Gains from switching and evolutionary stability in multi-player matrix games.

In this paper we unify, simplify, and extend previous work on the evolutionary dynamics of symmetric N-player matrix games with two pure strategies. In such games, gains from switching strategies depend, in general, on how many other individuals in the group play a given strategy. As a consequence, the gain function determining the gradient of selection can be a polynomial of degree N-1. In order to deal with the intricacy of the resulting evolutionary dynamics, we make use of the theory of polynomials in Bernstein form. This theory implies a tight link between the sign pattern of the gains from switching on the one hand and the number and stability of the rest points of the replicator dynamics on the other hand. While this relationship is a general one, it is most informative if gains from switching have at most two sign changes, as is the case for most multi-player matrix games considered in the literature. We demonstrate that previous results for public goods games are easily recovered and extended using this observation. Further examples illustrate how focusing on the sign pattern of the gains from switching obviates the need for a more involved analysis.

Managing the size of the Olympic Games

The last two decades have seen dramatic increases in the size and scope of the Summer Olympic Games. In many ways, London 2012 reached even higher summits than the Beijing Games in 2008. This growth is a major challenge for the Olympics and its future organizers, as it is making the Games increasingly difficult to stage and has greatly reduced the number of cities capable of hosting them. This study shows how various participation and organization indicators have expanded over six Olympiads, from Barcelona 1992 to London 2012, and examines the reasons for this growth. It suggests ways of reducing the size of the Summer Olympic Games in order to make them more manageable and to encourage candidatures from smaller cities and countries.

Using group role-playing games with gifted children and adolescents: A psychosocial intervention model

Gifted children develop asynchronously, often advanced for their age cognitively, but at or between their chronological and mental ages socially and emotionally (Robinson, 2008). In order to help gifted children and adolescents develop and practice social and emotional self-regulation skills, we investigated the use of an Adlerian play therapy approach during pen-and-paper role-playing games. Additionally, we used Goffman's (1961, 1974) social role identification and distance to encourage participants to experiment with new identities. Herein, we propose a psychosocial model of interactions during role-playing games based on Goffman's theory and Adlerian play therapy techniques, and suggest that role-playing games are an effective way of intervening with gifted children and adolescents to improve their intra- and interpersonal skills. We specifically targeted intrapersonal skills of exercising creativity, becoming self-aware, and setting individual goals by raising participants' awareness of their privately logical reasons for making decisions and their levels of social interest. We also targeted their needs and means of seeking significance in the group to promote collaboration and interaction skills with other gifted peers through role analysis, embracement, and distancing. We report results from a case study and conclude that role-playing games deserve more attention, both from researchers and clinical practitioners, because they encourage change while improving young clients' social and emotional development.

Religions in Play. Games, Rituals, and Virtual Worlds

Often dismissed as "not serious," the notion of play has nevertheless been at the center of classical theories of religion and ritual (Huizinga, Caillois, Turner, Staal, etc.). What can be retained of these theories for the contemporary study of religions? Can a study of "play" or "game" bring new perspectives for the study of religions? The book deals with the history of games and their relation to religions, the links between divination and games, the relations between sport and ritual, the pedagogical functions of games in religious education, and the interaction between games, media and religions. Richly illustrated, the book contributes to the study of religions, to ritual, game and media studies, and addresses an academic as well as a general public.

Evolutionary games on complex networks : the emergence and maintenance of cooperation

