# Department of Operations Research and Actuarial Sciences

### About the Department

In both undergraduate and master’s programmes, the Department teaches operations research, optimum calculation, and decision theory subjects, as well as multivariate data analysis and multivariate statistical modelling.

In the master’s programme in Actuarial and Financial Mathematics, we primarily teach actuarial subjects to students of the Actuarial specialization.

Actuaries are professionals who are able to solve problems that occur in the practice of insurance institutions, using mathematical methods. They can use their knowledge in the fields of life and other insurance, the design and operation of pension schemes, and the evaluation of investments.

In the study programme of Economic and Financial Mathematical Analysis, we teach a number of subjects, primarily aimed at students who want to learn and apply processes for formalizing and completing decision-making tasks that occur in corporate and institutional practice; and computer models of decision support; and data analysis.

Corvinus Game Theory Seminar

Seminar Archives

### Events

## Corvinus Game Theory seminar

## 18 Febr, 14-15, Zoom. Jochen Staudacher (University of Kempten, Germany): Dynamic Programming for Computing Power Indices for Weighted Voting Games with Precoalitions

We study the efficient computation of power indices for weighted voting games with precoalitions amongst subsets of players (reflecting, e.g., ideological proximity) using the paradigm of dynamic programming. Starting from the state-of-the-art algorithms for computing the Banzhaf and Shapley–Shubik indices for weighted voting games, we present a framework for fast algorithms for the three most common power indices with precoalitions, i.e., the Owen index, the Banzhaf–Owen index and the symmetric coalitional Banzhaf index, and point out why our new algorithms are applicable for large numbers of players. We discuss implementations of our algorithms for the three power indices with precoalitions in C++ and review computing times, as well as storage requirements.

If you wish to receive a link for the zoom meeting on the day of the event, please send an email to Tamás Solymosi (tamas dot solymosi at uni dash corvinus dot hu)

## 25 Febr, 12:30-13:30, Zoom. Mikel Álvarez-Mozos (University of Barcelona, Spain): Dynamic Programming for Computing Power Indices for Weighted Voting Games with Precoalitions

On convexity in cooperative games with externalities

We introduce new notions of superadditivity and convexity for games with coalitional externalities. We show parallel results to the classic ones for transferable utility games without externalities. In superadditive games the grand coalition is the most efficient organization of agents. The convexity of a game is equivalent to having non decreasing contributions to larger embedded coalitions. We also see that convex games can only have negative externalities.

If you wish to receive a link for the zoom meeting on the day of the event, please send an email to Tamás Solymosi (tamas dot solymosi at uni dash corvinus dot hu)

## 4 Mar, 15-16, Zoom. Christian Trudeau (University of Windsor, Canada): Minimum cost spanning tree problems as value sharing problems and as airport problems

Minimum cost spanning tree (mcst) problems study situations in which agents must connect to a source to obtain a good, with the cost of building an edge being independent of the number of users. I reinterpret mcst problems as value sharing problems and show that the folk and cycle-complete solutions, two of the most studied cost-sharing solutions for mcst problems, do not share values in a consistent way. More precisely, two mcst problems yielding the same value sharing problem might lead to value being shared in different ways. In addition, while airport problems are special cases of mcst problems, I show that the folk and cycle-complete solutions do not always propose cost allocations that make sense for these problems. A weakening of the Value Equivalence concept and modifications to the folk and cycle-complete solutions are explored.

If you wish to receive a link for the zoom meeting on the day of the event, please send an email to Tamás Solymosi (tamas dot solymosi at uni dash corvinus dot hu)

## 11 Mar, 14-15, Zoom. Bas Dietzenbacher (Maastricht University, The Netherlands): Two-bound core games and the nucleolus

This paper introduces the new class of two-bound core games, where the core can be described by a lower bound and an upper bound on the payoffs of the players. Many classes of games turn out to be two-bound core games. We show that the core of each two-bound core game can be described equivalently by the pair of exact core bounds, and study to what extent the exact core bounds can be stretched while retaining the core description. We provide explicit expressions of the nucleolus for two-bound core games in terms of all pairs of bounds describing the core, using the Talmud rule for bankruptcy problems, and study to what extent these expressions are robust against game changes.

If you wish to receive a link for the zoom meeting on the day of the event, please send an email to Tamás Solymosi (tamas dot solymosi at uni dash corvinus dot hu)

## 18 Mar, 14-15, Zoom. **Arantza Estévez-Fernandez **(Free University Amsterdam, The Netherlands): **On the 1-nucleolus**

In this lecture we introduce the concept of the 1-nucleolus and, in particular, its relation to the nucleolus. It is seen that, contrary to the nucleolus, the 1-nucleolus can be computed in polynomial time due to a characterization using a combination of standard bankruptcy rules for associated bankruptcy problems. Sufficient conditions on a compromise stable game are derived such that the 1-nucleolus and the nucleolus coincide.

If you wish to receive a link for the zoom meeting on the day of the event, please send an email to Tamás Solymosi (tamas dot solymosi at uni dash corvinus dot hu)

## 25 Mar, 14-15, Zoom. Dávid Csercsik (Pázmány Catholic University): The problem of optimal bidding in day-ahead electricity marekts – a probabilistic approach

Portfolio bidding day-dahead electricity marekts are multiperiod two-sided multiunit auctions, where (in the simplest case) bids are described by tow parameters: Quantity and price. There is a wide range of literature discussing the strategic behavior of market participants (mostly producers) of such martkets, under diffeent assumptions (for a review of earlier approaches, see e.g. David and Wen ‘Strategic Bidding in Electricity Markets: A literature survay’, 2000). A recent article of Richstein et al. (‘An auction story: How simple bids struggle with uncertainty, 2020 ‘) approaches the question from a novel perspective, using a more realistic cost model of generating units, while considering the market clearing price (MCP) as a random variable. In this article the authors assume uniform distribution of the MCP. We show that this assumption is not realistic, and analyze how the analytical results of the article may be generalized, if the assumption about the distribution of the MCP is different.

