The Local Minority Game

Ecologists and economists try to explain collective behavior in terms of competitive systems of selfish individuals with the ability to learn from the past. Statistical physicists have been investigating models which might contribute to the understanding of the underlying mechanisms of these systems. During the last three years one intuitive model, commonly referred to as the Minority Game, has attracted broad attention. Powerful yet simple, the minority game has produced encouraging results which can explain the temporal behaviour of competitive systems. Here we switch the interest to phenomena due to a distribution of the individuals in space. For analyzing these effects we modify the Minority Game and the Local Minority Game is introduced. We study the system both numerically and analytically, using the customary techniques already developped for the ordinary Minority Game

Solvent-induced micelle formation in a hydrophobic interaction model

We investigate the aggregation of amphiphilic molecules by adapting the two-state Muller-Lee-Graziano model for water, in which a solvent-induced hydrophobic interaction is included implicitly. We study the formation of various types of micelle as a function of the distribution of hydrophobic regions at the molecular surface. Successive substitution of non-polar surfaces by polar ones demonstrates the influence of hydrophobicity on the upper and lower critical solution temperatures. Aggregates of lipid molecules, described by a refinement of the model in which a hydrophobic tail of variable length interacts with different numbers of water molecules, are stabilized as the length of the tail increases. We demonstrate that the essential features of micelle formation are primarily solvent-induced, and are explained within a model which focuses only on the alteration of water structure in the vicinity of the hydrophobic surface regions of amphiphiles in solution.Comment: 11 pages, 10 figures; some rearrangement of introduction and discussion sections, streamlining of formalism and general compression; to appear in Phys. Rev.

Structure-preserving desynchronization of minority games

Perfect synchronicity in $N$-player games is a useful theoretical dream, but communication delays are inevitable and may result in asynchronous interactions. Some systems such as financial markets are asynchronous by design, and yet most theoretical models assume perfectly synchronized actions. We propose a general method to transform standard models of adaptive agents into asynchronous systems while preserving their global structure under some conditions. Using the Minority Game as an example, we find that the phase and fluctuations structure of the standard game subsists even in maximally asynchronous deterministic case, but that it disappears if too much stochasticity is added to the temporal structure of interaction. Allowing for heterogeneous communication speeds and activity patterns gives rise to a new information ecology that we study in details.Comment: 6 pages, 7 figures. New version removed a section and found a new phase transitio

Statistical Mechanics of Dilute Batch Minority Games with Random External Information

We study the dynamics and statics of a dilute batch minority game with random external information. We focus on the case in which the number of connections per agent is infinite in the thermodynamic limit. The dynamical scenario of ergodicity breaking in this model is different from the phase transition in the standard minority game and is characterised by the onset of long-term memory at finite integrated response. We demonstrate that finite memory appears at the AT-line obtained from the corresponding replica calculation, and compare the behaviour of the dilute model with the minority game with market impact correction, which is known to exhibit similar features.Comment: 22 pages, 6 figures, text modified, references updated and added, figure added, typos correcte

Body Talk: Attributes to Body Weight in Eating Disorder Patients

Aims: Eating disorders are typically associated with high self-criticism of one’s body, and there are hints that patients also stigmatize other people for their weight more than healthy people do. In this study, we use questionnaire data as well as two desktop computer tasks to investigate (1) whether people with eating disorders assign negative attributes to increasing weight and (2) whether weight-related stigmatization is stronger than in healthy controls. Methods: 30 eating disorder patients and 30 healthy controls are assessed. To measure evaluation of the own body, we use a set of established questionnaires (EDE-Q, BIQ-20, EDI-2). Weight bias is assessed with the Fat Phobia Scale and with two computer tasks. In task 1, we present computer generated bodies of varying body mass index (BMI; kg/m²) and ask for ratings how much a set of adjectives apply to this body. Also, we collect valence ratings for the adjectives. In task 2, participants freely model bodies to fit the same adjectives, and we afterwards compute the bodies’ BMI. Results: We assessed 10 patients with anorexia nervosa, 5 patients with bulimia nervosa and 10 patients with binge eating disorder. Pilot analyses with seven patients suggested significant correlations between BMI and attribution of adjectives. Heavier bodies were evaluated as fatter and more pear shaped, but also as more clumsy, lazy and less goal-oriented. In task 2, the adjusted body weight was significantly correlated with valence of the adjective. Conclusions: Preliminary data show that our tasks are appropriate to capture weight stigma. More detailed analyses will be presented at the conference. A multi-center assessment is planned to enable comparisons between different diagnoses

Assessing body image disturbance in patients with anorexia nervosa using biometric self-avatars in virtual reality: Attitudinal components rather than visual body size estimation are distorted

