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.

A general class of adaptative strategies

We exhibit and characterize an entire class of simple adaptive strategies,in the repeated play of a game, having the Hannan-consistency property: In the long-run, the player is guaranteed an average payoff as large as the best-reply payoff to the empirical distribution of play of the otherplayers; i.e., there is no "regret." Smooth fictitious play (Fudenberg and Levine [1995]) and regret-matching (Hart and Mas-Colell [1998]) areparticular cases. The motivation and application of this work come from the study of procedures whose empirical distribution of play is, in thelong-run, (almost) a correlated equilibrium. The basic tool for the analysis is a generalization of Blackwell's [1956a] approachability strategy for games with vector payoffs.

Implementation, elimination of weakly dominated strategies and evolutionary dynamics

This paper is concerned with the realism of mechanisms that implementsocial choice functions in the traditional sense. Will agents actually playthe equilibrium assumed by the analysis? As an example, we study theconvergence and stability properties of Sj\"ostr\"om's (1994) mechanism, onthe assumption that boundedly rational players find their way to equilibriumusing monotonic learning dynamics and also with fictitious play. Thismechanism implements most social choice functions in economic environmentsusing as a solution concept the iterated elimination of weakly dominatedstrategies (only one round of deletion of weakly dominated strategies isneeded). There are, however, many sets of Nash equilibria whose payoffs maybe very different from those desired by the social choice function. Withmonotonic dynamics we show that many equilibria in all the sets ofequilibria we describe are the limit points of trajectories that havecompletely mixed initial conditions. The initial conditions that lead tothese equilibria need not be very close to the limiting point. Furthermore,even if the dynamics converge to the ``right'' set of equilibria, it stillcan converge to quite a poor outcome in welfare terms. With fictitious play,if the agents have completely mixed prior beliefs, beliefs and play convergeto the outcome the planner wants to implement.

The handaxe and the microscope: individual and social learning in a multidimensional model of adaptation

When individuals learn by trial-and-error, they perform randomly chosen actions and then reinforce those actions that led to a high payoff. However, individuals do not always have to physically perform an action in order to evaluate its consequences. Rather, they may be able to mentally simulate actions and their consequences without actually performing them. Such fictitious learners can select actions with high payoffs without making long chains of trial-and-error learning. Here, we analyze the evolution of an n-dimensional cultural trait (or artifact) by learning, in a payoff landscape with a single optimum. We derive the stochastic learning dynamics of the distance to the optimum in trait space when choice between alternative artifacts follows the standard logit choice rule. We show that for both trial-and-error and fictitious learners, the learning dynamics stabilize at an approximate distance of root n/(2 lambda(e)) away from the optimum, where lambda(e) is an effective learning performance parameter depending on the learning rule under scrutiny. Individual learners are thus unlikely to reach the optimum when traits are complex (n large), and so face a barrier to further improvement of the artifact. We show, however, that this barrier can be significantly reduced in a large population of learners performing payoff-biased social learning, in which case lambda(e) becomes proportional to population size. Overall, our results illustrate the effects of errors in learning, levels of cognition, and population size for the evolution of complex cultural traits. (C) 2013 Elsevier Inc. All rights reserved.

On learning dynamics underlying the evolution of learning rules.

In order to understand the development of non-genetically encoded actions during an animal's lifespan, it is necessary to analyze the dynamics and evolution of learning rules producing behavior. Owing to the intrinsic stochastic and frequency-dependent nature of learning dynamics, these rules are often studied in evolutionary biology via agent-based computer simulations. In this paper, we show that stochastic approximation theory can help to qualitatively understand learning dynamics and formulate analytical models for the evolution of learning rules. We consider a population of individuals repeatedly interacting during their lifespan, and where the stage game faced by the individuals fluctuates according to an environmental stochastic process. Individuals adjust their behavioral actions according to learning rules belonging to the class of experience-weighted attraction learning mechanisms, which includes standard reinforcement and Bayesian learning as special cases. We use stochastic approximation theory in order to derive differential equations governing action play probabilities, which turn out to have qualitative features of mutator-selection equations. We then perform agent-based simulations to find the conditions where the deterministic approximation is closest to the original stochastic learning process for standard 2-action 2-player fluctuating games, where interaction between learning rules and preference reversal may occur. Finally, we analyze a simplified model for the evolution of learning in a producer-scrounger game, which shows that the exploration rate can interact in a non-intuitive way with other features of co-evolving learning rules. Overall, our analyses illustrate the usefulness of applying stochastic approximation theory in the study of animal learning.

