What exactly is game theory and how can it help in procurement and supplier management? Angus Craig and Daniel Crease do the maths.

Working life is all about our interactions with other people and the way we choose to react to different people in different situations.

In procurement, our interactions are often about influencing people and may mean persuading a stakeholder to adopt our strategy, or a supplier to improve their offer. In these situations, we often use the term “win:win” or “zero-sum game”.

You may not be aware of it, but the actions people elect to take in these situations have been studied by academics for decades and go under the banner of ‘game theory’. The origins of game theory are in mathematics, but it is now used in fields as diverse as economics, political science, biology and psychology. You can also find it in a number of popular forms, like the game ‘paper, scissors, rock’ (and, of course, the evolved version of that, from the comedy series The Big Bang Theory, ‘paper, scissors, rock, lizard, Spock’). It has also been seen in Hollywood blockbusters such as A Beautiful Mind.

What is game theory?
In brief, it is about how people make decisions, knowing that other people’s decisions will have an impact on what happens in the end. Game theory applies mathematical models to decision-making in order to predict the outcome of competition or co-operation. By analysing how people make decisions (games) when two or more people are involved (players), it is possible to predict the best course of action. Each player has to make suppositions about the plan of action (or strategy) of the other players. It’s a bit like chess: you have to anticipate how your opponent will react to your actions when you make a move. Sound like the day job? It should…

Here’s an example: a supplier knows that if he lowers his prices, he can steal customers from other suppliers. But other suppliers, having lost their customers, will be forced to lower their own prices too, so that their customers return. In the end, all the suppliers are worse off (since they have lower prices and the same amount of sales).

Supermarkets play the game by regularly discounting the price of some products to the point where they make a loss. They hope that customers will be drawn into the store or website and buy not only the discounted product, but other products as well. They also hope that the customers will return after the discount period has come to an end.

The prisoner’s dilemma
One of the most popular ways in which game theory is explained is through the prisoner’s dilemma. We have all faced a similar situation: perhaps when we were children and had done something wrong, but felt that someone else should take the blame. Or maybe in team meetings when we realise we could have helped to improve an outcome, but didn’t take the time to get involved. We are faced with a choice of staying quiet and risk being found out later, or owning up to admit we were involved.

We can also see the prisoner’s dilemma at work in a negotiation between suppliers and buyers. On one hand, if the supplier reveals his prices, then the buyer can take advantage of this information and agree only to the supplier’s lowest price. On the other hand, if the buyer talks and reveals his budget, then the supplier knows the maximum price he can charge and still be within budget. And finally, if they both talk and reveal their positions, they will settle on a price somewhere in the middle.

The prisoner’s dilemma can help us understand basic negotiations. It assumes that the buyer and supplier only meet once to discuss the price. This is called a ‘single play’. The buyers may ‘win’ by getting the supplier’s lowest price. The game ends when the transaction is complete.

But life as a buyer is rarely that simple. Most negotiations involve more than just a one-off discussion about price and take place over long periods of time, from the initial contracting process through to delivery during the contract term and then again at renewal. Furthermore, both the buyer and the supplier have to perform against the contract, possibly over a number of years. For game theory to be really useful in our day-to-day lives, we have to understand how these ‘repeat plays’ affect buyer and supplier strategies.

Game theory can changethe way you think about procurement
Research in the 1980s by political scientist Robert Axelrod found that non-co-operative behaviour is the dominant strategy in the single-play situations.
The opportunity to benefit from co-operation is significantly less and more risky than the gain from acting solely in your own interest. From an economic perspective, the academic Mari Sako showed that identifying mutual expectation of repeated business is the only incentive for co-operation. Both the buyer and the supplier are looking beyond the existing requirements and thinking about future requirements and how the other party might be involved.

With repeat plays, such as strategic collaborations, co-operation is more common (as is non-opportunistic behaviour) and it is actually maintained as each firm compares the immediate gain from cheating or getting one over on their opponent, with the possible sacrifice of future gains that may result from violating an agreement. The longer the period over which repeated transactions are expected to occur, the less it pays to behave opportunistically due to the retaliation inherent in a ‘tit-for-tat’ strategy, and the more advantageous it becomes to risk betrayal and take the first move to co-operate.

Strategic collaboration and the positive behaviour that underpins such relationships can be further facilitated and enhanced through fulfilling promises – “doing what you’d said you’d do” – investing the time and effort in effective communication and sharing timely, appropriate and useful information. All these actions serve to make the role of the other player easier in some way and, with increased predictability in the opponent’s moves, trust increases which further reduces their incentive to behave opportunistically.

How can game theory help me in my day-to-day role?
Procurement includes a wide range of specialisms that can be broadly divided into sourcing, category management and supplier management. Game theory can help us do our jobs better in each.

