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.

Music performance anxiety among full-time music students

Introduction Music performance anxiety (MPA, often referred to as "stage fright") is one of the leading severe medical problems among musicians. For about 15-25% of musicians MPA is a serious problem. Particularly high levels of MPA are observed among music students. Musical performance can induce negative emotions, including anxiety, which in some individuals can approach extreme levels of terror and take the form of panic attack, impair the quality of the performance, lead to avoidance of performance situations, and consequently have debilitating effects on the career. Coping efforts used by musicians in their attempts to manage MPA, such as sedatives, alcohol, and β-blockers can have deleterious health side-effects. Music ranks high in the cultural and economic life of Switzerland. In ten university music schools, students from all around the world are educated to become professional musicians. Despite the importance of musical education in Switzerland, data concerning the phenomenon of MPA are largely lacking. Goal and Methods The main goal of this research was to survey the occurrence, experience, and management of MPA among full-time music students in French Swiss conservatories. A questionnaire was developed based on the literature and interviews with music students and teachers and distributed to all the students of the conservatories of Fribourg, Geneva, Lausanne, and Neuchâtel in the spring 2007. 194 students (61% women) returned the questionnaire. Results The size of the problem: MPA is a major problem for 1/3 of the students (ranks 3 and 4). The consequences of MPA: 22% and 35% of the students think that they have failed exams and auditions, respectively, because of MPA. Further, 25% of the students have already avoided performing and 11% have interrupted public performances because of MPA. Coping with MPA: 90% of the students have never used alcohol prior to performing, whereas 97% and 81%, respectively, have never used recreation drugs and medication. The majority of students use relaxation exercises, respiratory exercises, and meditation techniques to prepare themselves. About ¾ of the students think that the use of alcohol and recreational drugs to manage MPA is never justified. 53% of the students think that the use of medication is justified on some occasions. Need for information and support: 66% of the students would like to receive more support and help to cope with music performance situations. This support should mainly come from their teachers and specialists. 53% of the students know nothing or little about possible means for the management of MPA. About 50% consider themselves not at all or little informed about the possible risks associated with the consumption of alcohol, recreational drugs, and medication for the management of performance situations. 89% would like to know more about MPA and 94% think that this topic should be discussed much more in their musical education at the conservatory. Conclusions The results of this survey indicate that MPA is a major problem for 1/3 of the students with serious consequences on their career. There is a huge need for more information and support on how to manage the stress due to performance situations. The use of alcohol, recreational drugs, and medication is modest but the students are poorly informed about possible side-effects of these coping strategies. It seems clear that more should be done in the French Swiss conservatories about music performance anxiety to inform, educate, and prepare the students for their future professional career.

The Limits of Discrete Time Repeated Games:Some Notes and Comments

This paper studies the limits of discrete time repeated games with public monitoring. We solve and characterize the Abreu, Milgrom and Pearce (1991) problem. We found that for the "bad" ("good") news model the lower (higher) magnitude events suggest cooperation, i.e., zero punishment probability, while the highrt (lower) magnitude events suggest defection, i.e., punishment with probability one. Public correlation is used to connect these two sets of signals and to make the enforceability to bind. The dynamic and limit behavior of the punishment probabilities for variations in ... (the discount rate) and ... (the time interval) are characterized, as well as the limit payo¤s for all these scenarios (We also introduce uncertainty in the time domain). The obtained ... limits are to the best of my knowledge, new. The obtained ... limits coincide with Fudenberg and Levine (2007) and Fudenberg and Olszewski (2011), with the exception that we clearly state the precise informational conditions that cause the limit to converge from above, to converge from below or to degenerate. JEL: C73, D82, D86. KEYWORDS: Repeated Games, Frequent Monitoring, Random Pub- lic Monitoring, Moral Hazard, Stochastic Processes.

The role of role uncertainty in modified dictator games

We compare behavior in modified dictator games with and without role uncertainty. Subjectschoose between a selfish action, a costly surplus creating action (altruistic behavior) and acostly surplus destroying action (spiteful behavior). While costly surplus creating actions are themost frequent under role uncertainty (64%), selfish actions become the most frequent withoutrole uncertainty (69%). Also, the frequency of surplus destroying choices is negligible with roleuncertainty (1%) but not so without it (11%). A classification of subjects into four differenttypes of interdependent preferences (Selfish, Social Welfare maximizing, Inequity Averse andCompetitive) shows that the use of role uncertainty overestimates the prevalence of SocialWelfare maximizing preferences in the subject population (from 74% with role uncertainty to21% without it) and underestimates Selfish and Inequity Averse preferences. An additionaltreatment, in which subjects undertake an understanding test before participating in theexperiment with role uncertainty, shows that the vast majority of subjects (93%) correctlyunderstand the payoff mechanism with role uncertainty, but yet surplus creating actions weremost frequent. Our results warn against the use of role uncertainty in experiments that aim tomeasure the prevalence of interdependent preferences.

