Ask anybody to name two of Australia’s supermarkets and undoubtedly the answers will be Coles and Woolworths. Together, these two giants have 67% share of the market (ACCC, 2025).
Nathan Wong
ESSA Monash Clayton
[Nathan is currently in his second year a Bachelor of Engineering and a Bachelor of Commerce degree at Monash University, specialising in Electrical and Computer Systems Engineering. He is fascinated by behavioural economics, game theory, and the mathematics underpinning economic phenomena.]
Disclaimer: The views expressed in this article are those of the author and do not necessarily reflect the views of affiliated organisations.
Their dominance has often prompted the ACCC to investigate their competitive practices, most significantly resulting in the recent ban on price gouging (Steinwell, 2026). Coles has also been found by the ACCC to have misled consumers with their ‘Down Down’ promotion (ACCC, 2026). All this is hardly surprising, given the lack of competition; but the precise dynamics of this duopolistic phenomenon are much more nuanced. As this article explores, a more precise explanation can be found from a rather obscure source—a branch of mathematics known as game theory.
What is game theory?
Game theory is a branch of mathematics that studies interactions between ‘players’ (economic agents) who each have different ‘payoffs’ (economic utility) depending on their actions (‘strategies’) and the resulting outcome of the interaction (Hayes, 2026). A simplistic definition would be ‘games, and how to win them’.
The classic example of applying game theory to model strategic interaction is called the prisoner’s dilemma (Poundstone, 1992). Here, the players are two prisoners who can choose to either stay silent (cooperate) or incriminate the other prisoner (defect). If both prisoners cooperate, there is enough evidence to convict them only of a minor charge, and each will be sentenced to 1 year in prison. If one prisoner cooperates but the other defects, the silent prisoner will be sentenced to 3 years while the defecting prisoner goes free. If both prisoners defect, both get 2 years. This is illustrated by the following table, called a payoff matrix.
| Prisoner 1,2 | Stay silent | Defect |
| Stay silent | 1,1 | 0,3 |
| Defect | 3,0 | 2,2 |
The key point here is that neither prisoner has an incentive to cooperate. Let us put ourselves in one of the prisoners’ shoes. We do not know what the other prisoner chooses, but if they cooperate, then we are better off defecting so that we go free. If the other prisoner defects, then we are better off defecting too so that we get 2 years instead of 3. Unfortunately, the other prisoner has exactly the same reasoning—no matter what the other does, each prisoner’s best choice is to defect. The resulting outcome (both prisoners defecting) is called a Nash equilibrium (Nash, 1950; Nash, 1951). As the reasoning above shows, if both players think logically through the possibilities of their interaction (and are rationally self-interested), the outcome of this game will be both prisoners defecting and getting 2 years in prison.
But notice that both prisoners would be better off cooperating and getting only 1 year in prison each. Thus, the outcome of a strategic interaction predicted by game theory will not always maximise the utility of its players—so-called Pareto-efficiency—and that is the key insight of this thought experiment.
How does this apply to Coles and Woolworths?
While the prisoner’s dilemma may seem contrived, it can model real-world economic phenomena. Coles and Woolworths’ large market share essentially reduces the supermarket industry into a duopoly where each chain’s actions are strategies in a two-player game and the ‘payoffs’ are profits. A simple model is that both companies have two strategies: set high prices or set low prices. If both set low prices, both will also make little profit. If one sets high prices and the other low, customers will flock to the latter and they will make high profits at the expense of the other. If both set high prices then both make high profits (because consumers have nowhere else to go).
If we think through this game just as we did for the prisoner’s dilemma, we find that the Nash equilibrium is for both supermarkets to set low prices, and suffer from reduced profits compared to if they both set high prices. Neither has the incentive to set high prices because of the threat of being undercut by the other. This is equivalent to the Nash equilibrium in the prisoner’s dilemma game, where both prisoners end up with the harshest sentences.
