## The Game of Black Friday

Everybody knows about Black Friday. They either partake in the great discounted sales or just mock the crazy people who flock to the stores. Many people don’t think about Black Friday shopping until the shopping season arrives, but researchers, such as those at ShopperTrac, have already begun looking forward at the upcoming season. It has been predicted that foot traffic (traffic at physical stores) will decrease by 8% for electronics and appliances due to an increase in online sales. With the convenience of the internet, online shopping has been growing rapidly in popularity. As a side note, this applies only to the sales of items which people do not feel the need to buy in person, such as clothes, accessories, etc.

Thus, people have the option either to go to the store to buy an item or to just buy it online. Assuming equal pricing (as in going to the Walmart store or the Walmart website), this can be simply represented by the following diagram which I have created (I am claiming no degree of accuracy for the values, they have just been produced for example): where A is the state of not having an item (let’s say a TV), B is the state of having purchased the item, and B is the physical store.

One choice is to go to the physical store B with a travel time of 10 minutes and then spending x/100 minutes before purchasing the item where X is the number of total customers in the store. When there are more people, it is more crowded, and it will take more time for you to make your purchase. The other option to getting the item is to buy it online which takes Y/300 minutes where Y is the amount of people who are online at the same time. At a certain point, the more people online at the same time, the slower the store’s server will become. As shown in the second article about the failure of Walmart’s server during Black Friday, not only does the number of customers matter in the physical store, but it can also affect the speed of the online store.

If we assume there are 5000 total customers, we can obtain Nash Equilibrium values for this model by setting the total physical time to the total online time (10+x/100= y/300). We would then get that 2000 customers would shop at the store and 3000 would shop online for the times of each choice to be the same. Here, more people are shopping online than in the store due to the convenience and speed of using online shopping.

Not only is this useful for customers, but stores can also use this to predict (with much less simplicity) the distribution of customers to each type of shopping and prepare marketing strategies and sale day logistics accordingly.