Emergence of cooperation in static networks - Evolutionary Dynamics of Coordination Games with Switching Costs
Author(s)
Markou, Nikolitsa
Type
Thesis
Abstract
Brand loyalty is tightly connected with competition for market share between brands,
as it describes consumers' willingness to maintain compatibility between subsequent
purchases. Imposed by exogenous or endogenous factors, the reasons for brand loyalty
can be summarized in the switching cost. However, consumers do not live in isolation, instead they influence and get influenced by peers. Especially if influence propagates via "word-of-mouth" and not direct marketing, peer pressure becomes
invaluable as consumers reach for compatibility with other consumers.
The evolution of market share competition can be described by coordination games
played in networks over multiple periods. Consumers, acting as the players of the
coordination game, contemplate the quality of the available choices while being
susceptible at others' influence. By considering switching costs, inertia in their
actions is also introduced. An important issue therefore arises - if the available
choices are qualitatively similar, how do the switching costs in combination with
network effects affect the competition outcome?
In this thesis, we address this issue by introducing switching costs into the standard
coordination game; the switching cost game thus describes potential losses inflicted on players by changing - switching - strategies. We particularly concentrate
our efforts on the proportions of strategies at equilibrium. Compared to the cost-free
game, the switching costs are responsible for the emergence of a coexistence region
where all available strategies coexist in equilibrium. Numerical results on various
network structures verified the coexistence outcome, along with the effect of cost
values and their symmetry on the determination of the coexistence limits.
Next, we investigate the monotonicity of the competition evolution. We exploit
the monotonous behaviour of the switching cost game limiting cases over time to
draw an analogy with bootstrap percolation and benefit from existing analytical
methods to calculate their final outcome and create bounds of the general case. We
also show how these bounds depend on the switching costs. Finally, we examine
the effects of switching costs on the critical behaviour of the system by studying the
properties of stable clusters.
as it describes consumers' willingness to maintain compatibility between subsequent
purchases. Imposed by exogenous or endogenous factors, the reasons for brand loyalty
can be summarized in the switching cost. However, consumers do not live in isolation, instead they influence and get influenced by peers. Especially if influence propagates via "word-of-mouth" and not direct marketing, peer pressure becomes
invaluable as consumers reach for compatibility with other consumers.
The evolution of market share competition can be described by coordination games
played in networks over multiple periods. Consumers, acting as the players of the
coordination game, contemplate the quality of the available choices while being
susceptible at others' influence. By considering switching costs, inertia in their
actions is also introduced. An important issue therefore arises - if the available
choices are qualitatively similar, how do the switching costs in combination with
network effects affect the competition outcome?
In this thesis, we address this issue by introducing switching costs into the standard
coordination game; the switching cost game thus describes potential losses inflicted on players by changing - switching - strategies. We particularly concentrate
our efforts on the proportions of strategies at equilibrium. Compared to the cost-free
game, the switching costs are responsible for the emergence of a coexistence region
where all available strategies coexist in equilibrium. Numerical results on various
network structures verified the coexistence outcome, along with the effect of cost
values and their symmetry on the determination of the coexistence limits.
Next, we investigate the monotonicity of the competition evolution. We exploit
the monotonous behaviour of the switching cost game limiting cases over time to
draw an analogy with bootstrap percolation and benefit from existing analytical
methods to calculate their final outcome and create bounds of the general case. We
also show how these bounds depend on the switching costs. Finally, we examine
the effects of switching costs on the critical behaviour of the system by studying the
properties of stable clusters.
Version
Open Access
Date Issued
2013-03
Date Awarded
2013-07
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Draief, Moez
Publisher Department
Electrical and Electronic Engineering
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)