Jenő Szép

Jenő Szép
Jenő Szép (right) and Guido Zappa (left)
Born	(1920-01-13)13 January 1920 Budapest
Died	18 October 2004(2004-10-18) (aged 84) Budapest
Citizenship	Hungarian
Known for	Group theory Game theory
Spouse(s)	Tésy Gabriella (1948-2004)
Scientific career
Institutions	Corvinus University of Budapest

Jenő Szép (13 January 1920 – 18 October 2004) was a Hungarian mathematician, professor of University of Economics, Budapest. His main research interests were group theory and game theory. He was founder of the journal Pure Mathematics and Applications (PU.M.A.).^[1] In mathematics, especially group theory, the Zappa–Szép product (also known as the Zappa–Rédei–Szép product, general product, knit product or exact factorization) describes a way in which a group can be constructed from two subgroups. It is a generalization of the direct and semidirect products. It is named after Guido Zappa (1940) and Jenő Szép (1950) although it was independently studied by others including B.H. Neumann (1935), G.A. Miller (1935), and J.A. de Séguier (1904).^[2] For references, see Matthew G. Brin. About Zappa-Szép. “The Zappa-Szép product was developed independently by Guido Zappa and Szép Jenő as a generalization of the semi-directional product: in the Zappa-Szép product, none of the factors should be normal. We examine the basic features of the product and show that it applies to more general settings than groups. The product is remarkable because it requires almost no hypothesis for the function and adapts to many situations. "^[3]

Biography[]

His father Pál Szép, mother Arabella Liebert. His wife Gabriella Tésy. He graduated from the Miklós Zrínyi Real High School in Budapest in 1938, then obtained a teacher's diploma in mathematics and physics at the Pázmány Péter University in 1943 and a doctorate in humanities in 1946. He was awarded the degree of Candidate of Mathematical Sciences in 1952 for his advanced activities so far. He received his degree of Doctor of Mathematical Sciences from Hungarian Academy of Sciences in 1957. He was an intern (1941–1943) and assistant professor (1943–1946) at the Pázmány Péter University Institute of Mathematics Lipót Fejér and Béla Kerékjártó. The Budapest Civic School Teacher Training College r. teacher (1946–1949), Szeged Pedagogical College, resp. a Szeged Teacher Training College Department of Mathematics r. teacher (1949–1952), college teacher (1952–1961) and head of the Department (1949–1961). Marx University of Economics (MKKE) Professor of the Department of Mathematics (August 10, 1961 - December 31, 1992) and Head of the Department (1961–1976), also Director of the Institute of Mathematics and Computer Science (1976-87). Even before his arrival, it was completed in 1960 - primarily Béla Krekó the curriculum of the plan-(economic) mathematics program and the later elite program. The leading individual in the introduction and maintenance of the curriculum Béla Krekó, Jenő Szép jointly. Jenő Szép achieved building and managing a team, which conducted scientific research and education not only in pure mathematics, but in the promising new methods too and gained experiences in wide range of applications. Beyond several series of textbooks, they issued a series - named Department of Mathematics, Karl Marx University of Economics - of research papers (cca. 100) in English between 1969 and 1988. He was the editor of a series of mathematical handbooks for economists in Hungarian. Professor Emeritus of the BKE (since 1995) and the Gyula Juhász Teacher Training College. Master of Emeritus (since 1995). As a matematician, his main research interests were algebraic structures, group theory. He is one of the authors of Zappa-Szép product, beyond papers, he published with co-authors the book titled Semigroups in 1991. As professor of an economics university, his main interest was in game theory, and dealt with many applications of mathematical methods in economics. He was the founding editor-in-chief of the international mathematical journal „ Pure Mathematics and Applications (PUMA)” in 1990, and worked on it until his death in 2004.. Kluwer Academic Publishers from 2000 he edited the series „ Advances in Mathematics” – with 7 books until his death. Jenő Szép was invited professor in Italian and Canadien universities for joint research and teaching courses (Róma (1961-62), Firenze (1968, 1972), Padova (1968-69), London (Kanada 1987), Lecce (1988-89), Siena (1990-2002) for several months in each case. The list of his works has about 180 items, the Mathematical Reviews referred to 95 of his papers/books.