If you wish to receive a link for the zoom meeting on the day of the event, please send an email to Tamás Solymosi (tamas dot solymosi at uni dash corvinus dot hu)

## 1 Apr, 14-15, C.107. **Zsuzsanna Jankó** (Corvinus University): **Stable matchings and lattices**

This talk is an overview of what we know about lattices of stable matchings: from the lattice of the classical marriage model to many-to-many matchings or trading networks. With some open questions at the end.

## 22 Apr, 14-15, C.107. Gergely Csáji (Eötvös Lóránd University): On the complexity of Stable Hypergraph Matching, Stable Multicommodity Flow and related problems

In this paper we study stable multicommodity flows, stable hypergraph matchings and some related problems, like the Hospital-Resident-Couple (hrc) problem. We give another proof of the existence of a stable multicommodity flow by reducing it to scarf. We show that finding a stable fractional solution of ahrc or a 3-dimensional stable matching (stable family) instance is PPAD-complete. Then we derive from these results that the Fractional hypergraph matching problem is PPAD-complete even if all hyperedge sizes and vertex degrees are at most 3. Furthermore, we prove that computing stable multicommodity flows is PPAD-complete even if the number of commodities is 3, the sum of in and out degrees are at most 3 at each vertex and all terminals and sources are the same. We also show that deciding if there exists a stable integer multicommodity flow is NP-complete even with only two commodities and similar restrictions. Finally, we give polynomial-time algorithms that can find stable integral matchings in some special classes of hypergraphs.

## 29 Apr, 14-15, E.338. Leanne Streekstra (BME): On the nucleolus of irreducible minimum cost spanning tree games

Computing the nucleolus of a minimum cost spanning tree game has been known to be NP-hard. In this paper, I therefore consider the computational complexity for a subset of these games; minimum cost spanning tree games with an irreducible cost matrix. I show that these games are a special case of connected balanced games and thus the existing algorithm which efficiently computes the nucleolus for these games, can be used here as well. Moreover, I show that the computational complexity of this algorithm can be reduced from O(n^{4}) to O(n^{3}) when applied to minimum cost spanning tree games with irreducible cost matrix, by reducing the size of the input set.

## 13 May, 14-15, Zoom. Balázs Sziklai (KRTK, Corvinus): Why do we see progressively more extreme opinions in politics?

After seven decades of successfully inseminating social science and popular culture, the allure of the Median Voter Theorem is starting to fade. Evident signs of polarization, observed in many aspects of life, especially in politics, challenges the idea that the voter occupying the center of the ideology space has the most influence. Although Duncan Black’s original paper was concerned about voting in committees, soon his model was generalized into a one size fits all theory to explain phenomena ranging from political science to macroeconomic decisions making. With the emergence of extremism in all sides of political discussion it is harder than ever to sustain the illusion that the center of the ideology space has any weight in social decision making.

Convex voting games present a completely new paradigm, that does not contradict the Median Voter Theorem, but can explain the observed polarization. The key is the ideological space’s dimensionality. If the political debate is driven by one issue, convex voting indeed predicts the dominance of the median voter. However, if there are more issues at stake — the ideology space consists of more than one dimension — extreme opinions emerge and the center vacates (at least when the number of voters exceeds 5). With extensive simulations we show how the debate can shift to the extreme. We also offer an explanation how and why political extremes of different sides collude sometimes.

## 20 May, 14-15, E.338. Pierre von Mouche (Wageningen University, Corvinus): The Selten-Szidarovszky Technique

The Selten-Szidarovszky technique (SS technique) is a powerful technique for analysing existence, semi-uniqueness and uniqueness of Nash equilibria of sum-aggregative games. In the presentation I start with showing how the technique applies to a concrete Cournot oligopoly game. Next I will give a modern presentation/overview of this technique. Finally, I will present recent results that I am working on together with Prof. Szidarovszky during my stay at CIAS. These concern:

- The integration of the SS-technique into the theory of variational inequalities with an aggregative structure.
- As an application of this theory: very practical and powerful Nash equilibrium uniqueness results for sum-aggregative games.

## Archives

### 2021/22/1

## 17 Sept, 14-15, room C.101. Márton Benedek (KRTK, Corvinus): Computing Balanced Solutions in Large International Kidney Exchange Schemes

To overcome incompatibility issues, kidney patients may swap their donors. In international kidney exchange programmes (IKEPs), countries merge their national patient-donor pools. We consider a recent credit system where in each round, countries are given an initial kidney transplant allocation which is adjusted by a credit function yielding a target allocation. The goal is to find a solution in the patient-donor compatibility graph that approaches the target allocation as closely as possible, to ensure long-term stability of the international pool. As solutions, we use maximum matchings that lexicographically minimize the country deviations from the target allocation. We first give a polynomial-time algorithm for computing such matchings. We then perform, for the first time, a computational study for a *large* number of countries. For the initial allocations we use, besides two easy-to-compute solution concepts, two classical concepts: the Shapley value and nucleolus. These are hard to compute, but by using state-of-the-art software we show that they are now within reach for IKEPs of up to fifteen countries. Our experiments show that using lexicographically minimal maximum matchings instead of ones that only minimize the largest deviation from the target allocation (as previously done)may make an IKEP up to 52% more balanced.

