5,283 research outputs found
Globule transitions of a single homopolymer: a Wang-Landau Monte Carlo study
The temperature-independent Wang-Landau Monte Carlo approach is implemented for an off-lattice model of flexible homopolymers and applied to the coil-globule and solidification transitions based on chain sizes up to N=300. An intermediate transformation from low-density liquid globule to high-density liquid globule is suggested. A scheme for identifying polymer structures representative of particular temperatures in the course of the simulation is presented and applied to illustrate intermediate states in the coil-globule transition. Transition temperatures are calculated and used to obtain a theta point of at least Θ=1.96, distinctly higher than the solid-liquid transition temperature TM=1.26
The Nash Threats Folk Theorem With Communication and Approximate Common Knowledge In Two Player Games
Abstract Not Available At This Time
Superstition and Rational Learning
We argue that some but not all superstitions can persist when learning is rational and players are patient, and illustrate our argument with an example inspired by the code of Hammurabi. The code specified an “appeal by surviving in the river” as a way of deciding whether an accusation was true, so it seems to have relied on the superstition that the guilty are more likely to drown than the innocent. If people can be easily persuaded to hold this superstitious belief, why not the superstitious belief that the guilty will be struck dead by lightning? We argue that the former can persist but the latter cannot by giving a partial characterization of the outcomes that arise as the limit of steady states with rational learning as players become more patient. These “subgame-confirmed Nash equilibria” have self-confirming beliefs at information sets reachable by a single deviation. According to this theory a mechanism that uses superstitions two or more steps off the equilibrium path, such as “appeal by surviving in the river,” is more likely to persist than a superstition where the false beliefs are only one step off of the equilibrium path.
Steady State Learning and the Code of Hammurabi
The code of Hammurabi specified a “trial by surviving in the river” as a way of deciding whether an accusation was true. This system is puzzling for two reasons. First, it is based on a superstition: We do not believe that the guilty are any more likely to drown than the innocent. Second, if people can be easily persuaded to hold a superstitious belief, why such an elaborate mechanism? Why not simply assert that those who are guilty will be struck dead by lightning? We attack these puzzles from the perspective of the theory of learning in games. We give a partial characterization of patiently stable outcomes that arise as the limit of steady states with rational learning as players become more patient. These “subgame-confirmed Nash equilibria” have self-confirming beliefs at certain information sets reachable by a single deviation. We analyze this refinement and use it as a tool to study the broader issue of the survival of superstition. According to this theory Hammurabi had it exactly right: his law uses the greatest amount of superstition consistent with patient rational learning.
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