Testing the TASP: An Experimental Investigation of Learning in Games with Unstable Equilibria

We report experiments designed to test between Nash equilibria that are stable and unstable under learning. The “TASP” (Time Average of the Shapley Polygon) gives a precise prediction about what happens when there is divergence from equilibrium under a wide class of learning processes. We study two versions of Rock-Paper-Scissors with the addition of a fourth strategy, Dumb. The unique Nash equilibrium places a weight of 1/2 on Dumb in both games, but in one game the NE is stable, while in the other game the NE is unstable and the TASP places zero weight on Dumb. Consistent with TASP, we find that the frequency of Dumb is lower and play is further from Nash in the high payoff unstable treatment than in the other treatments. However, the frequency of Dumb is substantially greater than zero in all treatments.games, experiments, TASP, learning, unstable, mixed equilibrium, fictitious play

Testing the TASP: An Experimental Investigation of Learning in Games with Unstable Equilibria

We report experiments designed to test between Nash equilibria that are stable and unstable under learning. The “TASP” (Time Average of the Shapley Polygon) gives a precise prediction about what happens when there is divergence from equilibrium under fictitious play like learning processes. We use two 4 x 4 games each with a unique mixed Nash equilibrium; one is stable and one is unstable under learning. Both games are versions of Rock-Paper-Scissors with the addition of a fourth strategy, Dumb. Nash equilibrium places a weight of 1/2 on Dumb in both games, but the TASP places no weight on Dumb when the equilibrium is unstable. We also vary the level of monetary payoffs with higher payoffs predicted to increase instability. We find that the high payoff unstable treatment differs from the others. Frequency of Dumb is lower and play is further from Nash than in the other treatments. That is, we find support for the comparative statics prediction of learning theory, although the frequency of Dumb is substantially greater than zero in the unstable treatments.games, experiments, TASP, learning, unstable, mixed equilibrium, fictitious play.

In The Valley Of Broken Hearts

https://digitalcommons.library.umaine.edu/mmb-vp/4921/thumbnail.jp

Testing the TASP: An Experimental Investigation of Learning in Games with Unstable Equilibria

We report experiments studying mixed strategy Nash equilibria that are theoretically stable or unstable under learning. The Time Average Shapley Polygon (TASP) predicts behavior in the unstable case. We study two versions of Rock-Paper-Scissors that include a fourth strategy, Dumb. The unique Nash equilibrium is identical in the two games, but the predicted frequency of Dumb is much higher in the game where the NE is stable. Consistent with TASP, the observed frequency of Dumb is lower and play is further from Nash in the high payoff unstable treatment. However, Dumb is played too frequently in all treatments

An experimental investigation of price dispersion and cycles

We report a continuous time experiment studying the classic Burdett and Judd (1983)model, whose unique Nash equilibrium (NE) features dispersed prices. Adaptive dy-namics predict that the NE is stable for one parameter set we use, and unstable foranother parameter set. The empirical price distribution turns out to be close to theNE distribution for the stable parameter set overall, but for the unstable parameterset the empirical distribution skews towards higher prices in its NE support interval.We offer an empirical definition of price cycles in terms of changes over time in robustmeasures of central tendency (median) and dispersion (interquartile range). By thatdefinition, the data exhibit persistent cycles in both treatments, but with larger cyclesfor the unstable parameters. Results are roughly similar for professional and studentsellers and for limited information treatments

Cycles and Instability in a Rock-Paper-Scissors Population Game: A Continuous Time Experiment

We report laboratory experiments that use new, visually oriented software to explore the dynamics of 3×3 games with intransitive best responses. Each moment, each player is matched against the entire population, here 8 human subjects. A “heat map” offers instantaneous feedback on current profit opportunities. In the continuous slow adjustment treatment, we see distinct cycles in the population mix. The cycle amplitude, frequency and direction are consistent with the standard learning models. Cycles are more erratic and higher frequency in the instantaneous adjustment treatment. Control treatments (using simultaneous matching in discrete time) replicate previous results that exhibit weak or no cycles. Average play is approximated fairly well by Nash equilibrium, and an alternative point prediction, “TASP” (Time Average of the Shapley Polygon), captures some regularities that Nash equilibrium misses

