Evolution of cooperation in stochastic games

Social dilemmas occur when incentives for individuals are misaligned with group interests 1-7 . According to the 'tragedy of the commons', these misalignments can lead to overexploitation and collapse of public resources. The resulting behaviours can be analysed with the tools of game theory 8 . The theory of direct reciprocity 9-15 suggests that repeated interactions can alleviate such dilemmas, but previous work has assumed that the public resource remains constant over time. Here we introduce the idea that the public resource is instead changeable and depends on the strategic choices of individuals. An intuitive scenario is that cooperation increases the public resource, whereas defection decreases it. Thus, cooperation allows the possibility of playing a more valuable game with higher payoffs, whereas defection leads to a less valuable game. We analyse this idea using the theory of stochastic games 16-19 and evolutionary game theory. We find that the dependence of the public resource on previous interactions can greatly enhance the propensity for cooperation. For these results, the interaction between reciprocity and payoff feedback is crucial: neither repeated interactions in a constant environment nor single interactions in a changing environment yield similar cooperation rates. Our framework shows which feedbacks between exploitation and environment - either naturally occurring or designed - help to overcome social dilemmas

Online scheduling of multiprocessor jobs with preemption

Abstract. The thesis is devoted to the problem of online preemptive scheduling of mul- tiprocessor jobs. It gives a summary of previous work on this problem. For some special variants of the problem, especially if we restrict the sizes of jobs to one and two, new results are given, both in the terms of lower bounds and in the terms of competitive al- gorithms. A previously published lower bound is showed to be computed incorrectly and it is replaced by a correct lower bound in this thesis. An algorithm is presented for the special case of four processors and sizes of jobs one and two that is conjectured to achieve the best possible competitive ratio

Výpočetní problémy vztahující se ke grafovým strukturám v evoluci

V této práci se zabýváme stochastickou hrou, která ilustruje koncept trestu a ukazuje, jak může trest navýšit kooperaci. Nejprve představíme základy teorie her, Markovových řetězců a stochastických her. Poté vysvětlíme, jak lze použít evoluci k výpočtu očekávaného množství kooperace ve hře. Na konci práce ukážeme výsledky simulací a numerických výpočtů, které potvrzují, že trest může mít pozitivní vliv na množství kooperace. Powered by TCPDF (www.tcpdf.org)In this work we study certain stochastic game that illustrates the concept of punishment and that shows how punishment can improve cooperation. First we introduce the basics of game theory, Markov chains and stochastic games. Then we explain how evolutionary dynamics can be used to evaluate the expected amount of cooperation in a game. Finally we run simulations and do some numerical computations that show how punishment can improve cooperation. Powered by TCPDF (www.tcpdf.org)Department of Applied MathematicsKatedra aplikované matematikyMatematicko-fyzikální fakultaFaculty of Mathematics and Physic

Online rozvrhování víceprocesorových úloh s preempcí

Abstract. The thesis is devoted to the problem of online preemptive scheduling of mul- tiprocessor jobs. It gives a summary of previous work on this problem. For some special variants of the problem, especially if we restrict the sizes of jobs to one and two, new results are given, both in the terms of lower bounds and in the terms of competitive al- gorithms. A previously published lower bound is showed to be computed incorrectly and it is replaced by a correct lower bound in this thesis. An algorithm is presented for the special case of four processors and sizes of jobs one and two that is conjectured to achieve the best possible competitive ratio.Abstrakt. Práce se věnuje problému preemptivního online rozvrhování paralelních úloh. Podává přehled předchozích výsledků pro tento problém. Pro některé speciální varianty problému, například pro úlohy na jeden a dva procesory, poskytuje nové výsledky, jak v podobě dolních odhadů, tak v podobě kompetitivních algoritmů. Je objevena chyba v dříve publikovaném dolním odhadu a opravena na správný dolní odhad. Je navržen algoritmus pro verzi problému se čtyřmi procesory a s úlohami na jeden a dva procesory, pro který je vyslovena hypotéza, že dosahuje nejlepšího možného kompetitivního poměru.Informatický ústav Univerzity KarlovyComputer Science Institute of Charles UniversityFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Computational Problems Related to Graph Structures in Evolution

In this work we study certain stochastic game that illustrates the concept of punishment and that shows how punishment can improve cooperation. First we introduce the basics of game theory, Markov chains and stochastic games. Then we explain how evolutionary dynamics can be used to evaluate the expected amount of cooperation in a game. Finally we run simulations and do some numerical computations that show how punishment can improve cooperation. Powered by TCPDF (www.tcpdf.org