Game theory[]

Ferenc Forgó: Professor Jenő Szép as an educator and game theorist.^[4] “I begin with a personal note that reaches back in the early sixties. I was a freshman at the University of Economics majoring in applied mathematics in economics and business. We students knew that the university had been in search of a senior mathematician to head the Department of Mathematics. Soon we learned that the position was filled and a young professor from Szeged was appointed for the job. It was Jenő Szép, whose reputation had already been established as an outstanding researcher in algebra and a demanding, charismatic teacher. The first course he taught us was not algebra but calculus. We were impressed by his teaching style which meant no notes, no books to help even when presenting such involved proofs as that of Brouwer’s fixed point theorem. There was no need for us to study at home because by working through the proofs with him, he at the board and we over our notebooks, at a pace comfortable for everybody, we understood not only the details but the underlying ideas as well. Then came the exams. Legend had it that he had been very tough and uncompromising at exams in Szeged where he had taught before. No one wanted to go first, we were pushing each other towards the door of his office. Finally, I took a deep breath and went in first. Then it was not as tough as expected. After a fairly good written test he asked only two short proofs which I presented in a trembling voice and soon I was out with an A. His signiture with this mark in my exam book has been one of my most cherished memorabilia. Another lesson to be learned is that rumors must always be taken with a grain of salt. In addition, this was the last time when I had a little chill in my blood when meeting Professor Szép. This was just the beginning of a long friendship with him. Friendship is the correct word to use even if he was my boss for 22 years. He never let me feel this asymmetric relationship though all of us at the department knew that he was on a much higher level and all we could do was trying to get closer. He had a way of leading the department. Always soft spoken, considerate, never pushing anybody but somehow his gentle nudging made everybody do his or her best. He was working along concepts and plans, never drifting aimlessly among projects and never getting lost in day-to-day small businesses. His concept when taking over was to find a special profile for the department. This was mathematics applicable in economics and business. He worked hard to get the textbooks ready for a new curriculum. He himself wrote an excellent book on calculus with lots of economic applications to cater to the needs of economics students. It is amazing how fast he acquired a feel for the kind of problems he had never met before in his previous career. He was absolutely not the joke-book mathematician confined to his narrow field of interest and out of touch with the rest of the world. I had the priviledge to work with him in several consulting jobs in industry and government. His deep and quick insight into the very heart of the problem, finding the appropriate methods to tackle the problem and the careful guidance he gave throughout the project were assets we missed a lot after he retired. There is another area where he was at his best: promoting and managing the scientific career of everybody seeking his advice and guidance. This can best be illustrated by my personal example. In the late sixties, in a lunchtime casual conversation he asked me whether I had any idea of a specific field of research that I could go deeper into and which also fits the profile of the university and the department. Then I recalled how impressed I was by his game theory course and also knew that this new field was up and coming at that time worldwide. Then he advised me that I should try game theory. In about five years we wrote the first game theory book ever published in Hungary (Szép, J. and Forgó, F.(1974)) which was followed later by the German version (Szép, J. und Forgó, F. (1983)), the English language edition (Szép, J. and Forgó, F. (1985)) and in 1999 the completely rewritten book published by Kluwer (Forgó, F., Szép, J. and Szidarovszky, F. (1999). For this, Ferenc Szidarovszky joined us as third co-author. These books have been used as graduate texts at several universities all over the world and have done well in the very competitive market of game theory texts. Writing a book with Professor Szép was both fun and a learning experience. Besides, he always treated me as an equal partner even sharing the burden of chores that writing a book entails. Last but not least, Professor Szép, as the head of the department and later that of the Institute of Mathematics and Computer Science provided a safe haven for us at times when preserving one’s integrity and keeping out of trouble of all sorts was not easy. His reputation, polite manners and moral strength helped us to live a normal life and concentrate on meeting the challenges of a profession of our choice. As mentioned earlier, I have a long history of working with Professor Szép writing books on game theory. Though his great scientific achievements are in algebra, he cared a lot about game theory where the connection with practical problems of different areas is more direct than in abstract algebra. Game theory as we know it now is an interdisciplinary science with applications mainly in economics. One thing is common in all applications: there should be an underlying mathematical model which is supposed to give insight into multiperson situations of conflict and cooperation unattainable by other scientific approaches. It is no wonder that mathematicians dominate the scene from the very beginnings to date. Hungarian mathematicians played a decisive part in the development of game theory from the ground breaking work of János von Neumann to the Nobel laurate János Harsányi. János von Neumann’s and János Harsányi’s contributions to modern game theory have had a great impact on what directions game theory has developed and their work is still a significant marker in contemporary research in the field. Hungarian mathematics, and science in general, must be very proud of their accomplishments and cherish the fame they have brought to Hungary. Though they got their first university degrees in Hungary (Harsányi and Professor Szép went to the same university at the same time in Budapest), due to several reasons and special historical circumstances they lived their active life mostly abroad, thereby sharing the fame and publicity they earned between the homeland and the country they lived in. Until the early sixties, any economic theory or methodology other than the Marxian was taboo in Hungary and completely missing from university curriculae. A few professors at the University of Economics in Budapest realized in the early sixties that part of the methodology of modern economics, such as activity analysis with the mathematical programming underpinning and game theory when stripped of any ideology and used for the analysis of economic problems existing in modern societies, let it be a free market economy or a (partially) planned and government controlled socialist economy, can be introduced in the curriculum of the university. Even a small, special group of students was selected with a special curriculum heavily loaded with mathematics and “western-style” economics. Beyond his great achievement in spreading knowledge, he used his mathematical ingenuity and creativity to be a forerunner of generalizations and refinements of the celebrated Nash equilibrium concept. Though his ideas never appeared in journals of wide circulation, they can be found in his books. Of these, two should be singled out as early versions of concepts that became subjects of thorough analysis later in different contexts. Both are strongly related to the classical Nash equilibrium concept. Given a game in normal form