Sourcing
There are a number of different techniques for gathering information and selecting a vendor such as requests for information, invitations to tender and e-auctions. Game theory challenges us to consider the possible outcomes and the best way to achieve the best one. If it’s a simple one-off requirement (single play) that could be met by a number of different suppliers, where the lowest price is the key success factor, then the prisoner’s dilemma shows us that buyers only need to share limited information with suppliers. Furthermore, if the buyer wishes to increase competition, he or she may consider using a reverse auction. The price starts high and suppliers offer decreasing bids, thus driving the overall price down. The auction relies on active competition among bidders and are usually best where there are four or more suppliers bidding.

Sourcing for more complex products and services that are delivered over a long period of time (repeat plays) requires a different approach. Game theory shows us that it is worth taking the time during the contracting process to understand what the other party needs – both in terms of providing you with what you want and ensuring that they get what they need in order to fulfil it. Failure to understand that win:win dynamic may result in poorer supplier performance and, ultimately, early termination and will almost certainly limit the value from the wider relationship and contract.

Category management
When buyers are researching a market, game theory can help them to consider how suppliers might react to changes in competitive forces. Take, for example, the market for specialist software. Demand is too small to warrant more than one supplier developing their own software. If more than one supplier develops the software, then they would all lose money. If one supplier develops a new release of the software that is much better than the previous version, then that company would make a lot of money and dominate the market; if neither develops a new release and continue to support the existing release, the status quo would prevail.

This emphasises the need for the buyer to understand product development, both in terms of the current and future needs of the buying organisation and the direction of the suppliers.

Not only will this help to avoid buying a product that has a limited life, but it also creates opportunities to shape development and drive additional value.
Game theory can also help to understand supply chain management. Take another example: if one supplier runs out of stock, customers will switch to a competitor. However, if the supplier orders too much, then all the money will be tied up in inventory and the supplier won’t be able to sell it all, resulting in a loss. Therefore, inventory decisions affect the profit of competing suppliers.

Supplier management
Many of the principles that apply to sourcing complex products and services also apply to the supplier management associated with managing them. Because organisations only manage suppliers in order to protect the value they contract for and ideally enhance it together over the term, supplier management requires even greater levels of information sharing and co-operation to be truly successful. Buyers and supplier managers should give more consideration to the following:

  • Accurate, timely and appropriate levels of information sharing are key to enabling effective communication, which improves the supplier’s ability to plan their business and has been shown for decades to facilitate trust between parties.
  • Effective internal co-ordination of the key people on the part of the buying organisation will mean that everyone involved knows their role in the management of the supplier and subsequently communications are significantly enhanced.
  • Maintaining a robust governance discipline underpinned by high-quality data metrics, rigorous annual objectives and accountability. Periodic involvement of senior management and executives also helps to maintain supplier visibility, confidence and strategic information sharing.
  • Maintaining a dynamic and competitive environment; a long-term relationship built on positive repeat transactions will reduce the risks of complacency.

The result of greater levels of information sharing and consideration of the other parties’ interests can ultimately lead to greater value for both players – such as buyer and supplier working together to reduce total cost rather than just the supplier struggling to reduce price. Some of the best examples of this can be found in automotive manufacturing, where relationships with the critical tier-one suppliers are an integral part of the original equipment manufacturer’s long-term success.

Summary
We all use game theory in our day-to-day lives. By being more aware of it, we can use it more effectively and help our colleagues and suppliers to use it as well. As the profile of procurement continues to rise, we are expected to find better ways to explain how different approaches will deliver better results. Game theory is another weapon in our armoury and can greatly contribute to the sophistication and success of procurement professionals.

Two suspects have been brought in for questioning, but the police have very little evidence, so they need to get them to talk. The suspects are taken to separate rooms and presented with this table.

The table shows that if suspects A and B talk, they both get four years in prison. If suspect A stays quiet and suspect B talks, suspect A gets eight years in prison and suspect B gets one year. If suspect A talks and suspect B stays quiet, then suspect B gets eight years in prison and suspect A gets one year. If they both stay quiet, then they only get two years each. Now, you might say, “Why don’t they both stay quiet? They’ll only get two years each.” But, can they trust each other to stay quiet? In this case, their best strategy would be to talk because it is better for them to talk, just in case the other person does.

A beautiful mind
A Beautiful Mind is a 2001 film based on the life of John Nash, a Nobel Laureate in economics. The story begins in 1947 when Nash wins a scholarship to Princeton University, where he is put under pressure to publish his ideas. He refuses until he comes up with a truly original idea. Inspiration comes when he and his friends discuss how to approach a group of women at the bar. One advocates “every man for himself”, but Nash argues that a co-operative approach will lead to better chances of success. He observes that “in competitive behaviour someone always loses” and that co-operation will result in a better outcome. This eventually leads to his revolutionary work on game theory.

Angus Craig is a director of Craig Hall Consulting. Daniel Crease is head of the Supplier Relationship Management Centre of Excellence at Barclays Bank.

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