Emergence of cooperation in static networks - Evolutionary Dynamics of Coordination Games with Switching Costs

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.