                                      G={ S1,..., Sn; f1,...,fn } 

where S1,...,Sn are strategy sets of players and f1,...,fn are the real-valued payoff functions defined on the set of strategy profiles S= S1×...×Sn , a Nash equilibrium is a strategy profile (t1,...,tn) such that the inequalities

                                     fi(t1,...,ti ,...,tn)≥  fi(t1,...,si ,...,tn)

hold for all siє Si and i=1,...,n. Professzor Szép defined an equilibrium concept which was new at that time and called it group equilibrium. Take a partition of the players (these are the groups) and define a new game in which these groups are the players and the payoff functions are the sums of the individual payoff functions. A Nash equilibrium in this game is said to be a group equilibrium subject to the particular partition. This definition is only meaningful if utilities within a group are transferable. This definition gives rise to both refinements and generalizations of the Nash equilibrium in the following way: • Given a set of partitions P of a game, a strategy profile that is a group equilibrium subject to all partitions in P is clearly a refinement of the Nash equilibrium if P contains the trivial partition (every single player is an element of the partition). • Any strategy profile that is a group equilibrium point subject to some partition p is a generalization of the Nash equilibrium point. Especially minimal partitions are of interest (no refinement of the partition gives rise to a group equilibrium). It is clear that group equilibrium points may exist even if there is no Nash equilibrium. Characterizations and axiomatizations of equilibrium concepts falling in these two categories appeared later (see e.g. Peleg, B and Tijs, S.(1996)) and refinement theory has developed into a whole branch of game theory as shown by the monography of van Damme, E. (1983). Another interesting idea of Professor Szép was to modify the normal form of a game by adding the “neighborhood” functions to the general description. Thus a game in normal form is given by

                         G={S1,...,Sn ; f1,...,fn, φ1,...,φn}  

where, as usual, we have the strategy sets for the players to choose their strategies from, the payoff function to evaluate the consequences of joint strategy choices and the neighborhood functions that assign to each strategy of a player a subset of the strategy set (always containing the particular strategy) that is available for the player when she decides to change her strategy. In the classical model, there is no need for neighborhood functions since it is assumed that any strategy in the strategy set can be changed to any other if deemed advantageous. Professor Szép’s model is much closer to reality since very often in real-life situations too much change is not admissible while moving in a possibly small neighborhood of a strategy is acceptable. Definition of an equilibrium is then similar to that of Nash’s: a strategy profile represents an equilibrium if it is in no player’s interest to change her strategy within the neighborhood assigned by the neighborhood function if the rest of the players stick to their strategies. It was also Professor Szép’s idea to include costs of changing a strategy to another in the payoff function. Of course group equilibrium and the neighborhood function version of the normal form can be combined giving rise to new results in a more general setting. One aspect of these two new concepts should also be mentioned. If in a traditional form of a game conditions for the existence of a Nash equilibrium are not met, both in certain group and neighborhood normal form games equilibria may exist. For an example it is enough to think of a game where individual payoff functions are not quasiconcave in their respective variables but certain sums are or where there is no Nash equilibrium if neighborhoods are the whole strategy sets but there can be if neighborhoods are smaller. An example of an existence theorem in the neighborhood setting is Theorem 11 in Forgó, F. and Joó, I.(1999). Professor Szép, as an educator, text-book author and inspirational source for generations of scientists and practitioners has done a lot to further the cause of meaningful and creative application of mathematics in economics in general and in game theory in particular. We will miss him and keep his memory as long as we live."