## 24 Sept, 14-15, room C.101. Zsófia Dornai (BME): Essential coalitions for non-balanced games

Huberman (1980) proves that in balanced games, essential coalitions have the property of being enough to be considered in the computation of the nucleolus of the game. In our paper we provide two generalizations of Huberman’s result. Both generalizations give classes of coalitions which are enough to be considered for computing the prenucleolus of an arbitrary TU-game. We also demonstrate that both generalizations are real generalizations of the class of essential coalitions used by Huberman (1980), and that the two introduced classes of coalitions are not related to each other.

## 8 Oct, 13:40-14:40, room C.101. Péter Biró (KRTK, Corvinus): Cutoff stability under distributional constraints with an application to summer internship matching

We introduce a new two-sided stable matching problem that describes the summer internship matching practice of an Australian university. The model is a case between two models of Kamada and Kojima on matchings with distributional constraints. We study three solution concepts, the strong and weak stability concepts proposed by Kamada and Kojima, and a new one in between the two, called cutoff stability. Kamada and Kojima showed that a strongly stable matching may not exist in their most restricted model with disjoint regional quotas. Our first result is that checking its existence is NP-hard. We then show that a cutoff stable matching exists not just for the summer internship problem but also for the general matching model with arbitrary heredity constraints. We present an algorithm to compute a cutoff stable matching and show that it runs in polynomial time in our special case of summer internship model. However, we also show that finding a maximum size cutoff stable matching is NP-hard, but we provide a Mixed Integer Linear Program formulation for this optimisation problem.

## 15 Oct, 14-15, room C.101. Kristóf Bérczi (ELTE): Dynamic pricing in combinatorial markets

Dynamic pricing schemes were introduced as an alternative to posted-price mechanisms. In the dynamic setting the prices can be updated between buyer-arrivals based on the remaining sets of items and buyers. The main advantage of this approach is that it can maximize social welfare without the need for a central coordinator. In this talk, we focus on two subclasses of valuation functions, multi-demand and matroid rank valuations, and present efficient algorithms that determines the optimal dynamic prices in polynomial time.

## 22 Oct, 14-15, Zoom. Silvia Miquel (U. of Lleida): Assignment games with a central player or with middlemen

Firstly we consider a two-sided market situation with a central player. This player plays both the role of buyer and seller. From this situation we consider the corresponding TU-game and describe some solutions of the game in terms of the market data. Secondly, we consider a three-sided market where each buyer-seller pair can attain a profit only if there is a middleman that connects them. This profit does not depend on the identity of the middlemen, and each buyer and seller can take part in at most one partnership while middlemen can establish multiple partnerships. We show that, the core is non-empty and (strictly) contains the set of competitive equilibrium payoff vectors that coincides with the set of solutions of the dual assignment problem.

## 29 Oct, 14-15, Zoom. Jochen Staudacher (Kempten University): Efficient computation of power indices via dynamic programming

Power indices are algorithms that can be used in order to analyse voting in committees or influence in networks. Currently, the applicability of these algorithms for analysing large problems is limited as available implementations are constrained due to storage requirements. In this presentation we will show how to overcome these limitations using the technique of dynamic programming providing truly efficient implementations for various different power indices for weighted voting games. We will be discussing algorithms and present new dynamic programming algorithms for computing lesser-used power indices for weighted voting games. We will present and discuss efficient C++ software for computing power indices via dynamic programming. In particular, we will discuss how to deal with the problem of handling very large integers in our software and present computation times for large examples.

## 19 Nov, 14-15, room C.101. Tamás Fleiner (BME): To pimp, or not to pimp: that is the question

We study housing markets as introduced by Shapley and Scarf. We investigate

the computational complexity of various questions regarding the situation of

an agent $a$ in a housing market $H$: we show that it is NP-hard to find an

allocation in the core of $H$ where (i) $a$ receives a certain house,

(ii) $a$ does not receive a certain house, or (iii) $a$ receives a house

other than her own.

Probably, our most interesting result is that the core of housing markets

respects improvement in the following sense: given an allocation in the

core of~$H$ where agent~$a$ receives a house~$h$, if the value of the

house owned by~$a$ increases, then the resulting housing market admits an

allocation where $a$ receives either $h$, or a house that she prefers to

$h$; moreover, such an allocation can be found efficiently.

We further show an analogous result in the Stable Roommates setting by

proving that stable matchings in a one-sided market also respect

improvement.

## 26 Nov, 14-15, room C.101. Zsombor Szádoczki (Corvinus): Optimal filling in sequences for incomplete pairwise comparison matrices

Pairwise comparisons form the basis of preference modelling and decision making. It is important from both theoretical and practical points of view to determine the number of questions and their arrangements to ask from the decision maker. We focus on incomplete pairwise comparison matrices, and provide the optimal filling in patterns, which result in the closest (LLSM) weight vectors on average to the complete case for at most six alternatives and for all possible number of comparisons, when the underlying representing graph is connected. These results are obtained by extensive numerical simulations with large sample sizes. Many of the optimal filling structures resulted in optimal filling in sequences, one optimal case can be reached by adding a comparison to a previous one, which are presented on GRAPH of graphs for the different number of alternatives. The star graph is revealed to be optimal among the cases with the same cardinality (spanning trees), while the optimal graphs are always close to bipartite ones. Regular graphs also correspond to optimal cases for the examined parameters. Regularity is important for all optimal graphs, as the degrees of the different vertices are always as close to each other as possible. Besides applying the optimal filling structure in given decision making problems, practitioners can utilize the optimal filling sequences in the cases, when the decision maker can abandon the problem at any period of the process. The effect of an additional comparison is also examined for the optimal cases, which can serve as a guide to determine the minimal sufficient number of comparisons in a given problem.

