Phase transitions in the public goods game on networks

V magistrskem delu preučujemo evolucijo kooperacije v igri javnih dobrin na dveh kvalitativno različnih interakcijskih mrežah ob različnih začetnih pogojih. S pomočjo numeričnih simulacij, minimalističnih modelnih pristopov in metode Monte Carlo se osredotočimo na efekte, ki so odvisni od različne velikosti skupin agentov in različnega sinergijskega faktorja. Modelu dodamo še dodatne strategije individualnega kaznovanja in nagrajevanja, pri čemer nas zanima kako vrednost kazni ali nagrade ter cena kazni ali nagrade vpliva na evolucijo strategij. Da raziščemo robustnost kooperacije med agenti prikažemo časovni potek evolucije igre javnih dobrin na 2D krajevnih slikah in tudi fazne diagrame s katerimi področja strategij natančneje opredelimo. Fazne prehode med čistimi in mešanimi strategijami kvalitativno določimo in napovemo zveznost ali nezveznost le teh. Rezultati in ugotovitve študije takšnega socio-ekonomskega problema kažejo na primernost metod statistične fizike in teorije grafov na raziskovanje izven meja splošne fizike.In this thesis, we study the evolution of cooperation in the public goods game in two qualitatively different interaction networks, and with different initial conditions. By means of Monte Carlo numerical simulations, we focus on the effects that are brought about by different group sizes of agents and by different enhancement factors that govern the multiplication of accumulated public goods. We also consider the public goods game with punishment and reward, and in particular on the impact of these additional strategies on the outcome of the evolutionary game. To investigate the evolution of cooperation, we present time courses of the spatial distribution of strategies and phase diagrams, in which we precisely define the various stable phases in different regions of the parameter space. We determine the properties of the phase transitions between pure and mixed strategies in terms of their continuity in dependence on the parameter change. We conclude that the study of socio-economic problems in general can benefit significantly from the application of methods of statistical physics