arXiv subjects

Robert D. Young

Publications and source records attributed to Robert D. Young.

4 recordsLinked to original sources

arXiv2019

Reciprocal and Extortive Strategies: Infinitely Iterated Prisoner's Dilemma

The Prisoner's Dilemma game has a long history stretching across the social, biological, and physical sciences. In 2012, Press and Dyson developed a method for analyzing the mapping of the 8-dimensional strategy profile onto the 2-dimensional payoff space in an infinitely iterated Prisoner's Dilemma game, based on Markov chain analysis and memory-one strategies. We generalize this approach and introduce the concept of strategy parameter to show that linear relations among player payoffs are a ubiquitous feature of the infinitely iterated Prisoner's Dilemma game. Our extended analysis is applied to various strategy profiles including tit-for-tat, win-stay-lose-shift, and other randomized strategy sets. Strategy profiles are identified that map onto the vertices, edges, and interior of the Prisoner's Dilemma quadrilateral in the 2-dimensional payoff (score) space. A DaMD strategy is defined based solely on "Defection after Mutual Defection" and leads to linear relations between player scores using strategy parameter analysis. The DaMD strategy is shown to result in an equal (reciprocal) or larger (extortive) score for its user compare to the other player, independent of the strategy of the other player. The extortive scores occur when the probabilities for the DaMD player to cooperate after conflicting plays (cooperate-defect or defect-cooperate) sum to less than 1. The equal reciprocal scores occur when the probabilities for the DaMD player to cooperate after conflicting plays (cooperate-defect or defect-cooperate) sum to 1. When one player selects the extortive DaMD, the opposing player can force the equal punishment payoffs for both players in the infinitely iterated Prisoner's dilemma by also choosing the DaMD strategy. Possible pathways to mutual cooperation based on DaMD are discussed.

physics.soc-ph↗

arXiv2018

Impulse-Response Approach to Elastobaric Model for Proteins

A novel energy landscape model, ELM, for proteins recently explained a collection of incoherent, elastic neutron scattering data from proteins. The ELM of proteins considers the elastic response of the proton and its environment to the energy and momentum exchanged with the neutron. In the ELM, the elastic potential energy is expressed as a sum of a temperature dependent term resulting from equipartition of potential energy among the active degrees of freedom and a wave vector transfer dependent term resulting from the elastic energy stored by the protein during the neutron scattering event. The elastic potential energy involves a new elastobaric coefficient that is proportional to the product of two factors: one factor depends on universal constants and the other on the incident neutron wave vector per degree of freedom. The ELM was tested for dry protein samples with an elastobaric coefficient corresponding to 3 degrees of freedom. A discussion of the data requirements for additional tests of ELM is presented resulting in a call for published data that have not been preprocessed by temperature and wave-vector dependent normalizations.

physics.bio-ph↗

arXiv2017

Press-Dyson Analysis of Asynchronous, Sequential Prisoner's Dilemma

Two-player games have had a long and fruitful history of applications stretching across the social, biological, and physical sciences. Most applications of two-player games assume synchronous decisions or moves even when the games are iterated. But different strategies may emerge as preferred when the decisions or moves are sequential, or the games are iterated. Zero-determinant strategies developed by Press and Dyson are a new class of strategies that have been developed for synchronous two-player games, most notably the iterated prisoner's dilemma. Here we apply the Press-Dyson analysis to sequential or asynchronous two-player games. We focus on the asynchronous prisoner's dilemma. As a first application of the Press-Dyson analysis of the asynchronous prisoner's dilemma, tit-for-tat is shown to be an efficient defense against extortionate zero-determinant strategies. Nice strategies like tit-for-tat are also shown to lead to Pareto optimal payoffs for both players in repeated prisoner's dilemma.

physics.bio-ph↗

arXiv2015

A wave-mechanical model of incoherent neutron scattering II. Role of the momentum transfer

We recently introduced a wave-mechanical model for quasi-elastic neutron scattering (QENS) in proteins. We call the model ELM for "Energy Landscape Model". We postulate that the spectrum of the scattered neutrons consists of lines of natural width shifted from the center by fluctuations. ELM is based on two facts: Neutrons are wave packets; proteins have low-lying substates that form the free-energy landscape (FEL). Experiments suggest that the wave packets are a few hundred micrometers long. The interaction between the neutron and a proton in the protein takes place during the transit of the wave packet. The wave packet exerts the force $F(t) = dQ(t)/dt$ on the protein moiety, a part of the protein surrounding the struck proton. $Q(t)$ is the wave vector (momentum) transferred by the neutron wave packet to the proton during the transit. The ensuing energy is stored in the energy landscape and returned to the neutron as the wave packet exits. Kinetic energy thus is changed into potential energy and back. The interaction energy is proportional to $Q$, not to $Q^2$. To develop and check the ELM, we use published work on dehydrated proteins after reversing improper normalizations. In such proteins only vibrations are active and the effects caused by the neutron momentum can be studied undisturbed by external fluctuations. ELM has predictive power. For example it quantitatively predicts the observed inelastic incoherent fraction $S(Q, T)$ over a broad range of temperature and momentum $Q$ with one coefficient if $S(0, T)$ is known.

physics.bio-ph↗