## 10 Dec, 14-15. Philippe Solal (Université Jean Monnet): Lexicographic solutions for coalitional rankings based on individual and collective performances

A coalitional ranking describes a situation where a nite set of agents can form coalitions that areranked according to a weak order. A social ranking solution on a domain of coalitional rankingsassigns an individual ranking, that is a weak order over the agent set, to each coalitional rankingof this domain. We introduce two lexicographic solutions for a variable population domain ofcoalitional rankings. These solutions are computed from the individual performance of the agents,then, when this performance criterion does not allow to decide between two agents, a collectiveperformance criterion is applied to the coalitions of higher size. We provide parallel axiomaticcharacterizations of these two solutions.

## 17 Dec, 14-15, room C.101. Toygar Tayyar Kerman (Corvinus): Belief Inducibility and Informativeness

We consider a group of receivers who share a common prior on a finite state space and who observe private correlated signals that are contingent on the true state of the world. We show that, while necessary, Bayes plausibility is not sufficient for a distribution over posterior belief vectors to be inducible, and we provide a characterization of inducible distributions. We classify communication strategies as minimal, direct, and language independent, and we show that any inducible distribution can be induced by a language independent communication strategy (LICS). We investigate the role of the different classes of communication strategies for the amount of higher order information that is revealed to receivers. We show that the least informative communication strategy which induces a fixed distribution over posterior belief vectors lies in the relative interior of the set of all language independent communication strategies which induce that distribution.

### 2020/21/2

## 5 Febr, 13:40-15:10 Zsuzsanna Jankó (KRTK, Corvinus): Trading networks with frictions

We show how frictions and continuous transfers jointly affect equilibria in a model of matching in trading networks. Our model incorporates distortionary frictions such as transaction taxes and commissions. When contracts are fully substitutable for firms, competitive equilibria exist and coincide with outcomes that satisfy a cooperative solution concept called trail stability. However, competitive equilibria are generally neither stable nor Pareto-efficient.

## 12 Febr, 14-15 Péter Bayer (Toulouse School of Economics): Optimism leads to optimality: Ambiguity in network formation

We analyze a model of endogenous two-sided network formation where players are affected by uncertainty in their opponents’ decisions. We model this uncertainty using the notion of equilibrium under ambiguity (Eichberger and Kelsey, 2014). Unlike the set of Nash equilibria, the set of equilibria under ambiguity does not always include underconnected and thus inefficient networks such as the empty network. On the other hand, it may include networks with unreciprocated, one-way links, which comes with an efficiency loss as linking e orts are costly. We characterize equilibria under ambiguity and provide conditions under which increased player optimism comes with an increase in efficiency in equilibrium. Next, we analyze the dynamic situation with one-sided, myopic updating with regular optimistic shocks and derive a global stability condition of bene t-maximizing equilibrium networks.

## 19 Febr, 14-15 Burak Gökgür (Sabanci University): Randomized Pricing of a Storable Packaged Good in the Presence of Consumer Stockpiling

Randomized pricing is a frequently observed practice in online retailing. Strategic customers adjust their purchase quantities and/or time their purchases by taking into account their beliefs about the timing of deals. We study a randomized pricing problem of an online retailer selling a single storable product to two customers segments that are heterogeneous in their product valuations and holding costs. To maximize their utility, these customers can stockpile a product without increasing their consumption. The retailer’s objective is to maximize expected revenue using a randomized pricing strategy that serves as an intertemporal price discrimination mechanism. We study two cases where customers act strategically using endogenously or exogenously set stockpile-up-to levels in response to randomized pricing. We first develop a model for the expected revenue maximization problem when stockpile-up-to levels are endogenous and present a decomposition scheme to effectively find the optimal randomized policy. For the case of exogenously set stockpile-up-to levels, we characterize the retailer’s optimal price randomization strategy with a first-order equation. With a computational study, we shed light on the segments’ attributes that make price randomization an attractive strategy for the retailer. Our analysis indicates that, from the retailer’s viewpoint, price randomization can be an effective alternative to commitment to a single and time-independent price in the presence of segments having similar sizes and marked differences in product valuations. We finally demonstrate that the results are also valid for the case of patient customers that wait to make one-time purchases in anticipation of a lower future price.

## 26 Febr, 13:40-15:10 Miklós Pálfia (Sungkyunkwan University / University of Szeged Tudományegyetem)

Firstly we briefly review some available versions of the strong law of large numbers in Banach spaces and nonlinear extensions provided by Sturm in CAT(0) metric spaces. Sturm’s 2001 L^2-result was directly applied to the case of the geometric (also called Karcher) mean of positive matrices, thus it suggests a natural formulation of the law for positive operators. However there are serious obstacles to overcome to prove the law in the infinite dimensional case. We propose to use a recently established gradient flow theory by Lim-P for the Karcher mean of positive operators and a stochastic proximal point approximation to prove the L^1-strong law of large numbers for the Karcher mean in the operator case.