Pipkiiα Is Widely Expressed In Hematopoietic-derived Cells And May Play A Role In The Expression Of Alpha- And Gamma-globins In K562 Cells.

Characterized for the first time in erythrocytes, phosphatidylinositol phosphate kinases (PIP kinases) belong to a family of enzymes that generate various lipid messengers and participate in several cellular processes, including gene expression regulation. Recently, the PIPKIIα gene was found to be differentially expressed in reticulocytes from two siblings with hemoglobin H disease, suggesting a possible relationship between PIPKIIα and the production of globins. Here, we investigated PIPKIIα gene and protein expression and protein localization in hematopoietic-derived cells during their differentiation, and the effects of PIPKIIα silencing on K562 cells. PIPKIIα silencing resulted in an increase in α and γ globins and a decrease in the proliferation of K562 cells without affecting cell cycle progression and apoptosis. In conclusion, using a cell line model, we showed that PIPKIIα is widely expressed in hematopoietic-derived cells, is localized in their cytoplasm and nucleus, and is upregulated during erythroid differentiation. We also showed that PIPKIIα silencing can induce α and γ globin expression and decrease cell proliferation in K562 cells.

Prolactin May Not Play a Role in Primary Antiphospholipid (Hughes') Syndrome

The relationship between prolactin (PRL) and the immune system has been demonstrated in the last two decades and has opened new windows in the field of immunoendocrinology. However, there are scarce reports about PRL in primary antiphospholipid syndrome (pAPS). The objective of this study was to evaluate PRL levels in patients with pAPS compared to healthy controls and to investigate their possible clinical associations. Fifty-five pAPS patients according to Sapporo criteria were age- and sex-matched with 41 healthy subjects. Individuals with secondary causes of hyperprolactinemia (HPRL) were excluded; demographic, biometric, and clinical data, PRL levels, antiphospholipid antibodies, inflammatory markers, and other routine laboratory findings were analyzed. PRL levels were similar between pAPS and healthy controls (8.94 +/- 7.02 versus 8.71 +/- 6.73 ng/mL, P = .876). Nine percent of the pAPS patients and 12.1% of the control subjects presented HPRL (P = .740). Comparison between the pAPS patients with hyper- and normoprolactinemia revealed no significant differences related to anthropometrics, clinical manifestations, medications, smoking, and antiphospholipid antibodies (P > .05). This study showed that HPRL does not seem to play a role in clinical manifestations of the pAPS, differently from other autoimmune rheumatic diseases.

Physiological demands of match-play in elite tennis: A case study

The physiological and perceptual demands together with match notation of a four-set tennis match were studied in two elite professional players during the preparation for the 2008 Davis Cup. The design of this case report is unique in that it is the first to describe the demands of prolonged match-play (197 min) over four sets in ecologically valid conditions. The variables measured before and after each set included blood lactate and glucose concentrations, body mass, and perception of effort. Stroke count for each rally and heart rate were recorded during each set while salivary cortisol concentration was determined before and after the match. The rally length decreased as the match progressed. The results showed significant physiological stress, with each player losing greater than 2.5% of body mass (as fluid) and having elevated salivary cortisol concentrations after the match. Heart rate and perception of effort were also increased following each set indicating increasing stress. However, blood lactate decreased following the fourth set while blood glucose was maintained. The results also suggest that elite players may adjust work rates or tactics to cope with the increased perception of effort. This report shows that four sets of tennis are associated with increasing stress and fatigue.

