# Publications

Global gridded crop models (GGCMs) are essential tools for estimating agricultural crop yields and externalities at large scales, typically at coarse spatial resolutions. Higher resolution estimates are required for robust agricultural assessments at regional and local scales, where the applicability of GGCMs is often limited by low data availability and high computational demand. An approach to bridge this gap is the application of meta-models trained on GGCM output data to covariates of high spatial resolution. In this study, we explore two machine learning approaches – extreme gradient boosting and random forests - to develop meta-models for the prediction of crop model outputs at fine spatial resolutions. Machine learning algorithms are trained on global scale maize simulations of a GGCM and exemplary applied to the extent of Mexico at a finer spatial resolution. Results show very high accuracy with R2>0.96 for predictions of maize yields as well as the hydrologic externalities evapotranspiration and crop available water with also low mean bias in all cases. While limited sets of covariates such as annual climate data alone provide satisfactory results already, a comprehensive set of predictors covering annual, growing season, and monthly climate data is required to obtain high performance in reproducing climate-driven inter-annual crop yield variability. The findings presented herein provide a first proof of concept that machine learning methods are highly suitable for building crop meta-models for spatio-temporal downscaling and indicate potential for further developments towards scalable crop model emulators.

This research is motivated by sustainability problems of oil palm expansion. Fast-growing industrial Oil Palm Plantations (OPPs) in the tropical belt of Africa, Southeast Asia and parts of Brazil lead to significant loss of rainforest and contribute to the global warming by the corresponding decrease of carbon dioxide absorption. We propose a novel approach to monitoring of the expansion of OPPs based on an application of state-of-the-art Fully Convolutional Neural Networks (FCNs) to solve Semantic Segmentation Problem for Landsat imagery. The proposed approach significantly outperforms per-pixel classification methods based on Random Forest using texture features, NDVI, and all Landsat bands. Moreover, the trained FCN is robust to spatial and temporal shifts of input data. The paper provides a proof of concept that FCNs as semi-automated methods enable OPPs mapping of entire countries and may serve for yearly detection of oil palm expansion.

This paper analyzes bankruptcy games with nontransferable utility as a generalization of bankruptcy games with monetary payoffs. Following the game theoretic approach to NTU-bankruptcy problems, we study some appropriate properties and the core of NTU-bankruptcy games. Generalizing the core cover and the reasonable set to the class of NTU-games, we show that NTU-bankruptcy games are compromise stable and reasonable stable. Moreover, we derive a necessary and sufficient condition for an NTU-bankruptcy rule to be game theoretic.

This paper takes an axiomatic bargaining approach to bankruptcy problems with nontransferable utility by characterizing bankruptcy rules in terms of properties from bargaining theory. In particular, we derive new axiomatic characterizations of the proportional rule, the truncated proportional rule, and the constrained relative equal awards rule using properties which concern changes in the estate or the claims.

We compare the Egalitarian rule (aka Egalitarian Equivalent) and the Competitive rule (aka Competitive Equilibrium with Equal Incomes) to divide bads (chores). They are both welfarist: the competitive disutility profile(s) are the critical points of their Nash product on the set of efficient feasible profiles. The C rule is Envy Free, Maskin Monotonic, and has better incentives properties than the E rule. But, unlike the E rule, it can be wildly multivalued, admits no selection continuous in the utility and endowment parameters, and is harder to compute. Thus in the division of bads, unlike that of goods, no rule normatively dominates the other.

We consider random public signals on the state of two-person zero-sum game with incomplete information on both sides (both players do not know the state of the game). To learn the state, each player chooses a finite automaton which receives the public signal; the player only sees the output of the automaton chosen. Supposing that the size of automata available to Player 1 is essentially bigger than that available to Player 2, we give an example of public signal with random length of output strings where the posterior belief of Player 1 is the state and the posterior belief of Player 2 is close to his original belief. Thus, we demonstrate that asymmetric information about the state of a game may appear not only due to a private signal but as a result of a public signal and asymmetric computational resources of players.Besides, for a class of random signals with fixed length of output strings, we estimate the fraction of signals such that some automaton of given size may help Player 2 to significantly reestimate prior probability of the state. We show that this fraction is negligible if the size of automata of Player 2 is sufficiently smaller than length of output strings.

The theory of tropical series, that we develop here, firstly appeared in the study of the growth of pluriharmonic functions. Motivated by waves in sandpile models we introduce a dynamic on the set of tropical series, and it is experimentally observed that this dynamic obeys a power law. So, this paper serves as a compilation of results we need for other articles and also introduces several objects interesting by themselves.

We prove that the number o fLegendrian rational cubics in CP^3 through three generic points and a line is three. Also, we classify all Legendrian curves on a quadric surface. Additionally, several computations are verified using Macaulay2 computer algebra system.

The paper is devoted to game-theoretic methods for community detection in networks. The traditional methods for detecting community structure are based on selecting dense subgraphs inside the network. Here we propose to use the methods of cooperative game theory that highlight not only the link density but also the mechanisms of cluster formation. Specifically, we suggest two approaches from cooperative game theory: the first approach is based on the Myerson value, whereas the second approach is based on hedonic games. Both approaches allow to detect clusters with various resolutions. However, the tuning of the resolution parameter in the hedonic games approach is particularly intuitive. Furthermore, the modularity-based approach and its generalizations as well as ratio cut and normalized cut methods can be viewed as particular cases of the hedonic games. Finally, for approaches based on potential hedonic games we suggest a very efficient computational scheme using Gibbs sampling.

