Dov Samet
Address: Coller School of Management Tel Aviv University Tel Aviv, 69978 ISRAEL |

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.

(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.

(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* 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.

(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.

(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

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.

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.

(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.

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

One observation behind two envelope puzzles + Agreeing to agree

Between Liberalism and Democracy

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