Abstract The object of game theory lies in the analysis of situations where different social actors have conflicting requirements and where their individual decisions will all influence the global outcome. In this framework, several games have been invented to capture the essence of various dilemmas encountered in many common important socio-economic situations. Even though these games often succeed in helping us understand human or animal behavior in interactive settings, some experiments have shown that people tend to cooperate with each other in situations for which classical game theory strongly recommends them to do the exact opposite. Several mechanisms have been invoked to try to explain the emergence of this unexpected cooperative attitude. Among them, repeated interaction, reputation, and belonging to a recognizable group have often been mentioned. However, the work of Nowak and May (1992) showed that the simple fact of arranging the players according to a spatial structure and only allowing them to interact with their immediate neighbors is sufficient to sustain a certain amount of cooperation even when the game is played anonymously and without repetition. Nowak and May's study and much of the following work was based on regular structures such as two-dimensional grids. Axelrod et al. (2002) showed that by randomizing the choice of neighbors, i.e. by actually giving up a strictly local geographical structure, cooperation can still emerge, provided that the interaction patterns remain stable in time. This is a first step towards a social network structure. However, following pioneering work by sociologists in the sixties such as that of Milgram (1967), in the last few years it has become apparent that many social and biological interaction networks, and even some technological networks, have particular, and partly unexpected, properties that set them apart from regular or random graphs. Among other things, they usually display broad degree distributions, and show small-world topological structure. Roughly speaking, a small-world graph is a network where any individual is relatively close, in terms of social ties, to any other individual, a property also found in random graphs but not in regular lattices. However, in contrast with random graphs, small-world networks also have a certain amount of local structure, as measured, for instance, by a quantity called the clustering coefficient. In the same vein, many real conflicting situations in economy and sociology are not well described neither by a fixed geographical position of the individuals in a regular lattice, nor by a random graph. Furthermore, it is a known fact that network structure can highly influence dynamical phenomena such as the way diseases spread across a population and ideas or information get transmitted. Therefore, in the last decade, research attention has naturally shifted from random and regular graphs towards better models of social interaction structures. The primary goal of this work is to discover whether or not the underlying graph structure of real social networks could give explanations as to why one finds higher levels of cooperation in populations of human beings or animals than what is prescribed by classical game theory. To meet this objective, I start by thoroughly studying a real scientific coauthorship network and showing how it differs from biological or technological networks using divers statistical measurements. Furthermore, I extract and describe its community structure taking into account the intensity of a collaboration. Finally, I investigate the temporal evolution of the network, from its inception to its state at the time of the study in 2006, suggesting also an effective view of it as opposed to a historical one. Thereafter, I combine evolutionary game theory with several network models along with the studied coauthorship network in order to highlight which specific network properties foster cooperation and shed some light on the various mechanisms responsible for the maintenance of this same cooperation. I point out the fact that, to resist defection, cooperators take advantage, whenever possible, of the degree-heterogeneity of social networks and their underlying community structure. Finally, I show that cooperation level and stability depend not only on the game played, but also on the evolutionary dynamic rules used and the individual payoff calculations. Synopsis Le but de la théorie des jeux réside dans l'analyse de situations dans lesquelles différents acteurs sociaux, avec des objectifs souvent conflictuels, doivent individuellement prendre des décisions qui influenceront toutes le résultat global. Dans ce cadre, plusieurs jeux ont été inventés afin de saisir l'essence de