37,190 research outputs found
Properly Quantized History Dependent Parrondo Games, Markov Processes, and Multiplexing Circuits
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
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
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
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
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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