Key parameters

The ACE model we design necessarily includes many parameters that remain invariant along the simulation. For a full list of the parameters and their possible values we refer to the software code (see Appendix B). In this section we highlight and brie‡y describe what we consider the key parameters of the model (Table 3.1). Some of these key parameters are kept …xed in the simulation while other vary. By doing so on the one hand we perform a sensitivity test of the estimates and, on the other hand, we also investigate the impact of some key parameters on the model’s behavior and predictions.

for other reasons might well decide to re…ll instead of losing other time.

Table 3.1: Key model parameters

EvalWeeks # of weeks in which the initial pro…ts are evalued 3

week length # of days in a simulated week 7

AvgCars average number of drivers generated in each step of the model

300

RL-share-based Reinforcement learning algorithm based on a noisy signal about # of customer as fraction of drivers passing by the stations. Otherwise the RL algorithm is only based on the pro…ts made by the refueling station

On; O¤

very-p-stve share of very active consumers 0.3; 0.15 p-stve-t share of active consumers 0.1; 0.25; 0.5; 0.75 fuel-concern treshold at which drivers start considering re…lling

options

0.33

emergency-fuel threshold of the emergency fuel level 0.1 t-red-bias Share of drivers that enter form the two ends of the

highways. Otherwise drivers enter form the gates along the way

0.4

per-exit Percentage of drivers that exit at each gate 0.2

The …rst three parameters in Table 3.1 enter the reinforcement learning algorithm and are explained in section 3.4.2.1. We set the parameter F 0 at the value of 3 such that the initial …tness of all rule is set to a relatively high value (i.e. three times the value of the median pro…ts realized during the evaluation period). This ensure that at least during the

…rst stages retailers tend to explore all the available rules. The memory parameter enters the equation of the RL …tness function. We model two di¤erent levels of memory, a …rst setting in which memory is set equal to 0:5 (equal weight between current pro…ts and past pro…ts) and a second setting in which memory is set equal to 0.75 (current pro…ts are valued more than the past realizations). The temp parameter (temperature of the RL algorithm) is also varied. It takes the values of 0:1 and 0:05:where the former value implies a tendency to vary more frequently the price strategy and the latter value imply a tendency to settle for the strategy(ies) that delivers the highest payo¤s.

EvalWeeks is set equal to 3 and represents the number of weeks in which the model is run to estimate the starting pro…ts (during this period retailers keep …xed and randomly

assigned price strategy). The week (weeklength) has the standard length of 7 days (although the model allows for shorter or longer week length). Notice that retailers make their pricing decisions at the beginning of each week, so by shortening the week length retailers will consider more often the opportunity to change price strategy.

AvgCars is set to 300 and represents the average number of cars that are generated in each cycle of the model (cars are generated with a random Poisson process). In each day there are …ve cycles in which cars are generated and the average numbers of cars created in each day is around 1800:

RL-share-based identi…es the type of information retailers use to assess their weekly sales. We distinguish between two cases. In the …rst case retailers only look at their weekly pro…ts. However this measure might be very noisy as the fuel sold in one station depends on the price of the station, on the average size of the tank of the driver, on the average fuel level that drivers have when refueling and on the size of the potential demand that varies randomly each week. To overcome this possible issue we also propose a second method to assess the e¢ cacy of the chosen rule. We assume that retailers can observe a noisy signal of their potential customer base (just by looking at the number of cars passing by the station’s premise). Hence, in this second case, instead of pro…ts, retailers will consider the share of cars refueling at their premises times the margin they earn as a share of costs.

The two parameters p-stve-t and very-p-stve control the share of active drivers and the share of very active drivers. Active drivers are those drivers that will make use of the price display, if they see one turned on along their way, whereas very active drivers are a subset of active drivers and are informed of all prices since they use the price comparison website. For these two parameters we do an extensive analysis and vary them in the simulation exercise.

Fuel-concern and emergency-fuel set the thresholds (in terms of the size of the fuel tank) at which drivers start considering refueling and at which drivers are "desperate" to refuel (as to avoid running out of fuel). The fuel tank capacity is a random number between 35 and 55 liters.

The last two parameters t-red-bias and per-exit determine where cars are been created.

There are two options, cars can be created at the two ends of the highway or at the urban intersections. The former mimic the travel of drivers coming from other highway segments while the latter mimic the persistent entrance of cars at each urban segments. The parameter

bias identify the share of cars that are created at the two ends of the highway (if t-red-bias=1 no cars enter at the urban intersections), and the parameter per-exit controls the share of cars that exits at each urban intersection.