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This paper analyzes the Lucas tree model with heterogeneous agents and one asset. We show the existence of a minimal state space Lipschitz continuous recursive equilibrium using Montrucchio (1987) results. The recursive equilibrium implements a sequential equilibrium through an explicit functional equation derived from the Bellman Equation. Our method also allows to prove existence of a recursive equilibrium in a general class of deterministic or stochastic models with several assets provided there exists a Lipschitz selection on the demand correspondence. We provide examples showing applicability of our results.

Adipose tissue is currently considered not only as an energy store but also as an organ of internal secretion. Numerous adipocytokines regulating a number of human body processes are important in many disease processes, including chronic kidney disease (CKD). Nowadays, the role of zinc α2-glycoprotein (ZAG) is being sought as a potential link between these two organs. ZAG, through its lipolytic effect, contributes to progressive malnutrition in patients undergoing dialysis, and this significantly increases their mortality. It seems that ZAG may be a new potential biomarker of kidney damage, and the specific pharmacotherapy will significantly reduce the progressive process of cachexia.

Fractalkine (CX3CL1) is a chemokine that plays a significant role in inflammation, one of the pathophysiological processes underlying end-stage renal disease (ESRD). Genetic factors are significantly involved in cytokine expression and have been studied as potential risk factors for chronic kidney disease (CKD). Objectives: We aimed to elucidate the association of CX3CR1 gene polymorphisms rs3732378 and rs3732379 with the levels of CX3CL1, CX3CL1 receptor (CX3CR1), as well as C-reactive protein (CRP). Patients and methods: We enrolled 198 participants, including 106 patients with ESRD and 92 controls. Peripheral blood samples were collected from each patient for genetic (rs3732378 and rs3732379 polymorphisms) and immunoenzymatic (fractalkine, CX3CR1, CRP) tests. Results: CX3CR1 and CRP levels were higher in patients with ESRD than in controls (p &lt, 0.05). Fractalkine levels were significantly higher in ESRD patients who were homozygous for the G allele of the rs3732378 polymorphism and for the C allele of the rs3732379 polymorphism than in homozygous controls. Moreover, carriers of these alleles among patients with ESRD had significantly higher CX3CR1 levels than controls. Conclusions: The G allele of the rs3732378 polymorphism and the C allele of the rs3732379 polymorphism of the CX3CR1 gene are associated with higher CX3CL1 and CX3CR1 levels. Our study suggests that CX3CR1 gene polymorphisms could be potentially involved in the pathogenesis of ESRD, but the study needs to be replicated in a larger population with a longitudinal follow-up study. Identification of genetic factors associated with inflammation in ESRD may contribute to the development of targeted gene therapies in the future.

Guillain–Barré syndrome, an acute autoimmune inflammatory polyneuropathy, is the most frequent cause of acute onset flaccid paresis. Various sources report its incidence of 1–4/100,000 individuals per year. A triggering factor in most cases is a previous respiratory or gastrointestinal tract infection. Apparently, via the molecular mimicry mechanism, antibodies against bacterial or viral antigens are formed and bind with similar epitopes in the peripheral nervous system. The clinical picture is highly diversified and may range from slight muscle weakness within the feet to full-blown tetraplegia with respiratory failure. The typical course of the disease consists of the progressive phase, the plateau phase and the recovery phase, lasting even 6–14 months. The diagnosis is based on the criteria published in 1978. They encompass clinical signs and symptoms as well as electrophysiological and pathomorphological parameters. A crucial sign leading to the diagnosis is progressive flaccid paresis of more than one limb with the absence or reduction of tendon reflexes. The treatment involves plasma exchange and intravenous immunoglobulin. The use of glucocorticosteroids, interferon beta, rituximab and eculizumab requires further investigation. Moreover, symptomatic treatment, kinesiotherapy, respiratory physiotherapy, thromboembolic prophylaxis, nutritional therapy and pain management are also very important. Prognosis is in most cases favourable, but mortality ranges from 4 to 15% despite appropriate treatment and intensive care. The aim of this article is to sum up current information about Guillain–Barré syndrome and to emphasise the relevance of this disease, which requires further investigation in both paediatric and adult patients.

In this note, we prove the existence of a Markov perfect equilibrium in a non-stationary version of a paternalistic bequest game. The method we advocate is general and allows to study models with unbounded state space and unbounded utility functions. We cover both, the stochastic and deterministic cases. We provide a characterization of the set of all Markov perfect equilibria by means of a set-valued recursive equation involving the best response operator. In the stationary case, we show that there exists a set of strategies that is invariant under the best response mapping.

