Preference Games and Sink Equilibria
type: CreativeWork
description: In this thesis we present a new foundation for game theory. Our model for a game is defined precisely by the response graph, a natural object underlying all classical games. We call this model a preference game. Preference games generalise classical games in that all classical games have an associated preference game. Preference games also have a natural choice of solution concept: the sink equilibria, which are the sink strongly connected components of this graph. These exist in all games, and generalise pure Nash equilibria. We argue that preference games and sink equilibria form a predictive and well-founded model of strategic interaction that both clarifies problems from classical game theory and presents new solutions and predictions. Our approach is three-pronged. First, we show preference games are axiomatically well-motivated and so are broadly-applicable models of strategic interaction. We obtain these games by weakening the classical formulation of game theory with two axioms: ordinality, asserting the model requires only that players know a discrete order over the outcomes; and relevance, asserting that our model depends only on preferences over outcomes players can choose between. We give a new discussion of the Prisoner's Dilemma, where we show that the paradox can be rephrased as a consequence of Nash equilibria satisfying the relevance axiom, while Pareto efficiency satisfies only the ordinality axiom. We show further that preference games implicitly capture in their graph structure the equivalences caused by renaming players or strategies, while expressing these equivalences in classical games is cumbersome. Second, we show preference games give new insight into strategic interaction. We examine two-player games, with a focus on zero-sum and potential games. Despite both being classically defined in terms of utility functions, we show that their strategic structure can be easily understood through preference games, which make clear the duality betwee…
abstract: In this thesis we present a new foundation for game theory. Our model for a game is defined precisely by the response graph, a natural object underlying all classical games. We call this model a preference game. Preference games generalise classical games in that all classical games have an associated preference game. Preference games also have a natural choice of solution concept: the sink equilibria, which are the sink strongly connected components of this graph. These exist in all games, and generalise pure Nash equilibria. We argue that preference games and sink equilibria form a predictive and well-founded model of strategic interaction that both clarifies problems from classical game theory and presents new solutions and predictions. Our approach is three-pronged. First, we show preference games are axiomatically well-motivated and so are broadly-applicable models of strategic interaction. We obtain these games by weakening the classical formulation of game theory with two axioms: ordinality, asserting the model requires only that players know a discrete order over the outcomes; and relevance, asserting that our model depends only on preferences over outcomes players can choose between. We give a new discussion of the Prisoner's Dilemma, where we show that the paradox can be rephrased as a consequence of Nash equilibria satisfying the relevance axiom, while Pareto efficiency satisfies only the ordinality axiom. We show further that preference games implicitly capture in their graph structure the equivalences caused by renaming players or strategies, while expressing these equivalences in classical games is cumbersome. Second, we show preference games give new insight into strategic interaction. We examine two-player games, with a focus on zero-sum and potential games. Despite both being classically defined in terms of utility functions, we show that their strategic structure can be easily understood through preference games, which make clear the duality betwee…
author: Biggar, Oliver
language: en_AU
keywords: Game Theory, response graphs, game dynamics, machine learning
date published: 2022
date modified: 2026-07-24T01:07:24Z
provider: Australian Catholic University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Australian Catholic University

PropertyValue
property ID: Handle
value: http://hdl.handle.net/1885/270351