Notable works[]

His works: ^[5]

• On Finite Groups Which Are Necessarily Commutative. (Commentarii Mathematicae Helvetici, 1947 vol. 20. fasc. 3. p. 223-224.)
• Über die als Produkt zweier Untergruppen darstellbaren endlicher Gruppen. (Commentarii Mathematicae Helvetici, 1949)
• On Simple Groups. (Publicationes Mathematicae, 1949)
• Jenő Szép – László Rédei: Über die endlichen nilpotenten Gruppen. (Monatshefte für Mathematik, 1951 bd. 55. p. 200-205)
• On the structure of groups which can be represented as the product of two subgroups. (Acta Scientarium Mathematicarium (Szeged), 1950. tom. 12. p. 57-61)
• Zur Theorie der endlichen einfachen Gruppen. (Acta Scientiarum Mathematicarum (Szeged), 1952. tom. 14. fasc. 4.p. 246)
• Jenő Szép – László Rédei: Eine Verallgemeinerung der Remakschen Zerlegung. (Acta Scientiarum Mathematicarum (Szeged), 1953. tom. 15. fasc.1. p. 85-86)
• Zur Theorie der faktorisierbaren Gruppen. (Acta Scientiarum Mathematicarum (Szeged), 1955. tom. 16. fasc. 1-2. p. 54-57)
• Zur Theorie der Halbgruppen. (Publicationes Mathematicae, (Debrecen), 1956. tom. 4. fasc. 3-4. p. 344-346)
• Gyűrűk egy új bővítéséről. Doctoral thesis. (Szeged, 1957) (in Hungarian)
• Analízis. Monograph. (Matematikai ismeretek gazdasági szakemberek számára. Bp., Közgazdasági és Jogi Könyvkiadó 1965 co-author: András Kósa. 2nd ed. 1972) (in Hungarian)
• On Foundation of Game Theory. (Bp., 1970. Department of Mathematics. Karl Marx University of Economics. ISSN 0134-1596 1970-3))
• Szép, J. and Hegedűs, M. (1973, 1974): On equilibrium of systems,I-II. Department of Mathematics, Karl Marx University of Economics, Budapest 1973/4, 1974/3
• Szép Jenő - Forgó Ferenc. Bevezetés a játékelméletbe. (in Hungarian) (Bp., 1974) (ISBN 963 220 010 1)
• Szép Jenő - Forgó Ferenc. Einführung in die Spieltheorie. Frankfurt/Main, 1983. (ISBN 963 05 2885 1).
• Szép Jenő - Forgó Ferenc. Introduction to the Theory of Games. Dordrecht–Boston–Lancaster, 1985) (ISBN 963 05 3357 X).
• A gazdasági kockázat és mérésének módszerei. Co-authors: Tamás Bácskai Tamás, Ernő Huszti, György Meszéna, Gyula Mikó (Korszerű matematikai Ismeretek gazdasági szakemberek számára. Bp., Közgazdasági és Jogi Könyvkiadó 1976. (in Hungarian) (ISBN 963 220 314 3). Published in Russian: Moscow, Ekonomika 1979.
• On a Special Decomposition of Regular Semigroups. Migliorini, F.-fel. (Acta Scientiarum Mathematicarum, 1978 tom. 40. fasc. 1-2. 121-128 p.)
• Jenő Szép – István Peák (ed.). Conference on System Theoretical Aspects in Computer Science. Salgótarján, 1982. May 24–26. (Bp., BKE Matematikai és Számítástudományi Intézet 238 o. 1982)
• Mathematical Analysis and System Theory. I–IV. ed. with Peter Tallos. (Bp., 1984–1988 Department of Mathematics, Karl Marx University of Economics 1984/5, 1985/2, 1986/5, 1987/3)
• Conference on Automata, Languages and Mathematical Systems. Salgótarján, 1984. máj. 21–23. Ed. with István Peák (Bp., BKE Matematika Tanszék 1984, 249 o.)
• Szép, Jenő - Jürgensen, Helmut - Migliorini, F.: Semigroups. (Bp., 1991. Akadémiai Kiadó) (ISBN 963 05 6046 1)
• Szép, Jenő - Migliorini, F. The Subsets Cn in Finite Groups and Inverse Semigroups I-II. (Pure Mathematics and Applications, 1994. Vol. 5. No. 2 205-216 p., 1995. Vol. 6. No. 1. 57-67 p.)
• Vectorproducts and Applications. – Monográph. Bp., 1998., Akadémiai Kiadó, 1998. 109 p. (ISBN 963 05 7534 5))
• Szép Jenő - Forgó Ferenc- Szidarovszky Ferenc. Introduction to the Theory of Games: Concepts, Methods, Applications. (Dordrecht : Kluwer Nonconvex Optimization and Its Applications. Vol. 32. Dordrecht–Boston–London, 1999). (ISBN 0 7923 5775 2)

Sources[]

• Szép Jenő professzor (1920 – 2004) Budapesti Corvinus Egyetem. Egyetemi Könyvtár.^[5]
• Szép Jenő. Névpont. Kozák Péter. Pályakép. 2013.^[6]
• Szép Jenő. História - Tudósnaptár. ^[7]

References[]