8,499 research outputs found
Learning backward induction: a neural network agent approach
This paper addresses the question of whether neural networks (NNs), a realistic cognitive model of human information processing, can learn to backward induce in a two-stage game with a unique subgame-perfect Nash equilibrium. The NNs were found to predict the Nash equilibrium approximately 70% of the time in new games. Similarly to humans, the neural network agents are also found to suffer from subgame and truncation inconsistency, supporting the contention that they are appropriate models of general learning in humans. The agents were found to behave in a bounded rational manner as a result of the endogenous emergence of decision heuristics. In particular a very simple heuristic socialmax, that chooses the cell with the highest social payoff explains their behavior approximately 60% of the time, whereas the ownmax heuristic that simply chooses the cell with the maximum payoff for that agent fares worse explaining behavior roughly 38%, albeit still significantly better than chance. These two heuristics were found to be ecologically valid for the backward induction problem as they predicted the Nash equilibrium in 67% and 50% of the games respectively. Compared to various standard classification algorithms, the NNs were found to be only slightly more accurate than standard discriminant analyses. However, the latter do not model the dynamic learning process and have an ad hoc postulated functional form. In contrast, a NN agent’s behavior evolves with experience and is capable of taking on any functional form according to the universal approximation theorem.
Stability of Mixed-Strategy-Based Iterative Logit Quantal Response Dynamics in Game Theory
Using the Logit quantal response form as the response function in each step,
the original definition of static quantal response equilibrium (QRE) is
extended into an iterative evolution process. QREs remain as the fixed points
of the dynamic process. However, depending on whether such fixed points are the
long-term solutions of the dynamic process, they can be classified into stable
(SQREs) and unstable (USQREs) equilibriums. This extension resembles the
extension from static Nash equilibriums (NEs) to evolutionary stable solutions
in the framework of evolutionary game theory. The relation between SQREs and
other solution concepts of games, including NEs and QREs, is discussed. Using
experimental data from other published papers, we perform a preliminary
comparison between SQREs, NEs, QREs and the observed behavioral outcomes of
those experiments. For certain games, we determine that SQREs have better
predictive power than QREs and NEs
Environmental statistics and optimal regulation
Any organism is embedded in an environment that changes over time. The
timescale for and statistics of environmental change, the precision with which
the organism can detect its environment, and the costs and benefits of
particular protein expression levels all will affect the suitability of
different strategies-such as constitutive expression or graded response-for
regulating protein levels in response to environmental inputs. We propose a
general framework-here specifically applied to the enzymatic regulation of
metabolism in response to changing concentrations of a basic nutrient-to
predict the optimal regulatory strategy given the statistics of fluctuations in
the environment and measurement apparatus, respectively, and the costs
associated with enzyme production. We use this framework to address three
fundamental questions: (i) when a cell should prefer thresholding to a graded
response; (ii) when there is a fitness advantage to implementing a Bayesian
decision rule; and (iii) when retaining memory of the past provides a selective
advantage. We specifically find that: (i) relative convexity of enzyme
expression cost and benefit influences the fitness of thresholding or graded
responses; (ii) intermediate levels of measurement uncertainty call for a
sophisticated Bayesian decision rule; and (iii) in dynamic contexts,
intermediate levels of uncertainty call for retaining memory of the past.
Statistical properties of the environment, such as variability and correlation
times, set optimal biochemical parameters, such as thresholds and decay rates
in signaling pathways. Our framework provides a theoretical basis for
interpreting molecular signal processing algorithms and a classification scheme
that organizes known regulatory strategies and may help conceptualize
heretofore unknown ones.Comment: 21 pages, 7 figure
Positive expectations feedback experiments and number guessing games as models of financial markets (revised version of WP 08-07)
In repeated number guessing games choices typically converge quickly to the Nash equilibrium. In positive expectations feedback experiments, however, convergence to the equilibrium price tends to be very slow, if it occurs at all. Both types of experimental designs have been suggested as modeling essential aspects of financial markets. In order to isolate the source of the differences in outcomes we present several new treatments in this paper. We conclude that the feedback strength (i.e. the ‘p-value’ in standard number guessing games) is essential for the results. Furthermore, positive expectations feedback experiments may provide good representations of highly speculative markets while standard number guessing games model financial markets with more emphasis on dividend yield and value stocks.
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