divers dilemmes rencontrés dans d'importantes situations socio-économiques. Bien que ces jeux nous permettent souvent de comprendre le comportement d'êtres humains ou d'animaux en interactions, des expériences ont montré que les individus ont parfois tendance à coopérer dans des situations pour lesquelles la théorie classique des jeux prescrit de faire le contraire. Plusieurs mécanismes ont été invoqués pour tenter d'expliquer l'émergence de ce comportement coopératif inattendu. Parmi ceux-ci, la répétition des interactions, la réputation ou encore l'appartenance à des groupes reconnaissables ont souvent été mentionnés. Toutefois, les travaux de Nowak et May (1992) ont montré que le simple fait de disposer les joueurs selon une structure spatiale en leur permettant d'interagir uniquement avec leurs voisins directs est suffisant pour maintenir un certain niveau de coopération même si le jeu est joué de manière anonyme et sans répétitions. L'étude de Nowak et May, ainsi qu'un nombre substantiel de travaux qui ont suivi, étaient basés sur des structures régulières telles que des grilles à deux dimensions. Axelrod et al. (2002) ont montré qu'en randomisant le choix des voisins, i.e. en abandonnant une localisation géographique stricte, la coopération peut malgré tout émerger, pour autant que les schémas d'interactions restent stables au cours du temps. Ceci est un premier pas en direction d'une structure de réseau social. Toutefois, suite aux travaux précurseurs de sociologues des années soixante, tels que ceux de Milgram (1967), il est devenu clair ces dernières années qu'une grande partie des réseaux d'interactions sociaux et biologiques, et même quelques réseaux technologiques, possèdent des propriétés particulières, et partiellement inattendues, qui les distinguent de graphes réguliers ou aléatoires. Entre autres, ils affichent en général une distribution du degré relativement large ainsi qu'une structure de "petit-monde". Grossièrement parlant, un graphe "petit-monde" est un réseau où tout individu se trouve relativement près de tout autre individu en termes de distance sociale, une propriété également présente dans les graphes aléatoires mais absente des grilles régulières. Par contre, les réseaux "petit-monde" ont, contrairement aux graphes aléatoires, une certaine structure de localité, mesurée par exemple par une quantité appelée le "coefficient de clustering". Dans le même esprit, plusieurs situations réelles de conflit en économie et sociologie ne sont pas bien décrites ni par des positions géographiquement fixes des individus en grilles régulières, ni par des graphes aléatoires. De plus, il est bien connu que la structure même d'un réseau peut passablement influencer des phénomènes dynamiques tels que la manière qu'a une maladie de se répandre à travers une population, ou encore la façon dont des idées ou une information s'y propagent. Ainsi, durant cette dernière décennie, l'attention de la recherche s'est tout naturellement déplacée des graphes aléatoires et réguliers vers de meilleurs modèles de structure d'interactions sociales. L'objectif principal de ce travail est de découvrir si la structure sous-jacente de graphe de vrais réseaux sociaux peut fournir des explications quant aux raisons pour lesquelles on trouve, chez certains groupes d'êtres humains ou d'animaux, des niveaux de coopération supérieurs à ce qui est prescrit par la théorie classique des jeux. Dans l'optique d'atteindre ce but, je commence par étudier un véritable réseau de collaborations scientifiques et, en utilisant diverses mesures statistiques, je mets en évidence la manière dont il diffère de réseaux biologiques ou technologiques. De plus, j'extrais et je décris sa structure de communautés en tenant compte de l'intensité d'une collaboration. Finalement, j'examine l'évolution temporelle du réseau depuis son origine jusqu'à son état en 2006, date à laquelle l'étude a été effectuée, en suggérant également une vue effective du réseau par opposition à une vue historique. Par la suite, je combine la théorie évolutionnaire des jeux avec des réseaux comprenant plusieurs modèles et le réseau de collaboration susmentionné, afin de déterminer les propriétés structurelles utiles à la promotion de la coopération et les mécanismes responsables du maintien de celle-ci. Je mets en évidence le fait que, pour ne pas succomber à la défection, les coopérateurs exploitent dans la mesure du possible l'hétérogénéité des réseaux sociaux en termes de degré ainsi que la structure de communautés sous-jacente de ces mêmes réseaux. Finalement, je montre que le niveau de coopération et sa stabilité dépendent non seulement du jeu joué, mais aussi des règles de la dynamique évolutionnaire utilisées et du calcul du bénéfice d'un individu.

