1 2 Mode and tempo of cultural evolution in video games Ivan Dmitriy Ortiz Sánchez BIOMEDICAL ENGINEERING 20 / THESIS S ´ BACHELOR Mode and tempo of cultural evolution in video games Ivan Dmitriy Ortiz Sánchez Bachelor’s Thesis UPF 2020/2021 Thesis Supervisors: Dr. Sergi Valverde Castillo, (Evolution of Technology Lab, CSIC-UPF) Dr. Salvador Duran Nebreda, (Evolution of Technology Lab, CSIC-UPF) Dedicatory To my family, for their unconditional presence and trust. To my friends and beloved, for being so far yet so close in such a different year. Finally, to Juan Ortiz and to Isabel Peñarroya. In Memoriam. Acknowledgments I would like to wholeheartedly thank my supervisors, Sergi and Salva, and acknowledge their help, advice and patience during this research. It has been a fascinating and worth- while experience and, without their time and enthusiasm, this study would have not been the same. I am also thankful for all the knowledge about cultural evolution and network theory and the computational methods they have taught me during the research, which have given me a better comprehension of such a beautiful and engaging field of research. Summary/Abstract The mechanisms of biological evolution also apply to artificial phenomena such as culture and technology, and the evolution of video games through history has been shaped by the evolution of technology itself. In particular, the so-called speedruns, which consist in completing video games in the least time possible, have become remarkably popular recently. Since the evolution of performance in video games has never been quantita- tively assessed, in the present study, we wonder whether there are universal patterns in the way speedrunning has evolved through video game history. Specifically, we aim to identify relations between performance improvement and the size and structure of the player community. Thus, a reliable dataset with the results of official speedruns has been manipulated and analyzed. First, we describe the dynamics of performance improvement and growth of the community since its origin. Second, we explore the effects of commu- nity structure with a game-player bipartite network framework and an infectious model of strategy and information propagation. Finally, we relate the model to the actual data and establish linkages between the properties of the network and the learning dynamics. Our results show how the growth of the community and the evolution of performance follow exponential descriptions and how the rank-ordered distribution of players accord- ing to their number of playthroughs follows a power law-like behaviour. A first minimal network model to describe the properties of the community is also provided. This study lays the foundation for a quantitative application of biological and evolutionary models to the video game field. Keywords computational modelling, complex networks, infection models, cultural evolution, learn- ing, video games, speedrunning Preface The evolution of video games has been shaped by the evolution of technology itself, and, in the current context, video games are highly influential. The relevance of the role they play in our society, not only for the youth but for people of all ages, especially with the rise of streaming platforms and the so-called speedrunning community, is undeniable. Cultural patterns are evolutionary, and those mechanisms which define biological evo- lution have been proven to work with cultural phenomena as well, and allow to either understand the past or forecast the future. Given the mathematical tools and the biologi- cal concepts learnt through the Biomedical Engineering degree, an application of cultural evolution methods to the video game field in order to assess how it has changed through time would represent a first insight into the topic from an evolutionary perspective, and a relevant scientific contribution. Given this context, we are motivated to explore video game performance and the structure of the community of players and to try to identify universal patterns in the way they have evolved which could be explained by means of simple mathematical descriptions, and to provide a basis for further analyses in such an unexplored and relatively novel area. Index 1 Introduction1 2 Stage I. Evolution of speedrunning and video game performance6 2.1 Methods.....................................6 2.1.1 The data set...............................6 2.2 Results......................................6 2.2.1 A DGBD model for cultural evolution in video games........6 2.2.2 An exponential decay model for performance improvement..... 10 3 Stage II. A minimal model for the structural growth of the community 12 3.1 Methods..................................... 12 3.1.1 The model................................ 12 3.1.2 Structural analysis of the community................. 15 3.2 Results...................................... 18 3.2.1 Properties of the community as a network.............. 18 3.2.2 Graph visualization........................... 23 4 Stage III. Community structure and learning capability of players 25 4.1 Methods..................................... 25 4.1.1 Learning capability as a node-specific property............ 25 4.2 Results...................................... 25 4.2.1 Influence of learning capability on the community.......... 25 4.2.2 A structural transition in time..................... 27 5 Discussion 28 Bibliography 31 Supplementary information 33 S.I Generation of multiple components in simulations.............. 33 S.II Learning capability............................... 34 List of Figures 1 Growth in the number of speedruns and player productivity........7 2 Rank-ordered distribution of players and DGBD fit.............8 3 Rank-ordered distribution of games and DGBD fit..............9 4 Example of evolution of performance in a video game............ 10 5 Probability density of learning rates...................... 11 6 Rank-ordered distribution of players and games; empirical and simulated. 15 7 Node degree occurrence distribution...................... 19 8 Average node degree in projections...................... 20 9 Centrality occurrence distribution in bipartite graphs............ 21 10 Centrality occurrence distribution in projections............... 21 11 Global efficiency of communities........................ 22 12 Number of edges and modularity in projections............... 22 13 Connectance of communities.......................... 23 14 Graph visualization: real and simulated.................... 23 15 Learning capability and node-specific properties of the community..... 26 16 Graph visualization: community evolution between 2012 and 2015..... 27 S1 Graph visualization: comparison in terms of ρ ................ 33 S2 Mean learning rate and node-specific properties of the community..... 34 S3 Influence of players with zero learning capability............... 35 List of Tables No tables have been included in this document. 1 Introduction The evolution of living beings is characterized by certain mechanisms which act in favour of the survival of those organisms who are better adapted to the environment, namely reproduction (and inheritance of genetic traits), mutation and selection, principally. Re- production allows the persistence of living beings through multiple generations, mutation is a source of randomness and, thus, allows to introduce change and innovation. Crossover between individuals with different characteristics also allows to obtain variability. Finally, selection is a natural mechanism by means of which the environment tests living beings’ condition and adaptability and allows to survive only those with the proper character- istics. Evolution does not only allow life to persist in time but also to generate a large variability of species (and even between individuals of the same species) and organisms with high complexity. Given the potential of these natural mechanisms, the human being has wondered whether they could be applied to artificial processes, systems and dynamics. Examples of these are the so-called evolutionary algorithms or the evolution of human culture. Evolutionary algorithms use the concepts of reproduction, mutation, crossover, selection, migration, etc. to find optimal solutions to a given problem. On the other hand, it is shown that human culture is itself an evolutionary process exhibiting those mechanisms which define Darwinian evolution [1]. Culture can be defined as group-typical behaviour patterns shared by members of a com- munity that relies on socially learned and transmitted information [2,3]. In cultural evolution, apart from culture itself, the concept of cumulative culture is also important, which refers to the fact that cultural traits are based on the legacy from previous gener- ations and the knowledge about that legacy [4]. Hence, cumulative culture means that culture can be spread through generations and grow, but it also depends on the population itself, since cultural traits must be learned properly in order to avoid losses through time. Cumulative culture also implies that the accumulated knowledge overcomes what a single individual would manage to invent on his or her own [5]. The accumulation of culture is also a punctuated process: remarkable innovations might appear after uninterrupted long technologically stable periods [3]. When a large number of innovations appear together or in rapid succession at a certain time or place, it is said that a technological transition has occurred [6,7]. Nevertheless, not many innovations manage to represent turning