable for an individual if the individual needs to "observe" the world in order to tell whether the formula or its negation is true, that is, if in some possible world the individual cannot tell this. A formula is said to be a priori discernable for an individual if in all possible worlds the individual can tell whether the formula or its negation is true. We show that the formulas that are a priori discernable by an individual are theorems, contradictions, and formulas that are logically equivalent to a description of the individual's knowledge. The knowledge of the individual in a given possible world is split into two parts: A priori knowledge — the a priori discernable formulas that the individual knows, and a posteriori knowledge — the a posteriori discernable formulas that the individual knows. We characterize these two types of knowledge and show that a posteriori knowledge can be retrieved from a prior knowledge and vice versa.

Non-Bayesian correlated equilibrium as an expression of non-Bayesian rationality (Games and Economic Behavior, 135 (2022) 1-15)
(with J. Hillas)

We study new non-Bayesian solutions of games in strategic form, based on four notions of dominance: weak or strict domination by either a pure or a mixed strategy. For each of these types of dominance, d, we define a family of sets of strategy profiles, called d-correlated equilibria. We study the structure and properties of these families. A player is d-dominance rational when she does not play a strategy that is d-dominated relative to what she knows about the play of the other players. A set of profiles is a d-correlated equilibrium if and only if it is the set of profiles played in a model where d-dominance rationality is commonly known. When d denotes strict domination by a mixed strategy, a set of profiles is a d-correlated equilibrium if and only if it is the set of profiles played in a model where Bayesian rationality is commonly known.

Desirability relations in Savage's model of decision making (Theory and Decision, forthcoming)
(with D. Schmeidler)

We propose a model of an agent's probability and utility that is a compromise between Savage (1954) and Jeffrey (1965). In Savage's model the probability-utility pair is associated with preferences over acts which are assignments of consequences to states. The probability is defined on the state space, and the utility function on consequences. Jeffrey's model has no consequences, and both probability and utility are defined on the same set of propositions. The probability-utility pair is associated with a desirability relation on propositions. Like Savage we assume a set of consequences and a state space. However, we assume that states are comprehensive, that is, each state describes a consequence, as in Aumann (1987). Like Jeffrey, we assume that the agent has a preference relation, which we call desirability, over events, which by definition involves uncertainty about consequences. For a given probability and utility of consequences, the desirability relation is presented by conditional expected utility, given an event. We axiomatically characterize desirability relations that are represented by a probability-utility pair. We characterize the family of all the probability-utility pairs that represent a given desirability relation.

The impossibility of agreeing to disagree: An extension of the sure thing principle (Games and Economic Behavior 132, 2022)

The impossibility of agreeing to disagree in the non-probabilistic setup means that agents cannot commonly know their decisions unless they are all the same. We study the relation of this property to the sure thing principle when it is expressed in epistemic terms. We show that it can be presented in two equivalent ways: one is in terms of knowledge operators, which we call the principle of follow the knowledgeable, the other is in terms of kens, that is, bodies of agents' knowledge, which we call independence of irrelevant knowledge. The latter can be easily extended to a property which is equivalent to the impossibility of agreeing to disagree.

Monologues, Dialogues, and Common Priors (Theoretical Economics, 17, 2022)
(with A. Di Tillio and E. Lehrer)

The main purpose of this paper is to provide a simple criterion enabling to conclude that two agents do not share a common prior. The criterion is simple, as it does not require information about the agents' knowledge and beliefs, but rather only the record of a dialogue between the agents. In each stage of the dialogue the agents tell each other the probability they ascribe to a fixed event and update their beliefs about the event. To characterize dialogues consistent with a common prior, we first study monologues, which are sequences of probabilities assigned by a single agent to a given event in an exogenous learning process. A dialogue is consistent with a common prior if and only if each selection sequence from the two monologues comprising the dialogue is itself a monologue.

A game theoretic approach reveals that discretizing clinical information can reduce antibiotic misuse
(Maya Diamant, Shoham Baruch, Eias Kassem, Khitam Muhsen, Dov Samet, Moshe Leshno, and Uri Obolski)
(Nature Communications, volume 12, Article number: 1148 (2021))

The overuse of antibiotics is exacerbating the antibiotic resistance crisis. Since this problem is a classic common-goodsdilemma, it naturally lends itself to a game-theoretic analysis. Hence, we designed a model wherein physicians weigh whether antibiotics should be prescribed, given that antibiotic usage depletes its future effectiveness. The physicians’ decisions rely on the probability of a bacterial infection before definitive laboratory results are available. We show that the physicians’ equilibrium decision-rule of antibiotic prescription is not socially optimal. However, we prove that discretizing the information provided to physicians can mitigate the gap between their equilibrium decisions and the social optimum of antibiotic prescription. Despite this problem’s complexity, the effectiveness of the discretization solely depends on the distribution of available information. This is demonstrated on theoretic distributions and a clinical dataset. Our results provide a game-theory based guide for optimal output of current and future decision support systems of antibiotic prescription

Interim agreements (Last revision: November, 2020)

Processes of bargaining are studied in which the players reach interim agreements that serve as status quo points for further bargaining. This is modeled in Nash’s setup of bargaining problems, where the solution is a time parameterized path of interim agreements rather than a single point. We characterize path solutions for linear problems that satisfy the axioms of restarting and covariance, and show that if a Pareto efficient agreement is not reached immediately, then it is never reached in finite time. Adding the axioms of individual rationality, relevance, and monotonicity, we characterize the family of continuous Raiffa solutions and show that these solutions converge to a Pareto efficient agreement but never reach it in finite time. Finally, if a deadline is added to the bargaining problem, and the speed of bargaining is proportionally inverse to the deadline, then a Pareto efficient agreement is reached exactly at the deadline.

An extension of Ceva's theorem to n-simplices (American Mathematical Monthly, 128(5), 2021)

Ceva's theorem concerns triangles, that is, 2-simplices. Instead of an abstract, here is a short narrated presentation that describes graphically the extension of this theorem to general simplices.

Dominance rationality: A unified approach (Games and Economic Behavior 119 (2020))
(with J. Hillas)

There are four types of dominance depending on whether domination is strict or weak and whether the dominating strategy is pure or mixed. Letting d vary over these four types, we say that a player is d-dominance rational when she does not play a strategy that she knows to be d-dominated. For weak dominance by mixed strategy Stalnaker (1994) introduced a process of iterative maximal elimination of certain profiles that we call here flaws. We define here, analogously, d-flaws for each type of dominance d, and show that for each d, iterative elimination of d-flaws is order independent. We then show that the characterization of common knowledge of d-dominance rationality is the same for all four types. A strategy profile can be played when d-dominance rationality is commonly known if and only if it survives an iterative elimination of d-flaws.

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

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

PowerPoint Presentations

Published papers

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) Games and Economic Behavior, 108, 2018.