KOLAWOLE, A. Rozhodovací modely na sítích [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2024.

Posudek vedoucího

Kisela, Tomáš

The main goals of the thesis were focused on introducing game theory model (Prisoner's dilemma was selected) on networks and exploring its basic properties through simulation. The student worked quite indepently and showed real interest in the classical prisoner's dilemma and its variations with altruism, visibility and sestitivity, which is visible from detail elaborations in chapter 2 devoted to this topic. Chapters 2 and 3 provide a good overview and show the effort that the author put into the thesis, although some points are unnecessary regarding the goals (some details on prisoner's dilemma not utilized on networks, description of BA and small worlds networks that are not used afterwards...), and some points that are directly related to the thesis goals are not explained sufficiently (e.g. iterated prisoner's dilemma). The goals of the thesis are addressed mainly in chapters 4 and 5 which unfortunately form a minor part of the thesis. In these parts I have the most points to raise. For example, in chapter 4, the algorithm is not clearly explained as it does not include discussion of the agents' decision criteria (how the cooperation level is calculated, how the agent decides to cooperate or defect?). Moreover, there seems to be a confusion regarding the range for altruism parameter: In chapter 2 it is mentioned from 0 to 1, in chapter 4 it is initialized between -1 and 1 and the unnumbered formula after (4.2) seems to theoretically admit all real values... Overall, it is very difficult for the reader to understand how the simulation on network practically works. In chapter 5 the author simulated scenarios with several initial altruism distributions and the results suggest very interesting network behaviour as some parameters' combinations lead to dominant cooperation and some to dominant defection. Unfortunately, the author himself does not pay attention to these differences and the above mentioned undiscussed decision criteria make it difficult to validate those results. Overall, the thesis is graphically very well processed, the references are used in proper extent. It shows the effort that the author put into it, I appreciate the striving for independence. My advice for the future projects is to more consciously work with the main goals and limit sidelines to increase both clarity and impact of the presented results. I recommend the thesis for the defence with the grade C.

Posudek oponenta

Hrdina, Jaroslav

The work is devoted to games on networks; it contains theoretical parts and practical results, including  implementation. Individual chapters have different qualities. The theoretical foundations contain errors, and the interpretation is sometimes confusing. It is not clear overall what is the result of the work.   The author speaks about sentences (page 17), but in my opinion, it is not a repeating strategy; he just describes Table 2.1. and only identifies 4 possible strategy profiles as T,R,P,S. The chapter goes on to discuss how the interplay between parameters affects the existence of NE.  In hypothesis 1 it is not clear how C can be a function of parameters T,R,P,S and further reading became complicated. In (2.16), he drops \partilal. In (2.21), there cannot be a reference to the table as an equation coefficient. The table contains a spearman`s rank coefficient, but it is not defined. Page 38 and later, illogical and inconsistent use of the symbol \equiv. There is confusion in the terms oriented and non-oriented graph. We have to add to the symmetry to have an unoriented graph. Remark 3.1:  By definition, the graph is oriented and edge-weighted, and additional conditions make it unoriented and unevaluated fig 3.1 poor image quality The chaotic use of two terms, graph and network, makes it unclear if they mean the same thing or if one means oriented and the other is an unoriented graph. But the series of definitions excludes both possibilities. In def 3.3 the term is described as network, but it refers to definition 3.1 where the term is described as graph and it is an oriented graph, but def 3.3 assumes it is not oriented. Definition 3.5 again refers to the term graph but assumes it is non-oriented, so the definition is unconsistent with def 3.1, and definition 3.6 again refers to the term network. Definition 3.7 is completely confusing. First of all, it should contain something like "if there exists A,B such that ....", but mainly it assumes an unoriented graph in the first half and an oriented graph in the second half. The author is aware of this confusion and tries to solve it with a note on page 40 below. I do not think, however, that it is possible to say in a mathematical text that by Cartesian product, we mean a set of two-element subsets. Definition 3.9 should follow 3.10 and be more formal. Def 3.17 could be more formal, but it is clear what the term means. Figure 3.4 looks like a series of three graphs, and it is not clear how the edges are manifested in the graph with any probability. It is not clear whether the ER model is a graph with the probability of edges or a method of creating graphs based on probabilities. The next chapter, the BA model, suggests the latter but does not explain how the generation works. missing citation page 46 the work ends with a series of implementations based on Matlab codes, but it is not clear on which parameters the codes were run, and it is not possible to verify them.  Overall, this is a rather weak work on a very interesting topic. The disadvantage is the larger number of inaccuracies. The overall level of the work is also poor, even at the level of the BUT template. Wrongly indented Abstract. The mix of English and Czech in the citation. A line containing only a dot in the introduction. Positive is the work with literature.

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