The Chipotle Chorizo Nash Equilibrium
Chipotle Mexican Grill has finally brought back chorizo! Chorizo is the spicy pork and chicken that Chipotle used to offer at restaurants in 2016 but was taken off the menu to make way for queso sauce. The move to take the spicy meat off the menu disappointed many Tex-Mex fans including myself, so after hearing that chorizo was making a comeback, I was excited to write about it in the context of our class. The move to bring chorizo back is an effort to bring back chorizo-loving customers. This is especially important for the restaurant after a disease outbreak in late July scared away customers. Seven hundred customers faced gastrointestinal problems as well as fevers after eating at the restaurant. So naturally, Chipotle is on damage control and has decided to bring back the beloved chorizo to bring back both new and old customers.
We have learned about game theory in class and thus we are well prepared to view this decision to bring back the spicy meat as a game. Let’s say that we have a chorizo-loving potential customer who stopped going to Chipotle either after the disease outbreak or after chorizo was taken off the menu (the type of person Chipotle is trying to attract with this new campaign). The potential customer REALLY likes chorizo and will become a regular customer if Chipotle brings back chorizo.
So, to reiterate, there are 2 players in this game, Chipotle and a potential customer. The strategies Chipotle faces are to either release chorizo or to not do so. The customer faces the strategies to buy food at Chipotle or to not buy food at Chipotle. The payoffs for Chipotle, Customer can be represented in this way:
No Chorizo, Buy: (1, -1): 1 represents the payoff Chipotle gains by having a new person buy their food. -1 represents the loss in satisfaction equal to the amount of money the customer paid for their food as the customer does not enjoy the food without chorizo.
No Chorizo, Don’t Buy (0,0): Both payoffs are 0 as in this option Chipotle spends no money in getting the chorizo and the customer spends no money buying the chorizo.
Chorizo, Buy: (2, 1): 2 can represent the payoff Chipotle gains by having a new person regularly buying their food there is a cost of getting chorizo back but the customer purchasing it offsets the cost as chorizo is only 3% of Chipotle’s protein menu. 1 represents the satisfaction gained by the customer by eating food that they enjoy regularly.
Chorizo, Don’t Buy: (-1/2,0). -1/2 represents the cost of bringing back chorizo which is not offset by anything if the customer chooses not to buy the food anyway. 0 is the payoff of not buying chorizo but also not eating it.
We learned in class that games can have multiple Nash Equilibria (can be both pure and mixed). In this example there are two pure Nash Equilibria, No Chorizo, Don’t Buy; and Chorizo, Buy. This is because if the restaurant chooses not to make chorizo, then the customer will not buy the food to avoid a negative payoff. Conversely, if the company chooses to make chorizo then the customer is incentivized to buy the chorizo for a higher payoff. In this example the restaurant makes the first move. Since Chipotle makes the first move, the customer does not need to think about the probability of whether or not Chipotle will bring back chorizo, all they need to do is react to what they see Chipotle do. For that reason, we are not looking at mixed Nash Equilibria. As the payoff matrix illustrates, the restaurant knows that chorizo-loving customers will choose to buy food at Chipotle if they choose to make chorizo and choose not to buy food at Chipotle if they do not make the chorizo. Since Chipotle knows how the chorizo-loving customer will react to their decision, Chipotle will choose to bring back chorizo as that will give Chipotle the highest payoff, and the customer will choose to buy the food as that grants them the highest payoff given Chipotle’s decision.
https://www.cnbc.com/2018/09/10/chipotle-brings-back-chorizo-in-bid-to-lure-back-customers.html