Causes of climate change over the historical record

This review addresses the causes of observed climate variations across the industrial period, from 1750 to present. It focuses on long-term changes, both in response to external forcing and to climate variability in the ocean and atmosphere. A synthesis of results from attribution studies based on palaeoclimatic reconstructions covering the recent few centuries to the 20th century, and instrumental data shows how greenhouse gases began to cause warming since the beginning of industrialization, causing trends that are attributable to greenhouse gases by 1900 in proxy-based temperature reconstructions. Their influence increased over time, dominating recent trends. However, other forcings have caused substantial deviations from this emerging greenhouse warming trend: volcanic eruptions have caused strong cooling following a period of unusually heavy activity, such as in the early 19th century; or warming during periods of low activity, such as in the early-to-mid 20th century. Anthropogenic aerosol forcing most likely masked some global greenhouse warming over the 20th century, especially since the accelerated increase in sulphate aerosol emissions starting around 1950. Based on modelling and attribution studies, aerosol forcing has also influenced regional temperatures, caused long-term changes in monsoons and imprinted on Atlantic variability. Multi-decadal variations in atmospheric modes can also cause long-term climate variability, as apparent for the example of the North Atlantic Oscillation, and have influenced Atlantic ocean variability. Long-term precipitation changes are more difficult to attribute to external forcing due to spatial sparseness of data and noisiness of precipitation changes, but the observed pattern of precipitation response to warming from station data supports climate model simulated changes and with it, predictions. The long-term warming has also led to significant differences in daily variability as, for example, visible in long European station data. Extreme events over the historical record provide valuable samples of possible extreme events and their mechanisms

Developing a framework for the analysis of power through depotentia

Stakeholder participation in tourism policy-making is usually perceived as providing a means of empowerment. However participatory processes drawing upon stakeholders from traditionally empowered backgrounds may provide the means of removing empowerment from stakeholders. Such an outcome would be in contradiction to the claims that participatory processes improve both inclusivity and sustainability. In order to form an understanding of the sources through which empowerment may be removed, an analytical perspective has been developed deriving from Lukes�s views of power dating from 1974. This perspective considers the concept of depotentia as the removal of �power to� without speculating upon the underlying intent and also provides for the multidimensionality of power to be examined within a single study. The application of this analytical perspective has been tested upon findings of the government-commissioned report of the Countryside and Community Research Unit in 2005. The survey and report investigated the progress of Local Access Forums in England created in response to the Countryside and Rights of Way Act 2000. Consideration of the data from this perspective permits the classification of individual sources of depotentia which can each be addressed and potentially enable stakeholder groups to reverse loss of empowerment where it has occurred

Avalanches in self-organized critical neural networks: A minimal model for the neural SOC universality class

The brain keeps its overall dynamics in a corridor of intermediate activity and it has been a long standing question what possible mechanism could achieve this task. Mechanisms from the field of statistical physics have long been suggesting that this homeostasis of brain activity could occur even without a central regulator, via self-organization on the level of neurons and their interactions, alone. Such physical mechanisms from the class of self-organized criticality exhibit characteristic dynamical signatures, similar to seismic activity related to earthquakes. Measurements of cortex rest activity showed first signs of dynamical signatures potentially pointing to self-organized critical dynamics in the brain. Indeed, recent more accurate measurements allowed for a detailed comparison with scaling theory of non-equilibrium critical phenomena, proving the existence of criticality in cortex dynamics. We here compare this new evaluation of cortex activity data to the predictions of the earliest physics spin model of self-organized critical neural networks. We find that the model matches with the recent experimental data and its interpretation in terms of dynamical signatures for criticality in the brain. The combination of signatures for criticality, power law distributions of avalanche sizes and durations, as well as a specific scaling relationship between anomalous exponents, defines a universality class characteristic of the particular critical phenomenon observed in the neural experiments. The spin model is a candidate for a minimal model of a self-organized critical adaptive network for the universality class of neural criticality. As a prototype model, it provides the background for models that include more biological details, yet share the same universality class characteristic of the homeostasis of activity in the brain.Comment: 17 pages, 5 figure

Social, Structural and Behavioral Determinants of Overall Health Status in a Cohort of Homeless and Unstably Housed HIV-Infected Men

Background: Previous studies indicate multiple influences on the overall health of HIV-infected persons; however, few assess and rank longitudinal changes in social and structural barriers that are disproportionately found in impoverished populations. We empirically ranked factors that longitudinally impact the overall health status of HIV-infected homeless and unstably housed men. Methods and Findings: Between 2002 and 2008, a cohort of 288 HIV+ homeless and unstably housed men was recruited and followed over time. The population was 60 % non-Caucasian and the median age was 41 years; 67 % of study participants reported recent drug use and 20 % reported recent homelessness. At baseline, the median CD4 cell count was 349 cells/ml and 18 % of eligible persons (CD4,350) took antiretroviral therapy (ART). Marginal structural models were used to estimate the population-level effects of behavioral, social, and structural factors on overall physical and mental health status (measured by the SF-36), and targeted variable importance (tVIM) was used to empirically rank factors by their influence. After adjusting for confounding, and in order of their influence, the three factors with the strongest negative effects on physical health were unmet subsistence needs, Caucasian race, and no reported source of instrumental support. The three factors with the strongest negative effects on mental health were unmet subsistence needs, not having a close friend/confidant, and drug use. ART adherence.90 % ranked 5th for its positive influence on mental health, and viral loa