37,190 research outputs found

    Properly Quantized History Dependent Parrondo Games, Markov Processes, and Multiplexing Circuits

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    In the context of quantum information theory, "quantization" of various mathematical and computational constructions is said to occur upon the replacement, at various points in the construction, of the classical randomization notion of probability distribution with higher order randomization notions from quantum mechanics such as quantum superposition with measurement. For this to be done "properly", a faithful copy of the original construction is required to exist within the new "quantum" one, just as is required when a function is extended to a larger domain. Here procedures for extending history dependent Parrondo games, Markov processes and multiplexing circuits to their "quantum" versions are analyzed from a game theoretic viewpoint, and from this viewpoint, proper quantizations developed

    Separable and Low-Rank Continuous Games

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    In this paper, we study nonzero-sum separable games, which are continuous games whose payoffs take a sum-of-products form. Included in this subclass are all finite games and polynomial games. We investigate the structure of equilibria in separable games. We show that these games admit finitely supported Nash equilibria. Motivated by the bounds on the supports of mixed equilibria in two-player finite games in terms of the ranks of the payoff matrices, we define the notion of the rank of an n-player continuous game and use this to provide bounds on the cardinality of the support of equilibrium strategies. We present a general characterization theorem that states that a continuous game has finite rank if and only if it is separable. Using our rank results, we present an efficient algorithm for computing approximate equilibria of two-player separable games with fixed strategy spaces in time polynomial in the rank of the game

    Evolutionary games and quasispecies

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    We discuss a population of sequences subject to mutations and frequency-dependent selection, where the fitness of a sequence depends on the composition of the entire population. This type of dynamics is crucial to understand the evolution of genomic regulation. Mathematically, it takes the form of a reaction-diffusion problem that is nonlinear in the population state. In our model system, the fitness is determined by a simple mathematical game, the hawk-dove game. The stationary population distribution is found to be a quasispecies with properties different from those which hold in fixed fitness landscapes.Comment: 7 pages, 2 figures. Typos corrected, references updated. An exact solution for the hawks-dove game is provide

    Emergent requirements for supporting introductory programming

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    The problems associated with learning and teaching first year University Computer Science (CS1) programming classes are summarized showing that various support tools and techniques have been developed and evaluated. From this review of applicable support the paper derives ten requirements that a support tool should have in order to improve CS1 student success rate with respect to learning and understanding

    Modeling the Psychology of Consumer and Firm Behavior with Behavioral Economics

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    Marketing is an applied science that tries to explain and influence how firms and consumers actually behave in markets. Marketing models are usually applications of economic theories. These theories are general and produce precise predictions, but they rely on strong assumptions of rationality of consumers and firms. Theories based on rationality limits could prove similarly general and precise, while grounding theories in psychological plausibility and explaining facts which are puzzles for the standard approach. Behavioral economics explores the implications of limits of rationality. The goal is to make economic theories more plausible while maintaining formal power and accurate prediction of field data. This review focuses selectively on six types of models used in behavioral economics that can be applied to marketing. Three of the models generalize consumer preference to allow (1) sensitivity to reference points (and loss-aversion); (2) social preferences toward outcomes of others; and (3) preference for instant gratification (quasi-hyperbolic discounting). The three models are applied to industrial channel bargaining, salesforce compensation, and pricing of virtuous goods such as gym memberships. The other three models generalize the concept of gametheoretic equilibrium, allowing decision makers to make mistakes (quantal response equilibrium), encounter limits on the depth of strategic thinking (cognitive hierarchy), and equilibrate by learning from feedback (self-tuning EWA). These are applied to marketing strategy problems involving differentiated products, competitive entry into large and small markets, and low-price guarantees. The main goal of this selected review is to encourage marketing researchers of all kinds to apply these tools to marketing. Understanding the models and applying them is a technical challenge for marketing modelers, which also requires thoughtful input from psychologists studying details of consumer behavior. As a result, models like these could create a common language for modelers who prize formality and psychologists who prize realism
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