## 5 Mar, 14-15 Bas Dietzenbacher (Maastricht University): Fair and Consistent Prize Allocation in Competitions

Given the final ranking of a competition, how should the total prize endowment be allocated among the competitors? We study consistent prize allocation rules satisfying elementary solidarity and fairness principles. In particular, we axiomatically characterize two families of rules satisfying anonymity, order preservation, and endowment monotonicity, which all fall between the Equal Division rule and the Winner-Takes-All rule. Specific characterizations of rules and subfamilies are directly obtained.

## 12 Mar, 14-15 Péter Biró (KRTK, Corvinus): Shapley-Scarf Housing Markets: Respecting Improvement, Integer Programming, and Kidney Exchange

In a housing market of Shapley and Scarf, each agent is endowed with one indivisible object and has preferences over all objects. An allocation of the objects is in the (strong) core if there exists no (weakly) blocking coalition. In this paper we show that in the case of strict preferences the unique strong core allocation (or competitive allocation) respects improvement: if an agent’s object becomes more attractive for some other agents, then the agent’s allotment in the unique strong core allocation weakly improves. We obtain a general result in case of ties in the preferences and provide new integer programming formulations for computing (strong) core and competitive allocations. Finally, we conduct computer simulations to compare the game-theoretical solutions with maximum size and maximum weight exchanges for markets that resemble the pools of kidney exchange programmes.

## 19 Mar, 14-15 Alexander Nesterov (Higher School of Economics, St.Petersburg): Measuring manipulations in matching markets by counting manipulating agents

Due to various objectives and constraints, many real life matching markets are vulnerable to preference and capacity misreports. A large amount of such “manipulations” poses a serious threat to the success of these markets. To address this issue, numerous matching systems have recently reformed their matching rules. Examples include the entry-level medical labor market in the US, school admissions systems in New York City, Chicago, Denver, Ghana and England. We use a simple method of counting the number of all relevant manipulating agents and show that these reforms reduced the scope of manipulations.

## 26 Mar, 13:40-15:10 László Kovács (Corvinus): Performance Testing of Feature Selection Algorithms for Generalized Additive Models

In machine learning, feature selection for generalized additive models (GAMs) is computationally expensive and challenging. This comes from the fact that in GAMs not only the inclusion or exclusion of a feature is a decision point –like in the case of linear models– but the non-linear form of the features that are selected for a given model. The increased complexity for the task means that best subset methods can be computationally expensive even with a feature space of only 8 features.

One of the most important drawbacks of existing methods for GAM feature selection, is the lack of parsimony. The models selected by the existing methods usually have a phenomenon called concurvity. Concurvity occurs when some non-linear terms in a model can be approximated by one or more of the other non-linear terms in the model. In our previous works, we proposed a hybrid genetic-improved harmony search algorithm (Hybrid Algorithm, HA) that applies thin plate splines in order to produce a best subset feature selector that is capable to find concurvity-free models.

Our previous research focused on developing the HA for GAMs and improving its expected runtime through parallelization. Some recent algorithms, like the mRMRe (De Jay et al., 2013) and the block HSIC Lasso (Climente-González et al., 2019) were used as benchmarks. We showed on real world datasets that our proposed HA results in more parsimonious models than the models proposed by the mRMRe and the block HSIC-Lasso algorithms. However, expected runtime of the HA is more substantial than that of the two benchmarks.

In this study, we investigate the performance of the HA against several other feature selection algorithms applied for GAMs. These algorithms can be separated to three clusters. One is the cluster of stepwise methods implemented with the help of Wood (2017) when the GAM applies thin plate splines. The second cluster is for regularization methods such as the COSSO (Lin – Zhang, 2006) and the penalized thin plate splines (Marra – Wood, 2011). The third cluster contains methods that are utilizing popular boosting techniques, like the GAMBoost algorithm (Schmid – Hothorn, 2008) or the Modified Backfitting procedure (Belitz – Lang, 2008). We also apply Recursive Feature Elimination (RFE) combined with a Random Forest learner as a benchmark algorithm that is not based on GAM learners.

The performance of these algorithms against the HA, mRMRe and HSIC-Lasso is tested on two real world datasets. In a smaller database with 8 features we investigate which none-redundant features are most important in predicting comprehensive strength of concrete girders. This dataset is mainly used to fine tune the parameters of the examined algorithms. Next, a more realistic case with 27 features is used. Here, we investigate which features are most significant in predicting the default of credit card clients.

We show that our proposed HA with the application of thin plate splines results in more parsimonious models than the models proposed by the other examined algorithms without having significantly lower predictive performance on a separate test set. Expected runtime are generally better for models proposed by the benchmark algorithms than the HA on a large dataset. However, from our results we can see that the expected runtime of HA is better than that of the GAMBoost and not significantly different than the expected runtime of the RFE combined with Random Forest.

References

Belitz, C., & Lang, S. (2008). Simultaneous selection of variables and smoothing parameters in structured additive regression models. Computational Statistics & Data Analysis, 53(1), 61-81.

Climente-González, H., Azencott, C. A., Kaski, S., & Yamada, M. (2019). Block HSIC Lasso: model-free biomarker detection for ultra-high dimensional data.

Bioinformatics, 35(14), i427-i435.

De Jay, N., Papillon-Cavanagh, S., Olsen, C., El-Hachem, N., Bontempi, G., & Haibe-Kains, B. (2013). mRMRe: an R package for parallelized mRMR ensemble feature selection. Bioinformatics, 29(18), 2365-2368.

Lin, Y., & Zhang, H. H. (2006). Component selection and smoothing in multivariate nonparametric regression. The Annals of Statistics, 34(5),

2272-2297.

