SummaryThe paper surveys the literature on the bandit problem, focusing on its recent development in the presence of switching costs. Switching costs between arms makes not only the Gittins index policy suboptimal, but also renders the search for the optimal policy computationally infeasible. This survey will first discuss the decomposability properties of the arms that make the Gittins index policy optimal, and show how these properties break down upon the introduction of costs on switching arms. Having established the failure of the simple index policy, the survey focus on the recent efforts to overcome the difficulty of finding the optimal policy in the bandit problem with switching costs: characterization of the optimal policy, exact derivation of the optimal policy in the restricted environments, and lastly approximation of optimal policy. The advantages and disadvantages of the above approaches are discussed.
We investigate a dynamic model of network marketing in a small-world network structure artificially constructed similarly to the Watts-Strogatz network model. Different from the traditional marketing, consumers can also play the role of the manufacturer's selling agents in network marketing, which is stimulated by the referral fee the manufacturer offers. As the wiring probability α is increased from zero to unity, the network changes from the one-dimensional regular directed network to the star network where all but one player are connected to one consumer. The price p of the product and the referral fee r are used as free parameters to maximize the profit of the manufacturer. It is observed that at α = 0 the maximized profit is constant independent of the network size N while at α = 0, it increases linearly with N . This is in parallel to the small-world transition. It is also revealed that while the optimal value of p stays at an almost constant level in a broad range of α, that of r is sensitive to a change in the network structure. The consumer surplus is also studied and discussed.
Air pollution is closely associated with the development of respiratory illness. Behavioral adaptations of people to air pollution may influence its impact, yet this has not been investigated in the literature. Our hypothesis is that people experience and learn the underlying air quality to decide their adaptation, and they have a stronger incentive to behaviorally adapt to the air quality as it deteriorates. We tested our hypothesis on a sample of approximately 25,700 individuals from South Korea from 2002 to 2013 that contained information on daily doctor’s visits due to respiratory disease. We matched individuals to the mean of the past seven-day concentration of the particulate matter of size between 2.5 and 10 micrometers (PM
10
) in their county of residence. We examined whether people living in counties with greater air pollution suffer less from respiratory disease when the concentration increases. For the analysis, we separated counties into quintiles based on their mean seven-day PM
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, and regressed the binary indicator of a daily doctor’s visit with a resulting diagnosis of respiratory disease on the seven-day PM
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concentration of the county of residence interacted with the quintile dummies. The key findings are that a 1-standard-deviation increase in the seven-day PM
10
concentration in the two lowest quintiles is associated with an increase of 0.054 percentage points in the likelihood of a doctor’s visit with a resulting diagnosis of respiratory disease, which is about 40% larger than the effect in higher quintiles, and the size of 1-standard-deviation gradually increases from 0.037 percentage points in the third quintile to 0.040 percentage points in the fifth quintile. The smaller increase in the likelihood of respiratory disease in more polluted locations can be explained by the behavioral adaptation to the environment, but the effectiveness of the adaptation seems limited among the highly polluted locations.
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