Perth Gas Prices

In 2001, the Western Australian government introduced a post and hold policy for retail gasoline. Each day every gas station provided the government with the transaction price for the next day. This gave motorists very detailed information about prices in the market. It also gave gas stations very detailed information.

What the heck is going on here? Above is a chart of the average daily retail gasoline (petrol) price in the Australian state of Western Australia for the year 2010. The chart also shows the daily price of gasoline at the terminal (the wholesale price).

If we zoom in on these prices we see that the oscillations are weekly. Every week the price peaks in the run up to the weekend and then slowly decreases during the week creating a saw-tooth pattern in the data. Why?

Price Regulation in Western Australia

Western Australia has a "post and hold" regulation for the retail gasoline prices. Each day the gas station must post the price for the next day and then it must hold it that price for 24 hours. These prices are then posted on a website: https://www.fuelwatch.wa.gov.au/

Markov Pricing Game

One explanation for the pricing pattern we see in Perth is a game developed by Eric Maskin and Jean Tirole. Let there be two players (two retail gasoline stations) who choose a price for each day. The two stations chooses prices every day but only one price per day. They observe each other's previous day's prices but not the price chosen on that particular day by the other station. Each station makes profits each day which are determined by the daily retail price less the daily wholesale price, with their margin multiplied by the number of liters of gasoline they sell on the day. Of course there are other costs such as wages for the attendant, electricity etc, but we will make it simple and just think about the margin between their retail price and the wholesale price.

Markov

Andrey Markov was a Russian mathematician who developed the idea we now call a Markov chain. This is a matrix with a set of states in the rows and the same set of states in the columns. Each cell provides the probability that the system transitions from one state to another. This idea is used in lots of different applications. Maybe the most profitable is as a way to determine which websites are of the most interest to someone using Google in the late 1990s. A state is a website and the probability represents the proportion of links that website directs to other websites. The matrix operation Google dubbed PageRank gives the average number of times a person will end up at a particular website if they click randomly on links when ever they visit a particular website.

Markov Strategy

A strategy is a function from the complete history of actions observed by the player to an action. In a simple game with just two prices and two stations, the complete history has 4 possible outcomes for 1 day, 16 possible outcomes for 2 days, 64 possible outcomes for 3 days and over 1 million possible outcomes after just 10 days. Maskin and Tirole thought we can make this game a lot simpler if we can categorize the histories. For example, a categorization could be based on the prices chosen the previous day by the two stations. If there are 2 possible prices then there are just 4 categories. We call these categories states. While there could be a large number of history every history can be categorized into 1 of 4 states. A Markov strategy is a function from each of these states to an action. A Markov strategy is still a strategy as it a function from every possible history to an action, we have just found a way to simplify our description of them.

Empirical Cycling Game

The table on the right shows if they both choose the low margin, then they will tend to stay at the low margin (state 1) similarly if they are at the medium margin (state 5). However, if they are both at the high margin (state 9) there is a high probability that one or both of the two firms will drop their price. 

Are Prices Too High?

It is not clear what the question means, but we can ask a different question. We can ask what would prices be if the two firms were playing a more standard pricing game.  To answer this question we need to know what the elasticity of demand is. This is because the margin in the standard pricing game is just a function of the elasticity of demand. So what is the elasticity of demand?

Bounds

We cannot determine the exact value of the elasticity of demand from the data, but we can bound it. At each state we know what both firms did and we know that what they actually did must be more profitable than some other choice. In this case we can test if BP (for example) cheats on the observed mixed strategy Nash equilibrium, what profits BP would earn for different elasticities of demand. If demand is very elastic, then BP can drop its price just a little bit and its market share will jump and its profits will also jump. If demand is not very elastic, then not much happens when BP drops its price except BP makes less money.

The data suggests that the margins made by the two firms in the cycling game are at least three times higher than they would have been if the two firms were playing a standard pricing game.

Post and Hold

Maskin and Tirole note that in their cycling game the "hold" is super important. It is the hold that leads to the cycling as equilibrium behavior. The posting is also useful because it allows the two firms to have pricing strategies that are a function of the observed prices from the previous day.

Having a website like fuelwatch.com.au, seems like a great idea that drives competition in the market. But there is reasonable evidence that it leads to higher prices for Western Australian drivers.