Marra, G., & Wood, S. N. (2011). Practical variable selection for generalized additive models. Computational Statistics & Data Analysis, 55(7), 2372-2387.

Schmid, M., & Hothorn, T. (2008). Boosting additive models using component-wise P-splines. Computational Statistics & Data Analysis, 53(2), 298-311.

Wood, S. N. (2017) Generalized Additive Models: An Introduction with R (2nd edition). Chapman and Hall/CRC.

## 16 Apr, 14-15 Vito Fragnelli (University of Eastern Piedmont): Minimal winning coalitions and orders of criticality

In this paper, we analyze the order of criticality in simple games, under the light of minimal winning coalitions. The order of criticality of a player in a simple game is based on the minimal number of other players that have to leave so that the player in question becomes pivotal. We show that this definition can be formulated referring to the cardinality of the minimal blocking coalitions or minimal hitting sets for the family of minimal winning coalitions; moreover, the blocking coalitions are related to the winning coalitions of the dual game. Finally, we propose to rank all the players lexicographically accounting for the number of coalitions for which they are critical of each order, and we characterize this ranking using four independent axioms.

## 23 Apr, 13:40-15:10 Előd Takáts (Corvinus): Inflation and demography through time

Demography accounts for a large share of low frequency inflation variation in 22 countries from 1870 to 2016. The dependent population (young and old) is associated with higher, and the working age population with lower inflation. The relationship is robust across different sub-samples and specifications, including dynamic Phillips curve settings, suggesting that it is not spurious. A natural experiment involving exogenous population shocks from the two world wars provides further support for the relationship. The observed pattern is broadly consistent with delayed monetary policy responses to demography-induced changes in the natural interest rate.

## 30 Apr, 14-15 József Dombi (University of Szeged) / Tamás Jónás (Eötvös Lóránd University): On certain types of monotone measures: the lambda-, the nu-, and the tau-additive measures

In many situations, the traditional additive measures are not sufficient to describe the uncertainty. Therefore, new demands have arisen for non-additive, but monotone (fuzzy) measures. Our lecture is based on our recent research related to the lambda-, nu-, and tau-additive measures, which are all monotone measures. Here, we present the general Poincaré formula for lambda-additive measures and provide new characterizations of belief- and plausibility measures. As a special case, we get the probability measure. We also show how a lambda-additive measure can be derived from a probability measure. Based on this property, the conditional lambda-additive measure can also be deduced. Next, we present the nu-additive measure as an alternatively parameterized lambda-additive measure. Here, we describe how this new measure is connected with the belief-, probability- and plausibility measures. Lastly, we introduce the tau-additive measure as an approximation to the lambda-additive measure.

## 7 May, 14-15 Dávid Csercsik (Pázmány University): Quantitative supply security related significance measures for gas reservoires

Investments and developments related to natural gas infrastructure are considered as top priority for every country. The cost of such projects is significant,

typically comparable to the national GDP. The two main aspects taken into account during the planning of natural gas network or reservoir developments are (I) the expected economic benefits of the project, and (II) the potential effects regarding the security of supply.

In contrast to economic analysis, which typically assumes normal operation of the infrastructure, the perspective of supply security focuses on scenarios, when the operation of the infrastructure and the network flows are negatively affected by external factors. The underlying causes may be of technical nature (as failures of pipeline elements or compressor stations), but they may be related to political disputes as well, as in the case of the 2006 and 2009 Ukrainian-Russian gas crises.

In the case of such events, when the consumption of certain network nodes is reduced due to disruptions in the transportation, we may distinguish two important elements in the restoration process. The first is the potential re-routing of gas available from sources already used during the normal operation of the network, and the other is the activation of additional sources as gas reservoires or previously unused LNG terminals in order to mitigate the damage.

Our aim is to develop quantitative methods in order to model the re-routing and reservoir-activation scenarios taking place during the restoration process, and to define quantitative measures for the general supply-security related significance of reservoires of natural gas.

## 14 May, 14-15 Roland Molontay (BME): Introducing HSDSLab: How data and network science can help to answer research questions in human and social sciences?

In this talk, I review some recent works of the Human and Social Data Science Lab (HSDSLab). HSDSLab is a newly established research group based in the Institute of Mathematics at the Budapest University of Technology and Economics. HSDSLab conducts both methodology oriented basic research in data and network science and applied research with a human-centred and societal focus. The talk will revolve around two main topics: (1) Social network analysis and (2) Educational data science. As a tribute to the achievements of the network science community in the past 20 years, I provide a bibliographic analysis and investigate the co-authorship network of network scientists to identify how the network science community has been evolving over time. I present our findings on the popularity of memes based on a content-based predictive analysis using memes from the Reddit social media site. Moreover, I also sketch some data-driven research projects from the educational domain: including identifying students at risk of dropping out using explainable artificial intelligence; assessing the predictive validity of the admission system, and quantifying the impact of interventions.

## 21 May, 14-15 Péter Vida (CY Cergy Paris Université): Designing Interrogations

We provide an equilibrium model of interrogations with two-sided asymmetric information. The suspect knows his status as guilty or innocent and the likely strength of law enforcers’ evidence, which is informative about the suspect’s status and may also disprove lies. We study the evidence strength standards for interrogating and for drawing adverse inferences from silence that minimize prosecution errors. We consider scenarios where interrogations can be delegated. We describe the optimal mechanism under full commitment and a dynamic interrogation with two-sided information revelation implementing the optimum in equilibrium.