WstępObecnie coraz częściej poszukuje się różnych wariantów genetycznych mających wpływ na długowieczność. Jednym z nich jest gen SIRT1, który koduje białka zwane sirtuinami. Sirtuiny, działając poprzez regulację tran-skrypcji, utrzymywanie stabilności genomu i wpływ na metabolizm węglowodanowo-lipidowy, są uważane za enzymy długowieczności.Cel pracyCelem pracy było wykazanie potencjalnego związku między polimorfizmami rs2273773 i rs7895833 genu SIRT1 a długowiecznością w kontekście zaburzeń metabolicznych.Materiał i metodyBadaniem objęto łącznie kolejnych 448 pacjentów z rejonu Polski południowej. Badanych podzielono na 2 grupy na podstawie ich wieku i zaburzeń metabolicznych. Genotypowanie polimorfizmów genu SIRT1 przeprowadzono z wykorzystaniem znakowanych fluorescencyjnie sond, używając gotowych zestawów do oznaczania polimorfizmu pojedynczego nukleotydu – TaqMan Pre-designed SNP Genotyping Assay (Applied Bio-systems). Do obliczeń poszczególnych parametrów w ujęciu statystycznym zastosowano program Statistica 9.0.WynikiW grupie badanej w obrębie polimorfizmu rs 2273773 częstość występowania genotypu TT wyniosła 86,93%, CT 13,07%, CC 0,00%, natomiast w grupie kontrolnej TT była równa 91,19%, CT 8,47%, CC 0,34%. W obrębie polimorfizmu rs 7895833 w grupie badanej rozkład genotypów przedstawiał się następująco: AA 67,32%, AG 28,76%, GG 3,92%, natomiast w grupie kontrolnej AA wynosił 68,47%, AG 28,47%, GG 3,05%.WnioskiNie wykazano związku między polimorfizmami genu SIRT1 a wydłużeniem życia u osób zamieszkujących teren Górnego Śląska.

WstępCelem pracy było wykazanie potencjalnego związku między występowaniem nadwagi i otyłości a polimorfizmem rs6602024 genu fosfofruktokinazy płytkowej (PFKP) u kolejnych pacjentów zgłaszających się do lekarza pierwszego kontaktu w POZ.Materiał i metodyBadaniem objęto łącznie kolejnych 438 pacjentów z rejonu Polski południowej, którzy zgłaszali się do poradni ogólnej POZ. Genotypowanie polimorfizmu genu PFKP rs6602024 prowadzono z wykorzystaniem znakowanych fluorescencyjnie sond. Do obliczeń poszczególnych parametrów w ujęciu statystycznym zastosowano program Statistica 8,0.WynikiU osób z nadwagą oraz otyłością, a także w całej badanej grupie osób z nadwagą lub otyłością wykazano występowanie określonych zaburzeń metabolicznych. Wyniki porównano z rezultatami osób bez nadwagi i otyłości. U badanych osób nie stwierdzono istotnych statystycznie różnic w rozkładzie genotypów i alleli polimorfizmu rs6602024 PFKP w porównaniu z kontrolą. W grupie kontrolnej wykazano znamienną statystycznie różnicę pomiędzy kobietami i mężczyznami w rozkładzie alleli. Wśród kobiet stwierdzono znamienną statystycznie różnicę w rozkładzie alleli G/A między osobami z grupy kontrolnej a osobami z nadwagą oraz nadwagą i otyłością razem wziętych.Wnioski1. Nadwaga i otyłość bardzo często występują u osób zgłaszających się do lekarza POZ. 2. Występowaniu allelu A polimorfizmu rs6602024 genu PFKP u kobiet towarzyszy zwiększone ryzyko nadwagi i otyłości.

We study the existence and computation of equilibrium in large games with strategic complementarities. Using monotone operators defined on the space of distributions partially ordered with respect to the first-order stochastic dominance, we prove existence of a greatest and least distributional Nash equilibrium. In particular, we obtain our results under a different set of conditions than those in the existing literature. Moreover, we provide computable monotone distributional equilibrium comparative statics with respect to the parameters of the game. Finally, we apply our results to models of social distance, large stopping games, keeping up with the Joneses, as well as a general class of linear non-atomic games.

