Matching Items (5)
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- All Subjects: Game Theory
- All Subjects: Mathematical Modeling
- Creators: Armbruster, Dieter
Description
Modern measurement schemes for linear dynamical systems are typically designed so that different sensors can be scheduled to be used at each time step. To determine which sensors to use, various metrics have been suggested. One possible such metric is the observability of the system. Observability is a binary condition determining whether a finite number of measurements suffice to recover the initial state. However to employ observability for sensor scheduling, the binary definition needs to be expanded so that one can measure how observable a system is with a particular measurement scheme, i.e. one needs a metric of observability. Most methods utilizing an observability metric are about sensor selection and not for sensor scheduling. In this dissertation we present a new approach to utilize the observability for sensor scheduling by employing the condition number of the observability matrix as the metric and using column subset selection to create an algorithm to choose which sensors to use at each time step. To this end we use a rank revealing QR factorization algorithm to select sensors. Several numerical experiments are used to demonstrate the performance of the proposed scheme.
ContributorsIlkturk, Utku (Author) / Gelb, Anne (Thesis advisor) / Platte, Rodrigo (Thesis advisor) / Cochran, Douglas (Committee member) / Renaut, Rosemary (Committee member) / Armbruster, Dieter (Committee member) / Arizona State University (Publisher)
Created2015
Description
Need-based transfers (NBTs) are a form of risk-pooling in which binary welfare exchanges
occur to preserve the viable participation of individuals in an economy, e.g. reciprocal gifting
of cattle among East African herders or food sharing among vampire bats. With the
broad goal of better understanding the mathematics of such binary welfare and risk pooling,
agent-based simulations are conducted to explore socially optimal transfer policies
and sharing network structures, kinetic exchange models that utilize tools from the kinetic
theory of gas dynamics are utilized to characterize the wealth distribution of an NBT economy,
and a variant of repeated prisoner’s dilemma is analyzed to determine whether and
why individuals would participate in such a system of reciprocal altruism.
From agent-based simulation and kinetic exchange models, it is found that regressive
NBT wealth redistribution acts as a cutting stock optimization heuristic that most efficiently
matches deficits to surpluses to improve short-term survival; however, progressive
redistribution leads to a wealth distribution that is more stable in volatile environments and
therefore is optimal for long-term survival. Homogeneous sharing networks with low variance
in degree are found to be ideal for maintaining community viability as the burden and
benefit of NBTs is equally shared. Also, phrasing NBTs as a survivor’s dilemma reveals
parameter regions where the repeated game becomes equivalent to a stag hunt or harmony
game, and thus where cooperation is evolutionarily stable.
occur to preserve the viable participation of individuals in an economy, e.g. reciprocal gifting
of cattle among East African herders or food sharing among vampire bats. With the
broad goal of better understanding the mathematics of such binary welfare and risk pooling,
agent-based simulations are conducted to explore socially optimal transfer policies
and sharing network structures, kinetic exchange models that utilize tools from the kinetic
theory of gas dynamics are utilized to characterize the wealth distribution of an NBT economy,
and a variant of repeated prisoner’s dilemma is analyzed to determine whether and
why individuals would participate in such a system of reciprocal altruism.
From agent-based simulation and kinetic exchange models, it is found that regressive
NBT wealth redistribution acts as a cutting stock optimization heuristic that most efficiently
matches deficits to surpluses to improve short-term survival; however, progressive
redistribution leads to a wealth distribution that is more stable in volatile environments and
therefore is optimal for long-term survival. Homogeneous sharing networks with low variance
in degree are found to be ideal for maintaining community viability as the burden and
benefit of NBTs is equally shared. Also, phrasing NBTs as a survivor’s dilemma reveals
parameter regions where the repeated game becomes equivalent to a stag hunt or harmony
game, and thus where cooperation is evolutionarily stable.
ContributorsKayser, Kirk (Author) / Armbruster, Dieter (Thesis advisor) / Lampert, Adam (Committee member) / Ringhofer, Christian (Committee member) / Motsch, Sebastien (Committee member) / Gardner, Carl (Committee member) / Arizona State University (Publisher)
Created2018
Description
This paper uses network theory to simulate Nash equilibria for selfish travel within a traffic network. Specifically, it examines the phenomenon of Braess's Paradox, the counterintuitive occurrence in which adding capacity to a traffic network increases the social costs paid by travelers in a new Nash equilibrium. It also employs the measure of the price of anarchy, a ratio between the social cost of the Nash equilibrium flow through a network and the socially optimal cost of travel. These concepts are the basis of the theory behind undesirable selfish routing to identify problematic links and roads in existing metropolitan traffic networks (Youn et al., 2008), suggesting applicative potential behind the theoretical questions this paper attempts to answer. New topologies of networks which generate Braess's Paradox are found. In addition, the relationship between the number of nodes in a network and the number of occurrences of Braess's Paradox, and the relationship between the number of nodes in a network and a network's price of anarchy distribution are studied.
ContributorsChotras, Peter Louis (Author) / Armbruster, Dieter (Thesis director) / Lanchier, Nicolas (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Economics Program in CLAS (Contributor)
Created2015-05
Description
Pogonomyrmex californicus (a species of harvester ant) colonies typically have anywhere from one to five queens. A queen can control the ratio of female to male offspring she produces, field research indicating that this ratio is genetically hardwired and does not change over time relative to other queens. Further, a queen has an individual reproductive advantage if she has a small reproductive ratio. A colony, however, has a reproductive advantage if it has queens with large ratios, as these queens produce many female workers to further colony success. We have developed an agent-based model to analyze the "cheating" phenotype observed in field research, in which queens extend their lifespans by producing disproportionately many male offspring. The model generates phenotypes and simulates years of reproductive cycles. The results allow us to examine the surviving phenotypes and determine conditions under which a cheating phenotype has an evolutionary advantage. Conditions generating a bimodal steady state solution would indicate a cheating phenotype's ability to invade a cooperative population.
ContributorsEngel, Lauren Marie Agnes (Author) / Armbruster, Dieter (Thesis director) / Fewell, Jennifer (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2017-05
DescriptionUnderstanding the evolution of opinions is a delicate task as the dynamics of how one changes their opinion based on their interactions with others are unclear.
ContributorsWeber, Dylan (Author) / Motsch, Sebastien (Thesis advisor) / Lanchier, Nicolas (Committee member) / Platte, Rodrigo (Committee member) / Armbruster, Dieter (Committee member) / Fricks, John (Committee member) / Arizona State University (Publisher)
Created2021