The paper applies Looking Forward Approach to analyze the world oil market with the framework of a differential game model of quantity competition oligopoly. Namely Looking Forward Approach is used to take into account dynami- cally updating information. Under the information we understand the forecast of the oil demand dynamics. We focus on the period from December 2015 to November 2016 and suppose that during this time interval countries did not cooperate offi- cially on the amounts of oil to be produced. Therefore, their behavior can be mod- eled using the non-cooperative game model. As a solution concept for this conflict- controlled process we use feedback Nash equilibrium. In order to define the pa- rameters of model open source data is used, results of numerical simulations and comparison with the historical data are presented.

We consider repeated zero-sum games with incomplete information on the side of Player 2 with the total payoff given by the non-normalized sum of stage gains. In the classical examples the value of such an N-stage game is of the order of N or of square root of N, as N tends to infinity. Our aim is to find what is causing another type of asymptotic behavior of the value observed for the discrete version of the financial market model introduced by De Meyer and Saley. For this game Domansky and independently De Meyer with Marino found that the value remains bounded, as N tends to infinity, and converges to the limit value. This game is almost-fair, i.e., if Player 1 forgets his private information the value becomes zero. We describe a class of almost-fair games having bounded values in terms of an easy-checkable property of the auxiliary non-revealing game. We call this property the piecewise property, and it says that there exists an optimal strategy of Player 2 that is piecewise-constant as a function of a prior distribution. Discrete market models have the piecewise property. We show that for non-piecewise almost-fair games with an additional non-degeneracy condition the value is of the order of square root of N.

We describe the configuration space **S** of polygons with prescribed edge slopes, and study the perimeter P as a Morse function on **S**. We characterize critical points of P (these are *tangential* polygons) and compute their Morse indices. This setup is motivated by a number of results about critical points and Morse indices of the oriented area function defined on the configuration space of polygons with prescribed edge lengths (flexible polygons). As a by-product, we present an independent computation of the Morse index of the area function (obtained earlier by Panina and Zhukova).

This paper considers a voting problem in which the individual preferences of electors are defined by the ranked lists of candidates. For single-winner elections, we apply the criterion of weak positional dominance (WPD, PD), which is closely related to the positional scoring rules. Also we formulate the criterion of weak mutual majority (WMM), which is stronger than the majority criterion but weaker than the criterion of mutual majority (MM). Then we construct two modifications for the median voting rule that satisfy the Condorcet loser criterion. As shown below, WPD and WMM are satisfied for the first modification while PD and MM for the second modification. We prove that there is no rule satisfying WPD and MM simultaneously. Finally, we check a list of 37 criteria for the constructed rules.

This paper defines the self-covariance property for the solutions of transferable utility cooperative games (TU-games) as a weakening of their covariance. Self-covariant solutions are positively homogenous and satisfy a “restricted” translation covariance so that feasible shifts are only the solution vectors themselves and their multipliers. A description of all non-empty, single-valued, efficient, anonymous, weakly and self-covariant solutions in the class of twoplayer TU-games is given. As demonstrated below, among them there exist just three solutions admitting consistent extensions in the Davis–Maschler sense. They are the equal share solution, the standard solution, and the constrained egalitarian solution for superadditive two-player TUgames. For the third solution mentioned, characterizations of some consistent extensions to the class of all TU-games are given.

Tropical geometry, an established field in pure mathematics, is a place where string theory, mirror symmetry, computational algebra, auction theory, and so forth meet and influence one another. In this paper, we report on our discovery of a tropical model with self-organized criticality (SOC) behavior. Our model is continuous, in contrast to all known models of SOC, and is a certain scaling limit of the sandpile model, the first and archetypical model of SOC. We describe how our model is related to pattern formation and proportional growth phenomena and discuss the dichotomy between continuous and discrete models in several contexts. Our aim in this context is to present an idealized tropical toy model (cf. Turing reaction-diffusion model), requiring further investigation.

Users share the cost of unreliable non-rival projects (items). For instance, industry partners pay today for R&D that may or may not deliver a cure to some viruses, agents pay for the edges of a network that will cover their connectivity needs, but the edges may fail, etc. Each user has a binary inelastic need that is served if and only if certain subsets of items are actually functioning. We ask how should the cost be divided when individual needs are heterogenous. We impose three powerful separability properties: *Independence of Timing* ensures that the cost shares computed ex ante are the expectation, over the random realization of the projects, of shares computed ex post. *Cost Additivity* together with *Separability Across Projects* ensure that the cost shares of an item depend only upon the service provided by that item for a given realization of all other items. Combining these with fair bounds on the liability of agents with more or less flexible needs, and of agents for whom an item is either indispensable or useless, we characterize two rules: the *Ex Post Service* rule is the expectation of the equal division of costs between the agents who end up served; the *Needs Priority* rule splits the cost first between those agents for whom an item is critical ex post, or if there are no such agents between those who end up being served.