Title Teorija igara i dizajn mehanizma Author Melita Vidov Mentor Lavoslav Čaklović (mentor)Committee member Lavoslav Čaklović (predsjednik povjerenstva)Committee member Miljenko Marušić (član povjerenstva)Committee member Dražen Adamović (član povjerenstva)Committee member Tomislav Pejković (član povjerenstva)Granter University of Zagreb Defense date and country 2016-09-27, Croatia Scientific / art field, NATURAL SCIENCES Abstract Ovaj diplomski rad je obradio temu dizajna mehanizma koja je temeljena na teoriji igara, podijeljenu obzirom na broj igrača. Za početak, obrađujemo mehanizme između jednog prodavača i jednog kupca. Prvo se bavimo davanjem cijene nerazdvojivom dobru gdje je prodavač dizajner mehanizma. Intuitivnim pristupom procjenjujemo da je prodavaču najbolje da na temelju procjene kupčevog tipa, koja je dana funkcijom distribucije, postavi cijenu te maksimizira očekivani profit. Zanima nas postoji li bolji
... More mehanizam. Uvodimo pojam direktnog mehanizma te ograničenja poticajne kompatibilnosti i individualne racionalnosti koje su nužne za lakšu analizu problema. Olakotna okolnost je što se ispostavilo (za sva poglavlja) da za svaki indirektni mehanizam gdje kupac ne mora prijavljivati istinit tip, postoji odgovarajući direktni mehanizam (princip otkrivenja). Nadalje, karakteriziramo svojstva takvih mehanizama koja su potrebna u potrazi za optimizirajućim mehanizmom. Na kraju se ispostavilo da je početna intuitivna strategija bila najbolji izbor pošto je prodavačeva objektivna funkcija linearna jer nema rizika. Nakon toga prelazimo na nelinearno davanje cijena, tj. davanje cijene razdvojivom dobru, primjerice šećeru. Problem je malo kompleksniji te rezultat nije toliko trivijalan jer korisnost kupca više nije linearna zbog dodatno definirane funkcije ν koja nam omogućuje manipuliranje. Na temelju pretpostavke da je distribucija slučajne varijable prijavljenog tipa regularna, dobijemo efektivan način za zadavanje mehanizma koji maksimizira profit. Na kraju poglavlja obrađujemo primjer u kojem vidimo da nam je uvedena funkcija ν dala popust na količinu. Drugo poglavlje obrađuje Bayesove mehanizme gdje u igri tražimo Bayes-Nash ravnotežu između igrača. Poglavlje počinje promatranjem aukcije jednog nerazdvojivog dobra gdje kupac daje na aukciju dobro za N ≥ 2 ψ N ≥ 2 Less Abstract (english) This thesis processed mechanism design topic which is based on game theory, divided due to the number of players. At the beginning we analyze mechanisms between a seller and a buyer. First we deal with giving prices to single indivisible good where the seller is a mechanism designer. With intuitive approach we estimate that the best for the seller to do is based on assessments of the buyer’s type, which is given by distribution function, to set the price and maximizes expected profit. We are
... More interested in whether there is better mechanism. We introduce the concept of direct mechanism and incentive compatibility and individual rationality constraints that are necessary for easier analysis of the problem. Mitigating circumstance is that it turned out (for all chapters) that for any indirect mechanism where the buyer does not have to report true type, there is appropriate direct mechanism (revelation principle). Furthermore, we bring characterizations of mechanisms that were necessary in pursuit of optimizing mechanism. At the end it turned out that the beginning strategy was the best choice because the seller’s objective function is linear because there is no risk. After that, we have moved to nonlinear pricing i.e., pricing divisible good, for example sugar. The outcome of this complex problem isn’t so trivial because buyer’s utility is no longer linear because of further defined function ν which enables us to manipulate. Based on assumptions that distribution of random variable for reported type is regular, we have got effective way for setting mechanism that maximizes profit. At the end of the chapter we have processed an example that shows that the introduced function ν gave as a discount on the amount. The second chapter process Bayesian mechanism where in the game we look for Bayes-Nash equilibrium between players. Chapter starts with observing an auction of one indivisible good where the buyer gives his good on an auction for N > 2 N ≥ 2 Less Keywords
dizajn mehanizma
teorija igara
direktni mehanizam
optimizirajući mehanizam
Bayesovi mehanizmi
Bayes-Nash ravnoteža
javna dobra
Kuch-Tucherov teorem
Keywords (english)
mechanism design
game theory
direct mechanism
optimizing mechanism
Bayesian mechanism
Bayes-Nash equilibrium
public goods
Kuch-Tucherov theorem
Language croatian URN:NBN urn:nbn:hr:217:261528 Study programme Title: Finance and Business Mathematics Type of resource Text File origin Born digital Access conditions Open access Terms of use Created on 2019-02-18 13:55:30
