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Game spaces in which an organism must repeatedly compete with an opponent for mutually exclusive outcomes are critical methodologies for understanding decision-making under pressure. In the non-transitive game rock, paper, scissors (RPS), the only technique that guarantees the lack of exploitation is to perform randomly in accordance with mixed-strategy. However, such behavior is thought to be outside bounded rationality and so decision-making can become deterministic, predictable, and ultimately exploitable. This review identifies similarities across economics, neuroscience, nonlinear dynamics, human, and animal cognition literatures, and provides a taxonomy of RPS strategy. RPS strategies are discussed in terms of (a) whether the relevant computations require sensitivity to item frequency, the cyclic relationships between responses, or the outcome of the previous trial, and (b) whether the strategy is framed around the self or other. The negative implication of this taxonomy is that despite the differences in cognitive economy and recursive thought, many of the identified strategies are behaviorally isomorphic. This makes it difficult to infer strategy from behavior. The positive implication is that this isomorphism can be used as a novel design feature in furthering our understanding of the attribution, agency, and acquisition of strategy in RPS and other game spaces.

Shares detailed episodes of children's work in repeatedly partitioning geometric shapes to highlight the process of recursion, which can lead to a deeper understanding of imagination and beauty in children's mathematics. (MKR)

Keynes (1921) and Ellsberg (1961) have articulated an aversion toward betting on an urn containing balls of two colors of unknown proportion to one with a 50-50 composition. Keynes views this as reflecting different preferences for bets arising from different sources of uncertainty. Ellsberg describes this as weighting the priors arising from the unknown urn pessimistically. In two experiments, we observe substantial links between attitude toward almost-objective uncertainty and attitudes toward multiple-prior uncertainties in terms of ambiguity and its corresponding compound risk. Our findings point to a shared component across domains of uncertainty and motivate the need for further theoretical development.

Over the last few decades the interest of logicians and mathematicians in constructive and computational aspects of their subjects has been steadily growing, and researchers from disparate areas realized that they can benefit enormously from the mutual exchange of techniques concerned with those aspects. A key figure in this exciting development is the logician and mathematician Helmut Schwichtenberg to whom this volume is dedicated on the occasion of his 70th birthday and his turning emeritus. The volume contains 20 articles from leading experts about recent developments in Constructive set theory, Provably recursive functions, Program extraction, Theories of truth, Constructive mathematics, Classical vs. intuitionistic logic, Inductive definitions, and Continuous functionals and domains.

Two instruments were developed in this study to measure aptitude in mathematical recursion problem solving, one with the latent trait approach and one with the achievement as aptitude approach. The latent trait approach instrument was designed to assess the cognitive traits, reasoning abilities, and mathematical skills essential to solve problems in mathematical recursion and the achievement as aptitude approach instrument was designed to assess the steps necessary to solve problems in mathematical recursion. The procedures from each phase of the four-phases of test construction were performed and documented for both instruments to evaluate each individually and in comparison with one another. There were two purposes for this study: to provide evidence of the advantages and disadvantages of the latent trait approach and achievement as aptitude approach to aptitude assessment development; and to obtain at least one instrument measuring aptitude in mathematical recursion problem solving with sufficient evidence of validity and reliability to support utility of the instrument. While content validity was established with the latent trait approach instrument, results of the descriptive statistics, item difficulty and item discrimination indices, factor analysis, and calculation of Cronbach's alpha indicated there is insufficient evidence of validity and reliability to support utility of this instrument in its current form. Similarly, results of the achievement as aptitude instrument indicate content validity was established, but evidence of validity and reliability collected from descriptive statistics, factor analysis, and calculation of Cronbach's alpha fail to support utility of this instrument in its current form. The comparison between the results of both instruments developed in this study revealed that the latent trait approach is the stronger of the two. Observation of both sets of item-level means in a 0 to 1 scale depicted higher values for items in the latent trait approach instrument. Cronbach's alpha values were also significantly higher in the latent trait approach instrument than in the achievement as aptitude instrument. Given the higher item-level means and Cronbach's alpha values in the latent trait approach instrument, this instrument is the more effective of the two and could be salvageable with revisions of some of the items.