1. XLVII National Conference on Applications of Mathematics, September 4-11, 2018, Zakopane-Kościelisko (Ł. Stettner) The 47th National Conference on Mathematics Applications was held on September 4-11, 2018 in Zakopane Kościelisko. Together with the conference, the XXIV National Conference on Mathematics Applications in Biology and Medicine (4-7 September 2018) was held simultaneously with two common first days of the meeting. The plenary lecture was delivered by Urszula Ledzewicz (Southern Illinois University Edwardsville, USA and Łodź University of Technology) and Heinz Schattler (Washington University, St. Louis, USA) with optimal control in biomedical problems. 2. GAMENET Conference Krakow 2018, 17 -- 21 września 2018, Krakow(F.Falniowski) On September 17-21, 2018 an international conference GAMENET Conference Krakow 2018 summarizing the first year of activity of the European network for game theoretic research GAMENET was held at the Cracow University of Economics. The main event of the first two days was a training school on the recent applications of Game Theory. The training school was build around three courses delivered by Olivier Baude (Electricite de France), Luiz DaSilva (Trinity College Dublin) and Vianney Perchet (CMLA, ENS Paris-Saclay & Criteo AI Lab). 3. Conference "Social sciences - mathematical or mathematizable?", 27 -- 28 września 2018, Krakow(Agnieszka Lipieta) The conference was held at Cracow University of Economics on September 27-28, 2018. It was devoted to the memory of outstanding mathematician, philosopher, and economist Professor Andrzej Malawski, who passed away in 2016. 4. VII Hurwicz Workshop on Mechanism Design Theory, 7--8 grudnia 2018 (Łukasz Woźny) IM PAN WarszawaThe 2018 Hurwicz Workshop on Mechanism Design Theory is a continuation of the initiative started in 2009 of holding an annual confernce to honour the 2007 Nobel Prize Laureate in Economics, professor Leonid Hurwicz. Leonid Hurwicz lived in Warsaw until 1938 and studied at the University of Warsaw. He frequently visited Poland in 1990's. In 1994 he obtained the Doctor Honoris Causa of Warsaw School of Economics. A special plaque commemorates his contacts with Warsaw School of Economics. Hurwicz is often credited with introducing rigorous mathematical approach to economic analysis. He received the Nobel Prize in Economic Sciences in 2007 for his fundamental contributions to the theory of the design of economic mechanisms. Theory of mechanism design relies heavily on mathematical methods of functional analysis, differential equations, differential topology, dynamical systems, etc. Hurwicz has made important contributions to mathematics as well as economics, in particular, to non-linear programming. 5. Conference “Mathematical Statistics”. Bedlewo, December 2--7, 2018 (Przemyslaw Grzegorzewski). On December 2--7, 2018, in Bedlewo, the XLIV Conference "Mathematical Statistics" was held, organized by the Banach Center of Institute of Mathematics Polish Accademy of Science, the Committee on Statistics of the Committee of Mathematics of the Polish Academy of Sciences, and the Faculty of Mathematics and Computer Science of the Nicolaus Copernicus University in Torun. During the 19 sessions, a total of 46 lectures and a series of lectures on "Bayesian Inference in Intractable Likelihood Models", i.e. on Bayesian modeling with a difficult likelihood function, were given. The lecture was delivered by Krzysztof Łatuszynski from the University of Warwick in Great Britain. 6. XLVIII Seminar on Applied Mathematics-XLVIII Seminarium Zastosowan Matematyki, 9-11.09.2018 Boguszow-Gorce (Mieczyslaw Chalfen)