### 2020/21/1

## 18 Sept, 14-15 Balázs Sziklai (Corvinus, KRTK): Influence maximization on social networks: testing proxy-based algorithms

We devise a testing framework to rank proxy-based influence maximisation algorithms. Earlier works compare these algorithms by calculating their top choices on a given network, then checking which set fares better in a diffusion simulation. In real-life applications, however, the top choices of these algorithms might be unaccessible for various reasons. Consequently, we have to choose our spreaders from a different set that might not contain any highly ranked agents at all. There is no guarantee that a proxy that is better at predicting the performance of the most popular agents will be equally successful for an arbitrary group of individuals. This calls for a systematic test, and in this paper, we provide one with the help of a novel statistical method, the Sum of Ranking Differences. For demonstration, we use the real-life social network, iWiW and a classical diffusion model, the Linear Threshold. The final ranking of the proxies is remarkably different from what we obtain by examining the performance of their top choices. The results highlight that the standard test alone is an inadequate predictor of performance and SRD should be a necessary, if not the primary tool for ranking proxies

If you wish to receive a link for the zoom meeting on the day of the event, please send an email to Tamás Solymosi (tamas dot solymosi at uni dash corvinus dot hu)

## 25 Sept, 16-17 Justin Toth (Univ. of Waterloo): A General Framework For Computing the Nucleolus Via Dynamic Programming

In a cooperative game when the problem of computing the minimum excess coalition for a given allocation can be formulated as a dynamic program we show that the nucleolus can be computed in time polynomial in the size of the dynamic program. This gives a general technique for designing efficient algorithms for computing the nucleolus of a cooperative game. This technique is inspired by a recent result of Pashkovich on weighted voting games. However, our technique significantly extends beyond the capabilities of previous work. We demonstrate this by applying it to give an algorithm for computing the nucleolus of b-matching games in polynomial time on graphs of bounded treewidt

If you wish to receive a link for the zoom meeting on the day of the event, please send an email to Tamás Solymosi (tamas dot solymosi at uni dash corvinus dot hu)

## 2 Oct Economic Modelling Meeting (Pécs)

## 9 Oct, 14-15 Franziska Holz (DIW, Berlin): Freedom Gas to Europe? Scenario Analyses with the Global Gas Model

When sanctioning construction works on the Russian offshore natural gas pipeline Nordstream 2 to Germany in late 2019, U.S. President Trump has drawn attention to the United States’ own natural gas exports.The United States of America started exporting liquefied natural gas (LNG) over the world’s seas only a few years ago. LNG export capacities and trade flows have increased at high speed since 2016. Observers have wondered whether the U.S. sanctions on Nordstream2 were in fact meant at supporting U.S. LNG exports. We shed some light on the role of U.S. LNG for Europe and analyze the impact of several politically motivated scenarios with a country level, global oligopolistic gas market model. We focus on EU importsand consumption and prices and discuss ripple effects throughout global markets.

Our Base Case to 2050 is calibrated to IEA World Energy Outlook (2018) and PRIMES European Reference Scenario (2016). In addition, we define three LNG support policy scenarios that we name after the mainpromoters of national gas policies: “Trump” assumes U.S. policies of Nordstream 2 sanctions and financial support to LNG shipments to Europe, “Altmaier” and “Jinping” assume financial support to LNG import terminals in Germany and China, respectively. In addition,the “Putin” scenario involves a total and lasting boycott of Russian exports to Europe.

We find that the interconnectedness of global gas markets through abundant LNG import capacity both in Europe and other regions – namely in Asia – allows for adjustments of global trade patterns that mitigatethe consequences of regional disturbances. Neither Chinese nor German subsidies on regasification terminals nor moderate financial support of US LNG exports affect aggregate EU consumption levels in a significant way. Only a Russian boycott or large subsidieson US LNG exports have a discernable effect. In any year, compared to the Base Case, EU consumption varies not more than between -5% and +3%, and average prices by -5% to +10% only.

If you wish to receive a link for the zoom meeting on the day of the event, please send an email to Tamás Solymosi (tamas dot solymosi at uni dash corvinus dot hu)

## 16 Oct, 13:40-15:10 Péter Biró, Márton Gyetvai (KRTK, Corvinus MSM Institute): Online voluntary mentoring: Optimising the assignment of students and mentors

Our talk will have two parts. First, we give an introduction to optimisation in two-sided matching markets by giving details also on practical results in different applications, such as the Hungarian university admission scheme. Then we present a novel application for allocating voluntary mentors to students. After the closure of the schools in Hungary from March 2020 due to the pandemic, many students were left at home with no or not enough parental help for studying, and, in the meantime some people had more free time and willingness to help others in need during the lockdown. In this paper we describe the optimisation aspects of a joint NGO project for allocating voluntary mentors to students using a web-based coordination mechanism. Our goal has been to form optimal pairs and study groups by taking into the preferences and the constraints of the participants. We present the optimisation concept, the integer programming techniques used, and some simulation results conducted on real and generated datasets.

If you wish to receive a link for the zoom meeting on the day of the event, please send an email to Tamás Solymosi (tamas dot solymosi at uni dash corvinus dot hu)

## 6 Nov, 14-15 Marina Núñez (Univ. de Barcelona): Stable cores in information graph games

In an information graph situation, some agents that are connected by an undirected graph can share with no cost some information or technology that can also be obtained from a source. If an agent is not connected to an informed player, this agent pays a unitary cost to obtain this technology. A coalitional cost game can be defined from this situation, and the core of this game is known to be non- empty. We prove that the core of an information graph game is a von Neumann-Morgenstern stable set if and only if the graph is cycle- complete, or equivalently if the information graph game is concave. When the graph is not cycle-complete, whether there always exists a stable set is an open question. In this regard, we show that if the information graph consists of a ring that contains the source, then a stable set always exists and it is the core of a related information graph situation where one edge has been deleted.

