A Mathematical Study of Purchasing Airline Tickets
We have sought to apply ideas from foraging theory to the purchase of airline tickets from competing websites in an online shopping environment. We explore how consumers might distribute themselves among websites and different tickets dependent on parameters such as price of ticket, number of stops, input rate of tickets into the site, and so on. To facilitate our exploration of consumer behavior, we have developed a system of difference equations and rules as to why consumers may prefer one website over another. By tuning parameters such as quality of a ticket and input rate of tickets, different distributions of consumers are observed. Based on these distributions, we seek to determine the best way - measured by the average quality of ticket purchased - for consumers to distribute themselves among websites and ticket types.
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