But this does not seem to reflect reality. As the ACCC’s action against Coles demonstrates, Coles and Woolworths can and do set high prices because of their market power, and their profit margins, according to the ACCC, have only increased in recent times (ACCC, 2025). So what is the game theory explanation missing?
An infinitely repeated game
The key is that so far we have considered only single or one-shot games, where only a single interaction takes place. The interaction between Coles and Woolworths, however, is a repeated game, where each player can keep reacting to the other player’s moves. Indeed, high barriers to entry into the supermarket industry essentially guarantee that Coles and Woolworths remain the only players for the foreseeable future, turning their interaction into an infinitely-repeated game. And since both firms realise that any lowering of prices will simply be matched by the other until a spiralling price war erupts—benefitting neither in the long-term—both keep prices high.
This observation was made in a 1971 paper by James Friedman, who developed a theory of finding equilibria in repeated games (or ‘supergames’) (Friedman, 1971). He concluded that a Pareto-efficient equilibrium can be sustained in such infinite games, and that this signifies ‘tacit collusion’. That is, through the lens of game theory, Coles and Woolworths set high prices because in their two-player game, the short-term profits of undercutting the competitor are outweighed by the long-term detriment of a price war. With no incentive to lower prices in the short-term, the players can settle on the Pareto-efficient outcome that was infeasible in the one-shot prisoner’s dilemma. In this way the two supermarkets collude without any explicit communication.
In the same paper Friedman went further and gave an explicit mathematical criterion for when the players will settle on the Pareto-efficient outcome. Over 50 years later, these ideas provide a remarkable model for our supermarket industry that extends beyond the simplistic notion that fewer competitors guarantees higher prices.
Conclusion
No matter which way it is spun, the Australian supermarket industry does lack competition. But barriers to entry, such as up-front investment and the capital-intensive nature of the industry, remain high. This is not to mention practices such as landbanking (buying land before anything can be built on them) (Grigg et. al, 2024). Nevertheless, consumers would surely welcome increased competition and a challenge to the two dominant players in the supermarket game.
References
Australian Competition and Consumer Commission. (2025, Feb). Supermarkets Inquiry: Final Report. https://www.accc.gov.au/system/files/supermarkets-inquiry_1.pdf
Australian Competition and Consumer Commission. (2026, May 14). Court finds that Coles misled customers over ‘Down Down’ claims. https://www.accc.gov.au/media-release/court-finds-that-coles-misled-customers-over-down-down-claims
Friedman, J. W. (1971). A Non-cooperative Equilibrium for Supergames. The Review of Economic Studies, 38(1), 1–12. https://doi.org/10.2307/2296617
Grigg, A., Potaka, E., Hildebrandt, C. (2024, Feb 20). The tactics Coles and Woolworths use to maintain their power over Australia’s grocery market. Australian Broadcasting Corporation. https://www.abc.net.au/news/2024-02-20/woolworths-coles-supermarket-tactics-grocery-four-corners/103405054
Hayes, A. (2026, June 9). Ultimate Guide to Game Theory: Principles and Applications. Investopedia. https://www.investopedia.com/terms/g/gametheory.asp
McLeod, C. (2026, 14 May). Court rules Coles misled shoppers with its ‘Down Down’ discount campaign. The Guardian. https://www.theguardian.com/australia-news/2026/may/14/accc-v-coles-down-down-federal-court-case
Nash, J. F. (1950). Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, 36(1), 48–49. https://doi.org/10.1073/pnas.36.1.48
Nash, J. F. (1951). Non-cooperative games. Annals of Mathematics, 54(2), 286-295. https://doi.org/10.2307/1969529
Poundstone, W. (1992). Prisoner’s Dilemma. New York. Anchor.
Steinwell, R. (2026, June 22). The new price gouging law starts on July 1. Can it rein in Coles and Woolworths?. The Conversation. https://theconversation.com/the-new-price-gouging-law-starts-on-july-1-can-it-rein-in-coles-and-woolworths-285062