If you wish to receive a link for the zoom meeting on the day of the event, please send an email to Tamás Solymosi (tamas dot solymosi at uni dash corvinus dot hu)

## 13 Nov, 13:40-15:10 Attila Tasnádi (Corvinus MSM Institute): Calculating and characterizing the eigenvector centrality measure based Eigenfactor score (EF) and Scimago Journal Rank indicator (SJR)

There are many ways of measuring the influence of scientific journals. We will survey most of these measures but in this talk we will focus on two important measures of journal impact (EF and SJR) both employing a similar algorithm to the PageRank algorithm. We will explain in detail how these indicators are computed and provide axiomatic characterizations to underline their employments. Finally, we will discuss where and how these indicators are applied, and speak in general about journal and university rankings.

If you wish to receive a link for the zoom meeting on the day of the event, please send an email to Tamás Solymosi (tamas dot solymosi at uni dash corvinus dot hu)

## 20 Nov, 14-15 Aleksei Y. Kondratev (National Research University Higher School of Economics, Saint Petersburg, Russia): How should we score athletes and candidates: geometric scoring rules

We study how to rank candidates based on individual rankings via positional scoring rules. Each position in each individual ranking is worth a certain number of points; the total sum of pointsdetermines the aggregate ranking. Our selection principle is consistency: once one of the candidates is removed, we want the aggregate ranking to remain intact. This principle is crucial whenever the set of the candidates might change and the remaining rankingguides our actions: whom should we interview if our first choice got a better offer? Who gets the cup once the previous winner is convicted of doping? Which movie should a group watch if everyone already saw the recommender system’s first choice? Will addinga spoiler candidate rig the election?Unfortunately, no scoring rule is completely consistent, but there are weaker notions of consistency we can use. There are scoring rules which are consistent if we add or remove a unanimouswinner — such as an athlete with suspiciously strong results. Likewise, consistent for removing or adding a unanimous loser — such as a spoiler candidate in an election. While extremely permissive individually, together these two criteria pin down a one-parameterfamily with the geometric sequence of scores. These geometric scoring rules include Borda count, generalised plurality (medal count), and generalised antiplurality (threshold rule) as edge cases, and we provide elegant new axiomatisations of these rules. Finally,we demonstrate how the one-parameter formulation can simplify the selection of suitable scoring rules for particular scenarios.

If you wish to receive a link for the zoom meeting on the day of the event, please send an email to Tamás Solymosi (tamas dot solymosi at uni dash corvinus dot hu)

## 26-27 Nov Annual Financial Market Liquidity Conference

Details here: http://afml.uni-corvinus.hu/

## 4 Dec, 13:40-15:10 Gyula Vastag (Corvinus MSM Institute): Sources of Competitive Advantage: Lessons I Learned

The presentation is a broad-brush summary of the overarching theme of my research with cherry-picking the latest and/or best papers. Briefly, using examples from my papers I attempt to show that sustainable competitive advantage, to a great extent, can be explained with soft, infrastructural factors that present the hardest barriers to imitation. Additionally, and informally, relying on my academic experience in Hungary, in the United States and in Europe, I offer three lessons for consideration for those who are willing to consider them.

If you wish to receive a link for the zoom meeting on the day of the event, please send an email to Tamás Solymosi (tamas dot solymosi at uni dash corvinus dot hu)

## 11 Dec, 14-15 Herbert Hamers (Tilburg University): On coloring games

In this presentation, we present an overview of the characterization of properties of several classes of coloring games in terms of the underlying graph.

First, we discuss the class of minimum coloring games introduced by Deng et al. (1999). Here totally balancedness, existence of PMAS and submodularity are characterized by perfect graphs, 2K2P4 -free graphs and complete r-partite graphs, respectively (cf. Deng et al. (2000), Hamers et al. (2014), Okamoto (2003)).

Second, we discuss the class of weighted minimum coloring games introduced by Hamers et al. (2019). Here global (local) totally balancedness and global (local) submodularity are characterized by perfect graphs (any graph) and complete r-partite graphs (2K2P4 -free graphs), respectively.

Finally, we discuss the class of multiple player coloring games introduced in Hamers et al. (2020). Here we present some preliminary results.

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Deng, X., Ibaraki, T., Nagamochi, H., 1999. Algorithmic aspects of the core of combinatorial optimization games. Mathematics of Operations Research 24(3), 751–766.

Deng, X., Ibaraki, T., Nagamochi, H., Zang, W., 2000. Totally balanced combinatorial optimization games. Mathematical Programming 87, 441–452.

Hamers, H., Miquel, S., Norde, H., 2014. Monotonic stable solutions for minimum coloring games. Mathematical Programming 145, 509–529.

Hamers, H., Horozoglu, N., Norde, H., Tornoe Platz, T. On totally balanced, submodular and PMAS-admissible weighted minimum coloring games (submitted).

Hamers, H., Miquel, S., Norde, H., Obadi, S. On submodular multiple minimum coloring games (in preparation).

Okamoto, Y., 2003. Submodularity of some classes of the combinatorial optimization games. Mathematical Methods of Operations Research 58(1), 131–139.

If you wish to receive a link for the zoom meeting on the day of the event, please send an email to Tamás Solymosi (tamas dot solymosi at uni dash corvinus dot hu)