Kooperativne evolucijske igre na mreži

master's thesis

• Title (english): Evolutionary cooperative games on networks
• Author: Petar Fumić
• Mentor: Vinko Zlatić (mentor)
• Mentor: Denis Sunko (mentor)
• Committee member: Denis Sunko (predsjednik povjerenstva)
• Committee member: Vinko Zlatić (član povjerenstva)
• Committee member: Matko Milin (član povjerenstva)
• Committee member: Hrvoje Buljan (član povjerenstva)
• Committee member: Davor Horvatić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2017-10-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

Zadatak rada je nalaženja kritičnih parametara za uspjeh kooperacije. Razmatramo evolucijske igre na mrežama, konkretno, zarobljeničku dilemu i igru javnog dobra. To je matematički zahtjevan problem koji općenito nije moguće riješiti analitički. Pokazat ćemo da postoji rješenje za proizvoljnu strukturu mreže ako smo u režimu slabe selekcije. Rješenje se bazira na koalescentnoj teoriji pomoću koje možemo izračunati prosječno vrijeme do susreta dva nasumična šetača na mreži. Naći ćemo vrijednosti kritičnih parametara za velik broj mreža te vidjeti kako struktura utječe na ishod različitih evolucionarnih igara. Također, pokazati ćemo da se analitički dobiveni rezultati dobro poklapaju s rezultatima dobivenim numeričkim simulacijama.

Abstract (english)

The goal of this paper is finding the critical cooperation parameters. We are considering evolutionary games on networks, specifically, the prisoner’s dilemma and the public goods game. Finding the critical parameters is mathematically non-trivial problem which is generally difficult to solve analytically. We will show that there exists a solution for an arbitrary network structure. The solution is based on the coalescent theory and uses it to calculate the average meeting time of two random walks on the network. We will find the values of the critical parameters for a large number of networks and analyze the effect of structural details on the outcome of different evolutionary games. Also, we will show that analytical and numerical solutions are a good match.

• Keywords: kooperativne evolucijske igre; mreža
• Keywords (english): evolutionary cooperative games; network
• Language: croatian
• URN:NBN: urn:nbn:hr:217:616812
• Study programme: Title: Physics; specializations in: Research; Course: Research; Study programme type: university; Study level: integrated undergraduate and graduate; Academic / professional title: magistar/magistra fizike (magistar/magistra fizike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2018-03-15 16:52:34