Cel pracyCelem pracy było znalezienie związku między polimorfizmem rs1421085 genu FTO a występowaniem nadciśnienia tętniczego u osób z nadwagą i otyłością.Materiał i metodykaBadaniem objęto łącznie kolejnych 391 pacjentów z rejonu Polski południowej, którzy zgłaszali się do poradni ogólnej POZ. Badanych podzielono na 3 grupy na podstawie wartości obwodu pasa (grupa kontrolna, grupa z nadwagą, grupa z otyłością). Genotypowanie polimorfizmu FTO rs1421085 prowadzono z wykorzystaniem znakowanych fluorescencyjnie sond, używając gotowych zestawów do oznaczania polimorfizmu pojedynczego nukleotydu – TaqMan Pre-designed SNP Genotyping Assay (Applied Biosystems). Do obliczeń poszczególnych parametrów w ujęciu statystycznym zastosowano program Statistica 9.0.WynikiCzęstość występowania nadwagi i otyłości ocenianej na podstawie obwodu pasa wynosiła w badanej grupie 71,35% (24,04% – nadwaga, 47,31% – otyłość brzuszna). W surowicy osób z nadwagą i otyłych stwierdzono istotnie statystycznie wyższe stężenia glukozy, insuliny, wartości średniego ciśnienia tętniczego i składowych profilu lipidowego w stosunku do osób z grupy kontrolnej (p < 0,001), w której żaden z genotypów nie korelował z wyższym średnim ciśnieniem skurczowym (p ≥ 0,05). W grupach z nadwagą i otyłością osobnicy homozygotyczni względem allelu T wykazują wyższe wartości średniego ciśnienia skurczowego niż inne genotypy (p < 0,05).Wnioski1. Polimorfizm rs1421085 genu FTO nie wykazuje znamiennej statystycznie korelacji z występowaniem nadwagi i otyłości w populacji Polski południowej. 2. Prawdopodobieństwo wystąpienia nadciśnienia tętniczego u osoby będącej homozygotą TT w obrębie polimorfizmu rs1421085 jest znamiennie statystycznie wyższe niż w przypadku innych genotypów u osób z nadwagą lub otyłością.

We study a class of infinite horizon stochastic games with uncountable number of states. We first characterize the set of all (nonstationary) short-term (Markovian) equilibrium values by developing a new (Abreu et al. in Econometrica 58(5):1041–1063, 1990)-type procedure operating in function spaces. This (among others) proves Markov perfect Nash equilibrium (MPNE) existence. Moreover, we present techniques of MPNE value set approximation by a sequence of sets of discretized functions iterated on our approximated APS-type operator. This method is new and has some advantages as compared to Judd et al. (Econometrica 71(4):1239–1254, 2003), Feng et al. (Int Econ Rev 55(1):83–110, 2014), or Sleet and Yeltekin (Dyn Games Appl doi: 10.1007/s13235-015-0139-1 , 2015). We show applications of our approach to hyperbolic discounting games and dynamic games with strategic complementarities.

We consider a principal–agent model, where a single agent exhibits problems of self control modeled using Gul and Pesendorfer (2001) type temptation preferences. For a general class of preferences, we characterize the optimal contract in such a setting using standard Grossman and Hart (1983) techniques. Our analysis shows that the incentive compatibility constraint is not necessarily binding at the optimal solution. As a result, the solution to the relaxed problem (without the incentive compatibility constraint) provides a variable pay, which contrasts with the standard results for the separable utility case. These observations result from the fact that in our setting the principal trade-offs incentives and insurance, but also reduction of self control cost for the agent. Our results shed some light on the justification of randomized contracts (see Holmstrom, 1979), the literature on behavioral contracts, but also show that in the presence of strong self-control problems moral hazard cost can be mitigated.

We study the question of existence and computation of time-consistent Markov policies of quasi-hyperbolic consumers under a stochastic transition technology in a general class of economies with multidimensional action spaces and uncountable state spaces. Under standard complementarity assumptions on preferences, as well as a mild geometric condition on transition probabilities, we prove existence of time-consistent solutions in Markovian policies, and provide conditions for the existence of continuous and monotone equilibria. We present applications of our methods to habit formation models, environmental policies, and models of consumption under borrowing constraints, and hence show how our methods extend the results obtained by Harris and Laibson (Econometrica 69:935–957, 2001) to a broad class of dynamic economies. We also present a simple successive approximation scheme for computing extremal equilibrium, and provide some results on the existence of monotone equilibrium comparative statics in the model’s deep parameters.

We develop a new multistep monotone map approach to characterize minimal state-space recursive equilibrium for a broad class of infinite horizon dynamic general equilibrium models with positive externalities, dynamic complementarities, public policy, equilibrium indeterminacy, and sunspots. This new approach is global, defined in the equilibrium version of the household’s Euler equation, applies to economies for which there are no known existence results, and existing methods are inapplicable. Our methods are able to distinguish different structural properties of recursive equilibria. In stark contrast to the extensive body of existing work on these models, our methods make no appeal to the theory of smooth dynamical systems that are commonly applied in the literature. Actually, sufficient smoothness to apply such methods cannot be established relative to the set of recursive equilibria. Our partial ordering methods also provide a qualitative theory of equilibrium comparative statics in the presence of multiple equilibrium. These robust equilibrium comparison results are shown to be computable via successive approximations from subsolutions and supersolutions in sets of candidate equilibrium function spaces. We provide applications to an extensive literature on local indeterminacy of dynamic equilibrium.

