# Publications

We give a criterion of positivity for the value of a matrix game. We use the criterion to investigate conditions of positivity of value for two classes of games: payoff matrices with all elements outside of the main diagonal having the same sign and symmetric payoff matrices.

We are dealing with a search game where one searcher looks for two mobile objects on a graph. The searcher distributes his searching resource so as to maximize the probability of detecting at least one of the mobile objects. Each mobile object minimizes its own probability of being found. In this problem the Nash equilibrium, i.e. the optimal transition probabilities of the mobile objects and the optimal values of the searcher’s resource, was found. The value of the game in a single-stage search game with non-exponential payoff functions was found.

This note shows that the egalitarian Dutta and Ray (1989) solution for transferable utility games is self-antidual on the class of exact partition games. By applying a careful antiduality analysis, we derive several new axiomatic characterizations. Moreover, we point out an error in earlier work on antiduality and repair and strengthen several related characterizations on the class of convex games.

We consider fair allocation of indivisible items under additive utilities. We show that there exists a strongly polynomial-time algorithm that always computes an allocation satisfying Pareto optimality and proportionality up to one item even if the utilities are mixed and the agents have asymmetric weights. The result does not hold if either of Pareto optimality or PROP1 is replaced with slightly stronger concepts.

This paper studies independence of higher claims and independence of irrelevant claims on the domain of bargaining problems with claims. Independence of higher claims requires that the payoff of an agent does not depend on the higher claim of another agent. Independence of irrelevant claims states that the payoffs should not change when the claims decrease but remain higher than the payoffs. Interestingly, in conjunction with standard axioms from bargaining theory, these properties characterize a new constrained Nash solution, a constrained Kalai–Smorodinsky solution, and a constrained Kalai solution.

The bibliography is published in onne tion with the ninetieth anniversary of the professor Robert John (Yisrael) Aumann. On the eighth of June the outstanding Israeli Ameri an game theorist Robert John (Yisrael) Aumann elebrates his 90-anniversary. A professor at the Center for the Study of Rationality in the Hebrew University of Jerusalem in Israel, he re eived in 2005 the Nobel Memorial Prize in E onomi S ien es for his work on oni t and ooperation through game-theory analysis. He shared the prize with Thomas S helling. At the Hebrew University of Jerusalem Prof. Aumann reated a ourishing game theory s hool whi h is one of the best in the world.

This paper axiomatically studies the equal split-off set (cf. Branzei et al. (Banach Center Publ 71:39–46, 2006)) as a solution for cooperative games with transferable utility which extends the well-known Dutta and Ray (Econometrica 57:615–635, 1989) solution for convex games. By deriving several characterizations, we explore consistency of the equal split-off set on the domains of exact partition games and arbitrary games.

Positive-Unlabeled (PU) learning is an analog to supervised binary classification for the case when only the positive sample is clean, while the negative sample is contaminated with latent instances of positive class and hence can be considered as an unlabeled mixture. The objectives are to classify the unlabeled sample and train an unbiased positive-negative classifier, which generally requires to identify the mixing proportions of positives and negatives first. Recently, unbiased risk estimation framework has achieved state-of-the-art performance in PU learning. This approach, however, exhibits two major bottlenecks. First, the mixing proportions are assumed to be identified, i.e. known in the domain or estimated with additional methods. Second, the approach relies on the classifier being a neural network. In this paper, we propose DEDPUL, a method that solves PU Learning without the aforementioned issues. The mechanism behind DEDPUL is to apply a computationally cheap postprocessing procedure to the predictions of any classifier trained to distinguish positive and unlabeled data. Instead of assuming the proportions to be identified, DEDPUL estimates them alongside with classifying unlabeled sample. Experiments show that DEDPUL outperforms the current state-of-the-art in both proportion estimation and PU Classification and is flexible in the choice of the classifier.

We consider a setting in which agents vote to choose a fair mixture of public outcomes. The agents have dichotomous preferences: Each outcome is liked or disliked by an agent. We discuss three outstanding voting rules. The *Conditional Utilitarian* rule, a variant of the random dictator, is strategyproof and guarantees to any group of like-minded agents an influence proportional to its size. It is easier to compute and more efficient than the familiar *Random Priority* rule. We show, both formally and by numerical experiments, that its inefficiency is low when the number of agents is low. The efficient *Egalitarian* rule protects individual agents but not coalitions. It is *excludable strategyproof*: An agent does not want to lie if she cannot consume outcomes she claims to dislike. The efficient *Max Nash Product* rule offers the strongest welfare guarantees to coalitions, which can force any outcome with a probability proportional to their size. But it even fails the excludable form of strategyproofness.

We study the set of possible joint posterior belief distributions of a group of agents who share a common prior regarding a binary state and who observe some information structure. Our main result is that, for the two-agent case, a quantitative version of Aumann's Agreement Theorem provides a necessary and sufficient condition for feasibility. For any number of agents, a related "no-trade" condition likewise provides a characterization of feasibility. We use our characterization to construct joint belief distributions in which agents are informed regarding the state, and yet receive no information regarding the other's posterior. We study a related class of Bayesian persuasion problems with a single sender and multiple receivers, and explore the extreme points of the set of feasible distributions.

We consider a cooperative game based on a network in which nodes represent players and the characteristic function is defined using a maximal covering by the pairs of connected nodes. Problems of this form arise in many applications such as mobile communications, patrolling, logistics and sociology. The Owen value, which describes the significance of each node in the network, is derived. We show that the method of generating functions can be useful for calculating this Owen value and illustrate this approach based on examples of network structures.

Among the bryophytes, biological growth rhythms have not yet been identified due to a lack of long‐term precision observations. Here we carry out precision field monitoring of the growth of the peat moss *Sphagnum riparium* using the recent geotropic curvature method. For four years, using the observation intervals of 2‐5 days, we measured 116 469 shoots and received 4 493 estimates of growth rates. We found three rhythmic growth components. The seasonal rhythm of growth has a period of about 180 days, which coincides with the seasonal temperature cycle. The circalunar growth rhythm has a period of about 29.5 days and coincides with the synodic lunar cycle. There is an acceleration near the new moon, and a slowdown in growth near the full moon. The third rhythm has a period of 7‐16 days and is always synchronized with the circalunar growth rhythm. From the models of the sums of sinusoids, we found that the total contribution of all three rhythms to the growth rate is R2 = 0.51‐0.78, and without taking into account the seasonal rhythm, R2 = 0.36‐0.42. Thus, our study gives the first data on the biological rhythms and the contribution of these rhythms to the growth process of bryophytes. We attribute the unexpectedly high contribution of rhythms to the synchronous growth of the Sphagnum mat, which is necessary to reduce the loss of moisture.