Matching Items (3)
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- All Subjects: Game Theory
- Creators: Lanchier, Nicolas
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
This dissertation investigates the dynamics of evolutionary games based on the framework of interacting particle systems in which individuals are discrete, space is explicit, and dynamics are stochastic. Its focus is on 2-strategy games played on a d-dimensional integer lattice with a range of interaction M. An overview of related past work is given along with a summary of the dynamics in the mean-field model, which is described by the replicator equation. Then the dynamics of the interacting particle system is considered, first when individuals are updated according to the best-response update process and then the death-birth update process. Several interesting results are derived, and the differences between the interacting particle system model and the replicator dynamics are emphasized. The terms selfish and altruistic are defined according to a certain ordering of payoff parameters. In these terms, the replicator dynamics are simple: coexistence occurs if both strategies are altruistic; the selfish strategy wins if one strategy is selfish and the other is altruistic; and there is bistability if both strategies are selfish. Under the best-response update process, it is shown that there is no bistability region. Instead, in the presence of at least one selfish strategy, the most selfish strategy wins, while there is still coexistence if both strategies are altruistic. Under the death-birth update process, it is shown that regardless of the range of interactions and the dimension, regions of coexistence and bistability are both reduced. Additionally, coexistence occurs in some parameter region for large enough interaction ranges. Finally, in contrast with the replicator equation and the best-response update process, cooperators can win in the prisoner's dilemma for the death-birth process in one-dimensional nearest-neighbor interactions.
ContributorsEvilsizor, Stephen (Author) / Lanchier, Nicolas (Thesis advisor) / Kang, Yun (Committee member) / Motsch, Sebastien (Committee member) / Smith, Hal (Committee member) / Thieme, Horst (Committee member) / Arizona State University (Publisher)
Created2016
Description
For fifty years, inquiry has attempted to capture how groups of people experience microaggression phenomena through multiple methodological and analytic applications grounded in psychology-influenced frameworks. Yet, despite theoretical advancements, the phenomenon has met criticisms trivializing its existence, falsifiability, and social significance. Unpacking possible interactive factors of a microaggressive moment invites a revisitation of the known and unknown pragmatic conditions that may produce and influence its discomforting situational “content.” This study employs an intentional, game-theoretic methodology based on brief, publicly-recorded, everyday conversation segments. Conversation segments of social interactions provide a means to conduct a mathematically-solid, computationally-tractable analysis of explaining what is happening during encounters where disability microaggressions are likely the result of partial (non)cooperation between communicators. Such analysis extends the microaggression research program (MRP) by: (1) proposing theoretical consequences for conversational repair phenomena, algorithmic programming, and experimental designs in negotiation research; and (2) outlining practical approaches for preventing microaggressions with new communication pedagogy, anti-oppression/de-escalation training programs, and calculable, focus-oriented psychotherapy. It concludes with an invitation for scholars to “be” in ambiguity so that they may speculate possible trajectories for the study of microaggressions as a communicative phenomenon.
ContributorsReutlinger, Corey Jon (Author) / de la Garza, Sarah Amira (Thesis advisor) / Alberts, Janet (Committee member) / Lanchier, Nicolas (Committee member) / Cherney, James L. (Committee member) / Arizona State University (Publisher)
Created2021