Gaming the system: predicting university fee decisions

Brody Viney


June 27th, 2014

With debate heating up over the future of university fees, Brody Viney tries his hand at fortune telling – the game theory way.

As any good shaman could probably tell you, predicting the future is never easy. There is always a range of factors at play and a vast array of possibilities to sort through, and often forecasts have to be made in the absence of much information.

With Australia’s tertiary education system about to go through an enormous transformation at the hands of the Abbott government, predicting the future is exactly what many people are now attempting to do.

Foremost among them is Education Minister and soothsayer-in-chief Christopher Pyne, who has embraced a neoliberal view of tertiary education. He sees universities as firms in a competitive market, competing on price and quality to deliver the best value for students, while arguing that fees are likely to go down as price controls are removed.

Others have suggested that fees are more likely to rise, arguing that the tertiary sector is far removed from the perfect market of a microeconomics textbook.

So who is right? Instead of speculating on the tarot-reading powers of different commentators, it is possible to explore these competing views in a structured way by employing game theory.

Setting up a game between two universities with differing levels of quality, we can imagine them choosing between low, moderate or high fee levels (which are represented by the values $1, $2 and $3). They compete for a share of variable student enrolments totalling 1, a figure which constitutes students who have met entry requirements at multiple institutions and hence are required to make a choice. Most universities probably have an additional base level of enrolments due to selection criteria, scholarships and the attraction of local students, but these are outside the game presented here.

In Pyne’s version of events, students make enrolment decisions by weighing up both the price of the degree and its quality, suggesting that students will choose the better quality university when fees are equal and be indifferent (thus splitting enrolments evenly each way) when fees are moderately higher at the better quality institution. If the fees become too different, students will eventually choose the cheaper option.

Here’s what that looks like:

Screen Shot 2014-07-01 at 1.17.11 pm

Assuming a starting point where both universities have moderate level fees (under the current system), the low quality university cuts its fees to break into the market, splitting enrolments 50/50 and establishing a Nash equilibrium where neither university can improve its outcome by changing its fees. This is Pyne’s purported expectation – fees at low quality universities will fall and high quality universities won’t be able to raise fees without bleeding enrolments.

However, this result depends entirely on the price elasticity of demand for places and the level of increases proposed. In this example, a 50% drop in enrolments is related to a 50% rise in fees, but research by Universities Australia suggests fees could actually double. Demand may also be significantly less elastic. Assuming a high fee level of $4 instead of $3, and a 25% fall in enrolments rather than 50% as a result, the model becomes:Assuming a high fee level of $4 instead of $3, and a 25% fall in enrolments rather than 50% as a result, the model becomes:

Screen Shot 2014-07-01 at 1.18.40 pm

Now, regardless of the actions of its competitor, the high quality university will raise its fees, and the low quality university will be indifferent between low and moderate fee levels. Given the already intense funding pressure on the tertiary sector, it seems a stretch to imagine lower quality universities would be able to cut fees very far, especially not without doing further damage to their reputation and course offerings, leaving a moderate/high fee level split as a result.

Thus, even within Minister-turned-fortune-teller Pyne’s version of the game, the outcome could easily be higher fees and not lower.

This model is even more flawed, however, because we know that when fees are equal, students don’t all flock to one ‘best quality’ institution. This suggests that quality is veiled and contested, and the model needs to be rethought.

Some, such as Ross Gittins and Emmaline Baxley, have proposed that income-dependent loans remove upfront costs for students, and thus demand is not negatively related to this price signal at all. Instead, because students have limited information about the quality of different universities, in a deregulated system they might in fact use price as a proxy for quality, choosing the more expensive institution on the assumption that it will offer the best education.

Under these conditions, the game looks like this:

Screen Shot 2014-07-01 at 1.07.37 pm
In this scenario, the universities split enrolments 50/50 if their prices are equal, regardless of quality, meaning that both are able to raise fees to a high level and retain the same share of students (0.5). A deregulated system would thus induce universities to compete to set the highest price, possibly causing them to rise in perpetuity.

A system where fees spiral rapidly upwards at all institutions, regardless of the quality of the courses they offer, is a long way from the paradise of affordable and world-beating institutions that Pyne would lead us to believe is coming.

While this is an extreme scenario, it points to a major risk of universities and students behaving differently to the way that free-marketeers might expect them to. Even a small miscalculation of the factors would render the vision in Pyne’s crystal ball a cheap con.

It remains to be seen whether these measures will pass the Senate, but if they do, it won’t be long before the future becomes the present that all university students have to contend with.

Then we’ll see for ourselves just how good a shaman Christopher Pyne really is.

The views expressed within this article are those of the author and do not represent the views of the ESSA Committee or the Society's sponsors. Use of any content from this article should clearly attribute the work to the author and not to ESSA or its sponsors.

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