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1

A TRAVELING SALESMAN PROBLEM AS A COMPETITIVE GAME

100%
Drabik E.
Przegląd Statystyczny
|
2006
|
vol. 53
|
issue 1
5-32
EN
The classical traveling salesman problem might be described as follows: a salesman starting from a given city, visiting each of the cities, and returning to the original point of departure should find the shortest way. More generally, he could consider in what order he should visit the cities to minimize the total distance traveled. For 'distance' we can substitute time, costs, or other measures of effectiveness as desired. Distance or costs between all city pair are presumed to be known. The authoress' version of this problem concerns two traveling salesmen SI and S2 who want to sell certain goods (commodities) in 'n' cities. The player SI starts from a city 'i' and S2 -from a city 'j' ('i' and 'j' are different and 'n' is greater than 1). Both players should visit each of (n-1) cities once and only once, and return to the starting point. The mathematical 'proposal' to minimize the travel costs is given
2
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Aukcja koni arabskich Pride of Poland jako aukcja asymetryczna

100%
Drabik E.
Problemy Rolnictwa Światowego
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2008
|
vol. 04(19)
EN
Auction theory is one of the most influential and widely studied topics in the economic theory over last fifty years. Trading rules in auctions are similar to rules in a game. Auctions might be divided into oral or written. In oral auction bidders hear each other’s bids and can make counteroffers. Each bidder knows his rivals. In written or closed auction bidders do not know how many rival bidders participate. A very important theorem in the theory of symmetric auction is the revenue equivalence theorem. This theorem predicts that expected seller revenue is independent of bidding rules. The symmetry assumption is violated in many real life auction environments and bidders often know how they differ. In practice, the auctioneer discriminates bidders in favour of selling to bidders whose values are drawn from lower distributions. Maskin and Riley (2000) showed that, when an auction is asymmetric, ”strong” buyers prefer the open auction, whereas ”weak” buyers prefer the closed auction. The revenue equivalence theorem does not concern an asymmetric auction. Every year in August at Janów Podlaski an auction of Arabian horses takes place. Our aim is to reinterpret that the Polish Arabian horse market is asymmetric.
PL
Teoria aukcji jest jedną z prężniej rozwijających się dziedzin teorii ekonomii. Reguły aukcyjne przypominają reguły gry. Aukcje dzielimy na ustne i pisemne. W przypadku aukcji pisemnych kupujący składają swoje oferty równocześnie i niezależnie, przy czym nie wiedzą ilu mają konkurentów. W przypadku aukcji ustnych oferty wpływają sekwencyjnie, kupujący zaś mogą śledzić zachowania swoich przeciwników. Bardzo ważnym twierdzeniem dotyczącym aukcji symetrycznych jest twierdzenie mówiące, że reguły aukcyjne nie wpływają na dochód z aukcji. W praktyce założenie o symetrii okazuje się zbyt restrykcyjne i w rzeczywistości o wiele częściej mamy do czynienia z aukcjami asymetrycznymi. Maskin i Riley [2000] pokazali, że „mocny” kupujący preferuje aukcję ustną, zaś „słaby” kupujący aukcję pisemną. Pokazali również, że twierdzenie o jednakowym dochodzie nie dotyczy aukcji asymetrycznych. Co roku, w sierpniu, w Janowie Podlaskim odbywa się aukcja koni arabskich Pride of Poland. Celem pracy jest pokazanie, że jest to typowa aukcja asymetryczna.
3

AN EXPERIMENTAL STUDY OF PRICE FORMATION IN DOUBLE AUCTION BASED ON DATA FROM THE WARSAW COMMODITY EXCHANGE

100%
Drabik E.
Przegląd Statystyczny
|
2006
|
vol. 53
|
issue 4
7-24
EN
Double auction markets are ones of the most common exchange institutions and they attract the attention of many traders. The double auction is used, for example in stock markets such as the Chicago Mercantile Exchange, and in markets for financial instruments, including options and futures. The trade on the Warsaw Commodity Exchange has also the certain features of the double auction market. The prevalence of the institution can be caused by its efficiency and by its capacity to respond quickly to changing market conditions. A variety of auction strategies are based on the game theory principles. In the double auctions, buyers and sellers are treated symmetrically with buyers submitting bids and sellers submitting asks. Both, the sellers and the buyers are players and the double auction rules are similar to the 'rules of the game'. In a static double auction, both the buyers and the sellers supply and demand schedules. A price is then selected and equates supply and demand at the price. If the price is nondiscriminating then all traders are consummated at the selected clearing price. This procedure is sometimes called a demand-submission game. In a dynamic double auction buyers and sellers have repeated opportunities to submit the bids and respectively the offers. It is commonly used in commodity market and some financial markets. Our aim is to show a stochastic algorithm of calculating the transaction price for the double auction. We are going to test the above algorithm for the data from the Warsaw Commodity Exchange.
4

ULAM'S SEQUENCE AND ITS APPLICATION ON FINANCIAL MARKETS

100%
Drabik E.
Przegląd Statystyczny
|
2007
|
vol. 54
|
issue 4
19-33
EN
The aim of this paper is to modify and to present one of technical analysis instruments that can be used for description of stock value diagrams as well as for forecasting the future asset prices- it is the so called Elliott Waves Theory. In classical version this theory is based on the Fibonacci sequence. Modification of Fibonacci sequence was introduced in the fifties of the 20th C. by American mathematician Stanislaw Marcin Ulam who was born in Poland and consists in introducing random elements. In this paper it was checked how the modification of Fibonacci sequence introduced by Ulam influenced the practical analysis of waves created by time series which are composed of asset prices at Warsaw Stock Exchange.
5

THE DYNAMIC COURNOT DUOPOLY GAME

100%
Drabik E.
Przegląd Statystyczny
|
2006
|
vol. 53
|
issue 2
7-23
EN
This paper attempts to describe an evolutionary game theoretic model of Cournot competition. Every discrete time period a large population of firms is matched in pairs randomly to play a Cournot duopoly game. The authoress assumes the firms to act according to behavioral rules. A behavioral rule specifies the quantity to be produced in current period as a function of past observation. That behavioral rules are costly to operate. The cost depend on the informational and computational requirements of implementing the rule. Each firm chooses a behavioral rule from a finite set of different rules, which are commonly known. A firm takes into account the past realized profits of the costs associated with the behavioral rules. The model of dynamic Cournot duopoly game is described by non-linear evolutionary dynamical system. The authoress focuses on two specifications of Cournot duopoly game: linear and linear-quadratic and shows that bifurcation routes complicating dynamics occur in a linear-quadratic model due to which fact strange atractors arise.
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