Choice of partners in multiple two-person prisoner's dilemma games: An experimental study

We examine the effect of unilateral and mutual partner selection in the context of prisoner's dilemmas experimentally. Subjects play simultaneously several finitely repeated two-person prisoner's dilemma games. We find that unilateral choice is the best system. It leads to low defection and fewer singles than with mutual choice. Furthermore, with the unilateral choice setup we are able to show that intendingdefectors are more likely to try to avoid a match than intending cooperators. We compare our results of multiple games with single game PD-experiments and find no difference in aggregate behavior. Hence the multiple game technique is robust and might therefore be an important tool in the future for testing the use of mixed strategies.

Measuring strategic uncertainty in coordination games

This paper explores three aspects of strategic uncertainty: its relation to risk, predictability of behavior and subjective beliefs of players. In a laboratory experiment we measure subjects certainty equivalents for three coordination games and one lottery. Behavior in coordination games is related to risk aversion, experience seeking, and age.From the distribution of certainty equivalents we estimate probabilities for successful coordination in a wide range of games. For many games, success of coordination is predictable with a reasonable error rate. The best response to observed behavior is close to the global-game solution. Comparing choices in coordination games with revealed risk aversion, we estimate subjective probabilities for successful coordination. In games with a low coordination requirement, most subjects underestimate the probability of success. In games with a high coordination requirement, most subjects overestimate this probability. Estimating probabilistic decision models, we show that the quality of predictions can be improved when individual characteristics are taken into account. Subjects behavior is consistent with probabilistic beliefs about the aggregate outcome, but inconsistent with probabilistic beliefs about individual behavior.

Max-convex decompositions for cooperative TU games

We show that any cooperative TU game is the maximum of a finite collection of convex games. This max-convex decomposition can be refined by using convex games with non-negative dividends for all coalitions of at least two players. As a consequence of the above results we show that the class of modular games is a set of generators of the distributive lattice of all cooperative TU games. Finally, we characterize zero-monotonic games using a strong max-convex decomposition

Max-convex decompositions for cooperative TU games

We show that any cooperative TU game is the maximum of a finite collection of convex games. This max-convex decomposition can be refined by using convex games with non-negative dividends for all coalitions of at least two players. As a consequence of the above results we show that the class of modular games is a set of generators of the distributive lattice of all cooperative TU games. Finally, we characterize zero-monotonic games using a strong max-convex decomposition

Axiomatization of the nucl eolus of assignment games

On the domain of general assignment games (with possible reservation prices) the core is axiomatized as the unique solution satisfying two consistency principles: projection consistency and derived consistency. Also, an axiomatic characterization of the nucleolus is given as the unique solution that satisfies derived consistency and equal maximum complaint between groups. As a consequence, we obtain a geometric characterization of the nucleolus. Maschler et al. (1979) provide a geometrical characterization for the intersection of the kernel and the core of a coalitional game, showing that those allocations that lie in both sets are always the midpoint of certain bargaining range between each pair of players. In the case of the assignment game, this means that the kernel can be determined as those core allocations where the maximum amount, that can be transferred without getting outside the core, from one agent to his / her optimally matched partner equals the maximum amount that he / she can receive from this partner, also remaining inside the core. We now prove that the nucleolus of the assignment game can be characterized by requiring this bisection property be satisfied not only for optimally matched pairs but also for optimally matched coalitions. Key words: cooperative games, assignment game, core, nucleolus

On reduced games and the lexmax solution

For a family of reduced games satisfying a monotonicity property, we introduced the reduced equal split-off set, an extension of the equal split-off set (Branzei et. al, 2006), and study its relation with the core. Regardless of the reduction operation we consider, the intersection between both sets is either empty or a singleton containing the lexmax solution (Arin et al., 2008). We also provide a procedure for computing the lexmax solution for a class of games that includes games with large core (Sharkey, 1982). [JEL Classification: C71]

Enjoying cooperative games: The R package GameTheory

This paper focuses on cooperative games with transferable utility. We propose the computation of two solutions, the Shapley value for n agents and the nucleolus with a maximum of four agents. The current approach is also focused on conflicting claims problems, a particular case of coalitional games. We provide the computation of the most well-known and used claims solutions: the proportional, the constrained equal awards, the constrained equal losses, the Talmud and the random arrival rules. Keywords: Cooperative game, Shapley value, nucleolus, claims problem, claims rule, bankruptcy.