Aims: Body image disturbance (BID) is a core symptom of Anorexia Nervosa (AN), but as yet its distinctive features are unknown. Here we use individual 3D-avatars in virtual reality to investigate contributions of weight perception and evaluation to BID. Method: We investigated n=24 women with AN and n=24 healthy controls. Based on 3D body scans, we created individual avatars for each participant. Each avatar was biometrically manipulated to gradually represent +/- 20 of the participant’s weight. Avatars were presented on a stereoscopic life-size screen and participants had to identify/adjust their current and desired body weight. Additionally, eating pathology, body dissatisfaction and self-esteem were assessed. Results: Both groups underestimated their weight, with a trend that women with AN underestimated more than controls. Both groups indicated a desired weight lower than their actual weight, and in percent of own body weight, controls even more so. Of note, the average desired body of women with AN was severely underweight, while the control’s desired body was normal weight. Correlation analyses revealed that desired body size, but not accuracy of body size estimation, was associated with eating disorder symptoms. Conclusions: Our results contradict the widespread assumption that BID is driven by overestimation and emphasize the role of attitudinal components for BID. According to our observations, clinical interventions should target a change in desired weight

Investigating body image disturbance in patients with anorexia nervosa using new biometric figure rating scales

Aims: Body image disturbance is a core symptom of anorexia nervosa (AN), and it is often assessed using Figure Rating Scales (FRS). Typically, FRS consist of a series of body drawings, and participants are asked to pick the body that corresponds best to their current and their desired body. So far, hardly any FRS is based on biometric data. Here, we use two new biometric FRS to investigate whether the presented weight spectrum influences a) accuracy in identifying the current weight and b) the desired weight in women with AN and controls. Method: Based on a statistical body model of human body shape and pose (Anguelov et al., 2005) and body scans of 2094 women from the CAESAR data set (Robinette et al., 1999) we generated biometric average bodies of women with predefined Body Mass Index (kg/m2, BMI). For the FRS 14-32 we used nine bodies with a BMI of 13.8 to 32.3 and for the FRS 18-42 we used nine bodies with BMI of 18 to 42. We administered the scales along with questionnaires assessing height, weight, body dissatisfaction, habits of social comparison and eating disorder symptoms to n= 104 women from the normal population (BMI= 23.90, SD=6.06) and n=24 women with anorexia nervosa (BMI= 15.07, SD=1.62). n=61 women from the normal population and n=18 women with AN completed both FRS. Results: In the FRS 18-42, both groups were accurate in picking the body that corresponded best to their current weight (average offset in weight steps: Controls M=0.12, SD=1.05; AN M=0.33, SD=0.97; F(1,120)=0.67, n.s.). In the FRS 14-32, women with AN were still accurate while controls significantly underestimated their size by about one step (Controls: M=-1.18, SD=0.97; AN M=0.10, SD=0.89; F(1,75)=27.32, p<.001). In both FRS, controls desired a body that was thinner than their actual body (FRS 18-42 M=-1.33, SD=1.72; FRS 14-32 M=-1.97, SD=1.23) and women with AN desired a body close to their actual weight (FRS 18-42 M=0.61, SD=0.61; FRS 18-42 M=0.36, SD=1.29). In the FRS 14-32, participants generally wanted a thinner body than in the FRS 18-42 (F(1)=23.54, p<.001). Conclusions: Our results suggest that the range of FRS can influence a) accuracy in identifying one’s weight and b) the desired weight. Different strategies, such as “comparing body features” versus “placing oneself in a range” could account for these differences. When interpreting FRS, the provided range should always be taken into account

Minority Games, Local Interactions, and Endogenous Networks

We study a local version of the Minority Game, where agents are placed on the nodes of a directed graph. Agents care about being in the minority of the group of agents they are currently linked to and employ myopic best-reply rules to choose their next-period state. We show that, in this benchmark case, the smaller the size of local networks, the larger long-run population-average payoffs. We then explore the collective behavior of the system when agents can: (i) assign weights to each link they hold and modify them over time in response to payoff signals; (ii) delete badly performing links (i.e., opponents) and replace them with randomly chosen ones. Simulations suggest that, when agents are allowed to weigh links but cannot delete/replace them, the system self-organizes into networked clusters that attain very high payoff values. These clustered configurations are not stable and can easily be disrupted, generating huge subsequent payoff drops. If, however, agents can (and are sufficiently willing to) discard badly performing connections, the system quickly converges to stable states where all agents get the highest payoff, independently of the size of the networks initially in place. Copyright Springer Science + Business Media, Inc. 2005adaptive agents, endogenous networks, local interactions, minority games,