On Seliger and Whitham`s variational principle for hydrodynamic systems from the point of view of `fictitious particles`

FAPESP, the Sao Paulo State Research Foundation[04/04611-5]

Stromal cells play a role in cervical cancer progression mediated by MMP-2 protein

Metalloproteinases, especially metal loprotemase-2 (MMP-2), are known for their role in the degradation of the extracellular matrix. Nevertheless, a thorough understanding of MMP-2 expression in neoplastic lesions of the uterine cervix has yet to be accomplished. This study aimed to analyze the MMP-2 expression in cervical intraepithelial neoplasia III (CIN3) and in cervical squamous cell carcinoma, in tumor cells and adjacent stromal cells. MMP-2 expression was assessed by an immunohistochernical technique. MMP-2 expression was greater in the stromal cells of invasive carcinomas than in CIN3 (p < 0.0001). MMP-2 expression in stromal cells correlates with the clinical stage, gradually increasing as the tumor progresses (p = 0.04). This study corroborates that stromal cells play an important role in tumor invasion and progression, mediated by the progressive enhancement of MMP-2 expression from CIN3 to advanced invasive tumor. The intense MMP-2 expression most probably is associated with poor tumor prognosis.

Does Cyclophosphamide Play a Protective Role Against Neuronal Loss in Chronic T. cruzi Infection?

In this study, we verified the possible role of cyclophosphamide (CY) in protecting or not against neuronal losses in young and aged male Calomys callosus chronically infected with the MORC-1 strain of Trypanosoma cruzi through numerical quantification of neurons from the myenteric plexus of the colon and quantification of nitric-oxide concentration (NO) during the acute and chronic phase of infection. For this purpose, groups of young C. callosus were infected with the MORC-1 strain of T. cruzi. A group of infected animals received i.p. 0.2 mg/ml genuxal dissolved in distilled water treatment with CY. NO concentration in aged animals displayed reduced levels when compared to those found in young animals. No significant alterations in the number of neurons were observed in young animals, but for aged ones, a protective role of CY in reducing neuron loss was noted, in addition to enhancing the neuronal volume, area, and perimeter. These results suggest that CY administration, depending on the dose and time span, can act as a protective agent against neuronal losses.

Molecular cloning reveals that the p160 myb-binding protein is a novel, predominantly nucleolar protein which may play a role in transactivation by Myb

We have previously detected two related murine nuclear proteins, p160 and p67, that can bind to the leucine zipper motif within the negative regulatory domain of the Myb transcription factor. We now describe the molecular cloning of cDNA corresponding to murine p160. The P160 gene is located on mouse chromosome 11, and related sequences are found on chromosomes 1 and 12. The predicted p160 protein is novel, and in agreement with previous studies, we find that the corresponding 4.5-kb mRNA is ubiquitously expressed. We showed that p67 is an N-terminal fragment of p160 which is generated by proteolytic cleavage in certain cell types. The protein encoded by the cloned p160 cDNA and an engineered protein (p67*) comprising the amino-terminal region of p160 exhibit binding specificities for the Myb and Jun leucine zipper regions identical to those of endogenous p160 and p67, respectively. This implies that the Myb-binding site of p160 lies within the N-terminal 580 residues and that the Jun-binding site is C-terminal to this position. Moreover, we show that p67* but not p160 can inhibit transactivation by Myb. Unexpectedly, immunofluorescence studies show that p160 is localized predominantly in the nucleolus. The implications of these results for possible functions of p160 are discussed.

Monooxygenases play only a minor role in resistance to synthetic pyrethroids in the cattle tick, Boophilus microplus

We investigated the role of monooxygenases in resistance to synthetic pyrethroids (SPs) in the cattle tick, Boophilus microplus. We found that monooxygenases play only a minor role in resistance to SPs in both resistant and susceptible strains of B. microplus. We blocked the monooxygenases with piperonyl butoxide (PBO) and simultaneously applied the SPs, flumethrin and cypermethrin to larval B. microplus. PBO increased the effect of flumethrin (synergism ratios 2.7-8.9) more than it increased the effect of cypermethrin (synergism ratios 1.9-3.1). Of the four strains tested, Parkhurst, which is resistant to SPs, was the least affected by the addition of PBO (synergism ratios after cypermethrin was applied 1.9; after flumethrin 2.7) whereas N.R.F.S., the strain susceptible to SPs, was the most affected by synergism between PBO and SPs (synergism ratio after cypermethrin was applied 3.1; after flumethrin 8.9). We hypothesize that B. microplus lacks monooxygenases capable of conferring resistance to SPs because it and its recent ancestors were blood-feeders rather than herbivores.