"Illusion of control" in Minority and Parrondo Games

Human beings like to believe they are in control of their destiny. This ubiquitous trait seems to increase motivation and persistence, and is probably evolutionarily adaptive. But how good really is our ability to control? How successful is our track record in these areas? There is little understanding of when and under what circumstances we may over-estimate or even lose our ability to control and optimize outcomes, especially when they are the result of aggregations of individual optimization processes. Here, we demonstrate analytically using the theory of Markov Chains and by numerical simulations in two classes of games, the Minority game and the Parrondo Games, that agents who optimize their strategy based on past information actually perform worse than non-optimizing agents. In other words, low-entropy (more informative) strategies under-perform high-entropy (or random) strategies. This provides a precise definition of the "illusion of control" in set-ups a priori defined to emphasize the importance of optimization.Comment: 17 pages, four figures, 1 tabl

Illusion of Control in a Brownian Game

Both single-player Parrondo games (SPPG) and multi-player Parrondo games (MPPG) display the Parrondo Effect (PE) wherein two or more individually fair (or Llosing) games yield a net winning outcome if alternated periodically or randomly. (There is a more formal, less restrictive definition of the PE.) We illustrate that, when subject to an elementary optimization rule, the PG displays degraded rather than enhanced returns. Optimization provides only the illusion of control, when low-entropy strategies (i.e. which use more information) under-perform random strategies (with maximal entropy). This illusion is unfortuntately widespread in many human attempts to manage or predict complex systems. For the PG, the illusion is especially striking in that the optimization rule reverses an already paradoxical-seeming positive gain - the Parrondo effect proper - and turns it negative. While this phenomenon has been previously demonstrated using somewhat artificial conditions in the MPPG (L. Dinios and J.M.R. Parrondo. Europhysics Letters 63, 319 (2003); J.M.R. Parrondo et al. Advances in Condensed Matter and Statistical Mechanics, eds. E. Korutcheva and R. Cuerno, Nova Science Publishers, 2003), we demonstrate it in the natural setting of a history-dependent SPPG.Comment: 8 page with 1 tabl

Nurturing Breakthroughs: Lessons from Complexity Theory

A general theory of innovation and progress in human society is outlined, based on the combat between two opposite forces (conservatism/inertia and speculative herding "bubble" behavior). We contend that human affairs are characterized by ubiquitous ``bubbles'', which involve huge risks which would not otherwise be taken using standard cost/benefit analysis. Bubbles result from self-reinforcing positive feedbacks. This leads to explore uncharted territories and niches whose rare successes lead to extraordinary discoveries and provide the base for the observed accelerating development of technology and of the economy. But the returns are very heterogeneous, very risky and may not occur. In other words, bubbles, which are characteristic definitions of human activity, allow huge risks to get huge returns over large scales. We outline some underlying mathematical structure and a few results involving positive feedbacks, emergence, heavy-tailed power laws, outliers/kings/black swans, the problem of predictability and the illusion of control, as well as some policy implications.Comment: 14 pages, Invited talk at the workshop Trans-disciplinary Research Agenda for Societal Dynamics (http://www.uni-lj.si/trasd in Ljubljana), organized by J. Rogers Hollingsworth, Karl H. Mueller, Ivan Svetlik, 24 - 25 May 2007, Ljubljana, Sloveni

Acquisition of ownership illusion with self-disownership in neurological patients

The multisensory regions in frontoparietal cortices play a crucial role in the sense of body and self. Disrupting this sense may lead to a feeling of disembodiment, or more generally, a sense of disownership. Experimentally, this altered consciousness disappears during illusory own-body perceptions, increasing the intensity of perceived ownership for an external virtual limb. In many clinical conditions, particularly in individuals with a discontinuous or absent sense of bodily awareness, the brain may effortlessly create a convincing feeling of body ownership over a surrogate body or body part. The immediate visual input dominates the current bodily state and induces rapid plastic adaptation that reconfigures the dynamics of bodily representation, allowing the brain to acquire an alternative sense of body and self. Investigating strategies to deconstruct the lack of a normal sense of bodily ownership, especially after a neurological injury, may aid the selection of appropriate clinical treatment

An Asset Allocation Puzzle

This paper examines popular advice on portfolio allocation among cash, bonds, and stocks. It documents that this advice is inconsistent with the mutual-fund separation theorem, which states that all investors should hold the same composition of risky assets. In contrast to the theorem, popular advisors recommend that aggressive investors hold a lower ratio of bonds to stocks than conservative investors. The paper explores various possible explanations of this puzzle. It concludes that the portfolio recommendations can be explained if popular advisors base their advice on the unconditional distribution of nominal returns. It also finds that the cost of this money illusion is small, as measured by the distance of the recommended portfolios from the mean-variance efficient frontier.