We analyze a three period production economy, where households exhibit problems of self-control and face credit constraints. Apart from liquid assets, a single commitment (illiquid) asset is available that allows to commit to a planned consumption path. We compare general equilibrium allocations of the two models: one, where households choices are determined using Gul and Pesendorfer (2001, “Temptation and Self-Control.” Econometrica 69:1403–35; GP, henceforth) model and the other, where households choices come from a (β–δ) quasi-hyperbolic discounting model. Contrary to the results of Kocherlakota (2001, “Looking for Evidence of Time-Inconsistent Preferences in Asset Market Data.” Quarterly Review 13–24) or Gabrieli and Ghosal (2013, “Non-Existence of Competitive Equilibria with Dynamically Inconsistent Preferences.” Economic Theory 52:299–313), we show that, when a production sector is incorporated into the economy with commitment asset and credit constraints, we can restore the equilibrium existence (without recalling measure space of consumers (see Luttmer and Mariotti 2006, “Competitive Equilibrium When Preferences Change Over Time.” Economic Theory 27:679–90)) and unlike Gul and Pesendorfer (2004b, “Self Control, Revealed Preferences and Consumption Choice.” Review of Economic Studies 7:243–64), we show that the equilibrium allocations of both models (GP and β–δ) imply positive consumption of the commitment asset and corner consumption of one of the liquid assets. We also provide an example showing, when equilibrium allocations of both models are different.

We introduce a new class of infinite horizon altruistic stochastic OLG model with capital and labor, but without commitment between the generations. Under mild regularity conditions, for economies with both bounded and unbounded state spaces, continuous monotone Markov perfect Nash equilibrium (MPNE) are shown to exist, and form an antichain in pointwise partial orders. Unlike existing results in related models with inelastic labor supply, these equilibrium are not necessarily Lipschitzian. For each such MPNE, we then construct corresponding stationary Markovian equilibrium invariant distributions. We then show that for many parameterizations of our economies used in applied work in macroeconomics, unique MPNE exist relative to a large space of pure strategy equilibrium (i.e., the space of bounded measurable functions). Using this result, we can directly relate this result to the promised utility/continuation methods based upon the work of Abreu, Pearce, and Stacchetti. As our results are constructive, we can provide characterizations of numerical methods for the uniform approximation of MPNE, and we construct error bounds for simple discretization methods. Decentralizing MPNE in the game as a recursive competitive equilibrium is discussed. Finally, a series of examples show potential applications and limitations of our results.

Recently Yang and Qi (2013) stated an interesting theorem on existence of complete lattice of equilibria in a particular class of large nonatomic supermodular games for general action and players spaces. Unfortunately, their result is incorrect. In this note, we detail the nature of the problem with the stated theorem, provide a counterexample, and then correct the result under additional assumptions. We also provide a number of new results per existence of equilibria in more general classes of games of strategic complementarities that are monotone in players' name/trait, as well as provide a class of constructive methods for computing monotone equilibrium comparative statics.

We study equilibrium in large games of strategic complementarities (GSC) with differential information. We define an appropriate notion of distributional Bayesian Nash equilibrium and prove its existence. Furthermore, we characterize order-theoretic properties of the equilibrium set, provide monotone comparative statics for ordered perturbations of the space of games, and provide explicit algorithms for computing extremal equilibria. We complement the paper with new results on the existence of Bayesian Nash equilibrium in the sense of Balder and Rustichini (J Econ Theory 62(2):385–393, 1994) or Kim and Yannelis (J Econ Theory 77(2):330–353, 1997) for large GSC and provide an analogous characterization of the equilibrium set as in the case of distributional Bayesian Nash equilibrium. Finally, we apply our results to riot games, beauty contests, and common value auctions. In all cases, standard existence and comparative statics tools in the theory of supermodular games for finite numbers of agents do not apply in general, and new constructions are required.

We study a class of discounted, infinite horizon stochastic games with public and private signals and strategic complementarities. Using monotone operators defined on the function space of values and strategies (equipped with a product order), we prove existence of a Stationary Markov Nash Equilibrium via constructive methods. In addition, we provide monotone comparative statics results for ordered perturbations of our space of stochastic games. We present examples from industrial organization literature and discuss possible extensions of our techniques for studying principal-agent models.