arXiv subjects

Michael J. Gagen

Publications and source records attributed to Michael J. Gagen.

3 recordsLinked to original sources

arXiv2012

Using strong isomorphisms to construct game strategy spaces

When applied to the same game, probability theory and game theory can disagree on calculated values of the Fisher information, the log likelihood function, entropy gradients, the rank and Jacobian of variable transforms, and even the dimensionality and volume of the underlying probability parameter spaces. These differences arise as probability theory employs structure preserving isomorphic mappings when constructing strategy spaces to analyze games. In contrast, game theory uses weaker mappings which change some of the properties of the underlying probability distributions within the mixed strategy space. In this paper, we explore how using strong isomorphic mappings to define game strategy spaces can alter rational outcomes in simple games, and might resolve some of the paradoxes of game theory.

cs.GT↗

arXiv2006

Variational optimization of probability measure spaces resolves the chain store paradox

In game theory, players have continuous expected payoff functions and can use fixed point theorems to locate equilibria. This optimization method requires that players adopt a particular type of probability measure space. Here, we introduce alternate probability measure spaces altering the dimensionality, continuity, and differentiability properties of what are now the game's expected payoff functionals. Optimizing such functionals requires generalized variational and functional optimization methods to locate novel equilibria. These variational methods can reconcile game theoretic prediction and observed human behaviours, as we illustrate by resolving the chain store paradox. Our generalized optimization analysis has significant implications for economics, artificial intelligence, complex system theory, neurobiology, and biological evolution and development.

math.OC↗

arXiv2003

Is prokaryotic complexity limited by accelerated growth in regulatory overhead?

Increased biological complexity is generally associated with the addition of new genetic information, which must be integrated into the existing regulatory network that operates within the cell. General arguments on network control, as well as several recent genomic observations, indicate that regulatory gene number grows disproportionally fast with increasing genome size. We present two models for the growth of regulatory networks. Both predict that the number of transcriptional regulators will scale quadratically with total gene number. This appears to be in good quantitative agreement with genomic data from 89 fully sequenced prokaryotes. Moreover, the empirical curve predicts that any new non-regulatory gene will be accompanied by more than one additional regulator beyond a genome size of about 20,000 genes, within a factor of two of the observed ceiling. Our analysis places transcriptional regulatory networks in the class of accelerating networks. We suggest that prokaryotic complexity may have been limited throughout evolution by regulatory overhead, and conversely that complex eukaryotes must have bypassed this constraint by novel strategies.

q-bio.MN↗