LEVERAGING SANDBOX IMMERSIVE 3D VIRTUAL WORLDS TO DEVELOP DO-IT- YOURSELF TEACHING GAMES: IMPLEMENTATION TO MARKETING CASE STUDY TEACHING IN SECOND LIFE

Games are powerful and engaging. On average, one billion people spend at least 1 hour a day playing computer and videogames. This is even more true with the younger generations. Our students have become the < digital natives >, the < gamers >, the < virtual generation >. Research shows that those who are most at risk for failure in the traditional classroom setting, also spend more time than their counterparts, using video games. They might strive, given a different learning environment. Educators have the responsibility to align their teaching style to these younger generation learning styles. However, many academics resist the use of computer-assisted learning that has been "created elsewhere". This can be extrapolated to game-based teaching: even if educational games were more widely authored, their adoption would still be limited to the educators who feel a match between the authored games and their own beliefs and practices. Consequently, game-based teaching would be much more widespread if teachers could develop their own games, or at least customize them. Yet, the development and customization of teaching games are complex and costly. This research uses a design science methodology, leveraging gamification techniques, active and cooperative learning theories, as well as immersive sandbox 3D virtual worlds, to develop a method which allows management instructors to transform any off-the-shelf case study into an engaging collaborative gamified experience. This method is applied to marketing case studies, and uses the sandbox virtual world of Second Life. -- Les jeux sont puissants et motivants, En moyenne, un milliard de personnes passent au moins 1 heure par jour jouer à des jeux vidéo sur ordinateur. Ceci se vérifie encore plus avec les jeunes générations, Nos étudiants sont nés à l'ère du numérique, certains les appellent des < gamers >, d'autres la < génération virtuelle >. Les études montrent que les élèves qui se trouvent en échec scolaire dans les salles de classes traditionnelles, passent aussi plus de temps que leurs homologues à jouer à des jeux vidéo. lls pourraient potentiellement briller, si on leur proposait un autre environnement d'apprentissage. Les enseignants ont la responsabilité d'adapter leur style d'enseignement aux styles d'apprentissage de ces jeunes générations. Toutefois, de nombreux professeurs résistent lorsqu'il s'agit d'utiliser des contenus d'apprentissage assisté par ordinateur, développés par d'autres. Ceci peut être extrapolé à l'enseignement par les jeux : même si un plus grand nombre de jeux éducatifs était créé, leur adoption se limiterait tout de même aux éducateurs qui perçoivent une bonne adéquation entre ces jeux et leurs propres convictions et pratiques. Par conséquent, I'enseignement par les jeux serait bien plus répandu si les enseignants pouvaient développer leurs propres jeux, ou au moins les customiser. Mais le développement de jeux pédagogiques est complexe et coûteux. Cette recherche utilise une méthodologie Design Science pour développer, en s'appuyant sur des techniques de ludification, sur les théories de pédagogie active et d'apprentissage coopératif, ainsi que sur les mondes virtuels immersifs < bac à sable > en 3D, une méthode qui permet aux enseignants et formateurs de management, de transformer n'importe quelle étude de cas, provenant par exemple d'une centrale de cas, en une expérience ludique, collaborative et motivante. Cette méthode est appliquée aux études de cas Marketing dans le monde virtuel de Second Life.

Blood corticosterone levels and intersexual selection games: best-of-bad-job strategies of male common lizards

Glucocorticoids affect physiology and behaviour, reproduction and potentially sexual selection as well. Shortterm and moderate glucocorticoid elevations are suggested to be adaptive, and prolonged and high elevations may be extremely harmful. This suggests that optimal reproductive strategies, and thus sexual selection, may be dose dependent. Here, we investigate effects of moderate and high elevations of blood corticosterone levels on intra- and intersexual behaviour and mating success of male common lizards Lacerta vivipara. Females showed less interest and more aggressive behaviour towards high corticosterone males and blood corticosterone levels affected male reproductive strategy. Males of moderate and high corticosterone elevations, compared with Control males, showed increased interest (i.e., higher number of chases, tongue extrusions, and approaches) towards females and high corticosterone males initiated more copulation attempts. However, neither increased male interest nor increased copulation attempts resulted in more copulations. This provides evidence for a best-of-a-bad-job strategy, where males with higher corticosterone levels compensated for reduced female interest and increased aggressive female behaviour directed towards them, by showing higher interest and by conducting more copulation attempts. Blood corticosterone levels affected intrasexual selection as well since moderate corticosterone levels positively affected male dominance, but dominance did not affect mating success. These findings underline the importance of female mate choice and are in line with adaptive compensatory behaviours of males. They further show that glucocorticoid effects on behaviour are dose dependent and that they have important implications for sexual selection and social interactions, and might potentially affect Darwinian fitness.

Hierarchy of interactive functions in father-mother-baby three-way games

In developmental research, the family has mainly been studied through dyadic interaction. Three-way interactions have received less attention, partly because of their complexity. This difficulty may be overcome by distinguishing between four hierarchically embedded functions in three-way interactions: (1) participation (inclusion of all participants), (2) organization (partners keeping to their roles), (3) focalization (sharing a common focus) and (4) affective contact (being in tune). We document this hierarchical model on a sample of 80 families observed in the Lausanne Trilogue Play situation across four different sites. Hierarchy between functions was demonstrated by means of Guttman scalability coefficient. Given the importance of the child's development in a threesome, the pertinence of this model for family assessment is discussed.