Individual Differences in Music Reward Experiences

Music is one of the most pleasant human experiences, even though it has no direct biological advantage. However little is known about individual differences in how people experience reward in music-related activities. The goal of the present study was to describe the main facets of music experience that could explain the variance observed in how people experience reward associated with music. To this end we developed the Barcelona Music Reward Questionnaire (BMRQ), which was administrated to three large samples. Our results showed that the musical reward experience can be decomposed into five reliable factors: Musical Seeking, Emotion Evocation, Mood Regulation, Social Reward, and Sensory-Motor. These factors were correlated with socio-demographic factors and measures of general sensitivity to reward and hedonic experience. We propose that the five-factor structure of musical reward experience might be very relevant in the study of psychological and neural bases of emotion and pleasure associated to music.

Flippable Pairs and Subset Comparisons in Comparative Probability Orderings and Related Simple Games

We show that every additively representable comparative probability order on n atoms is determined by at least n - 1 binary subset comparisons. We show that there are many orders of this kind, not just the lexicographic order. These results provide answers to two questions of Fishburn et al (2002). We also study the flip relation on the class of all comparative probability orders introduced by Maclagan. We generalise an important theorem of Fishburn, Peke?c and Reeds, by showing that in any minimal set of comparisons that determine a comparative probability order, all comparisons are flippable. By calculating the characteristics of the flip relation for n = 6 we discover that the regions in the corresponding hyperplane arrangement can have no more than 13 faces and that there are 20 regions with 13 faces. All the neighbours of the 20 comparative probability orders which correspond to those regions are representable. Finally we define a class of simple games with complete desirability relation for which its strong desirability relation is acyclic, and show that the flip relation carries all the information about these games. We show that for n = 6 these games are weighted majority games.

Multi-Prover and parallel repetition in non-classical interactive games

Depuis l’introduction de la mécanique quantique, plusieurs mystères de la nature ont trouvé leurs explications. De plus en plus, les concepts de la mécanique quantique se sont entremêlés avec d’autres de la théorie de la complexité du calcul. De nouvelles idées et solutions ont été découvertes et élaborées dans le but de résoudre ces problèmes informatiques. En particulier, la mécanique quantique a secoué plusieurs preuves de sécurité de protocoles classiques. Dans ce m´emoire, nous faisons un étalage de résultats récents de l’implication de la mécanique quantique sur la complexité du calcul, et cela plus précisément dans le cas de classes avec interaction. Nous présentons ces travaux de recherches avec la nomenclature des jeux à information imparfaite avec coopération. Nous exposons les différences entre les théories classiques, quantiques et non-signalantes et les démontrons par l’exemple du jeu à cycle impair. Nous centralisons notre attention autour de deux grands thèmes : l’effet sur un jeu de l’ajout de joueurs et de la répétition parallèle. Nous observons que l’effet de ces modifications a des conséquences très différentes en fonction de la théorie physique considérée.

De la relation d’aide à la rencontre créative : le récit numérique comme outil de reconnaissance mutuelle

Cette recherche exploratoire vise à documenter, du point de vue des intervenants, les conditions nécessaires à la mise en place de projets utilisant des outils de narrativité numérique, de même que les principaux apports de ces outils à l’intervention. Ces outils peuvent être des récits numériques qui sont de courtes vidéos (deux à cinq minutes) intégrant images, musique, texte, voix et animation, ou encore de courts fichiers audio, aussi appelés podcasting ou baladodiffusion. Il peut aussi s’agir de jeux vidéo interactifs ou d’un montage vidéo à partir d’extraits de témoignages. Dans un contexte où les pratiques d’intervention, dans les services publics en particulier, sont de plus en plus normées et standardisées, une recherche qui explore des outils d’intervention recourant à la créativité s’avère des plus pertinentes. Par ailleurs, ce champ n’a été que très peu exploré en service social jusqu’à maintenant. Des entrevues semi-dirigées ont été menées auprès de huit intervenants ayant utilisé ces outils dans leur pratique. L’analyse de leurs propos met d’abord en lumière les conditions nécessaires à la réalisation de ce type de projet, de même que les questions éthiques qui les accompagnent. Ensuite, du côté des principaux apports de ces outils, ils se situent, d’une part, dans le processus créatif collaboratif. Celui-ci permet d’enrichir l’intervention en donnant un espace de parole plus libre où intervenants et usagers créent des liens qui modifient le rapport hiérarchique entre aidant et aidé. D’autre part, l’attention professionnelle accordée à la réalisation des produits et à leur diffusion contribue à donner une plus grande visibilité à des personnes souvent exclues de l’espace public. Ainsi, en plus d’explorer les apports d’un outil artistique à l’intervention, cette recherche permet également d’analyser les enjeux de visibilité et de reconnaissance associés à l’utilisation de médias participatifs.