Game theory is a useful tool in understanding supply chain performance under certain conditions and may also be useful in supply chain decision processes.
In 1992, Bob Crandall, CEO of American Airlines and widely considered one of the best executives in the airline industry, said “This industry is always in the grip of its dumbest competitor.” What he meant was that despite having sophisticated computer systems, advanced decision-making processes, and very smart people, if one of his competitors dropped their price, he would have to follow suit. This is the consequence of operating in an industry with an interchangeable product and a lot of excess capacity. Keep in mind that up to that point, the cumulative profit of the entire airline industry over its nearly 50 years of existence was negative. And yet, despite being highly capital-intensive, the industry continued to attract new players.
The same fate befell the American automotive companies in the 1980s and 1990s. In this case, it was the result of a relatively inferior product, excess capacity, and long-term liabilities that had built up over 50 years of short-term decision making. If one automotive company offered a $5000 incentive, another had to offer the same. In both the airline and automotive examples, industry pricing always reached an equilibrium at the lowest level set by any one player (or as Crandall said its “dumbest competitor”). Today, the automotive industry, courtesy of the pandemic, has almost the opposite problem. The same can be said of the airline industry. More on that later.
What does this have to do with supply chains? This is an example of human behavior having significant impact on the overall performance of an industry. Throughout the past three years, much has been discussed about the dysfunction of our global supply chains. One of the topics that has not gotten its fair share of airtime is the impact of human behavior on supply chains and more importantly on the aggregate overall performance of global supply chains.
Here we bring this topic into focus using game theory. In the process we also discuss the use of game theory in supply chain decision making, particularly in the decision-rich sales and operations planning (S&OP) process.
But before we discuss the application of game theory to supply chains, let’s review the most known game associated with game theory followed by its application to the airline pricing problem.
Prisoner’s Dilemma
The prisoner’s dilemma is perhaps the best known and most often quoted game associated with game theory. It has wide applicability in helping understand decision making in a wide range of problem sets.
This game is a two player, non-zero-sum game in which players must choose to cooperate or not cooperate (defect). A non-zero-sum game is one in which it is possible for more than one player to come out ahead. This contrasts with a zero-sum game, in which the sum of winning and losing is zero. For example, poker is a zero-sum game. The amount of money won by one player equals the amount of money lost by the other players.
Prisoner’s dilemma gets its name from the original form of the game: two individuals are arrested under suspicion of having committed a crime together. They are placed in separate jail cells where they cannot communicate with each other. The police do not have sufficient evidence to try them, so they offer each a deal: if you defect (i.e., rat on your partner), you will go free, but your partner will serve a 5-year sentence. On the other hand, if both remain silent (that is, cooperate with each other), they will both go free, because the police lack sufficient evidence. If they both defect (i.e., rat on each other), they will both go to jail, but with a lighter sentence of 1 year. The game is typically represented with a 2x2 matrix as shown below.
Figure 1 – Classic Prisoner’s Dilemma Game Representation
The first number in the matrix is the number of years prisoner A gets; the second number is the number of years prisoner B gets.
As you can see from this representation, if both cooperate (keep quiet), they both will receive no prison time (0,0). If A keeps quiet, but B defects (rats on A), then A will receive 5 years and B will go free (-5,0). Likewise, if A defects (rats on B) and B keeps quiet, then B gets 5 years and A goes free (0,-5). Finally, if both defect (rat on each other), then both will get 1 year (-1,-1).
It has been shown through various experiments of this game and others like it that the most likely path that humans take is to defect. Even in situations where the players are partners, each assumes the other will defect, so they both defect. Even though the maximum value of the game is achieved through both remaining silent (cooperating with each other), this cooperation does not take place presumably because each assumes the other will defect.
Therefore, in this example, both prisoners get 1 year in prison. This is called the payoff of the game. This is also called an equilibrium; in game theory, an equilibrium is a point in which a player cannot improve her outcome by unilaterally changing her strategy. (This is known as a Nash equilibrium, named after the mathematician John Nash, who worked on this and other more advanced areas of game theory).
Now that we have seen the logic of the prisoner’s dilemma game, let’s see if we can apply it to the airline pricing problem discussed earlier and then to supply chain problems.
Airline Pricing Example
Let’s return to the airline industry as it was when Bob Crandall said, “this industry is always in the grip of its dumbest competitor.” As previously stated, that was a time when there was widespread excess capacity. The key lever to fill capacity was price. But what happened to the industry when a competitor lowered their price? Figure 2 is a directional depiction of what happened, using the prisoner’s dilemma game. In the matrix, the first number is the payoff for A; the second number is the payoff for B.
This could be a situation between competitor A and competitor B or between competitor B and all other competitors; thus, it can be used to understand what the payoff will be for the entire industry. If all companies maintain pricing discipline (i.e., cooperate), the payoff for all the players may still not be great, but it’s the best possible payoff for everyone. If competitor B tries to unilaterally defect, they will win, and the rest of the industry will lose (-5,5). But this never happens because as soon as competitor B defects, all other players defect to the new price point; thus, the entire industry loses (-3,-3). This worst possible scenario is a Nash equilibrium because no single player can unilaterally improve their position by changing their strategy. The only way for anyone to improve their position from the (-3,-3) quadrant is for everyone to move together to a new price point.
Figure 2 – Airline Pricing Game Under Conditions of Widespread Excess Capacity
Now let’s consider the airline industry of today, in which there is no excess capacity; indeed, there is a capacity shortage. The payoff matrix looks completely different, as shown in Figure 2. In this situation, the payoff for defecting (i.e., lowering price) is the exact opposite of before – when you lower your price you lose and everyone else wins. Therefore, the entire industry coalesces around the upper left quadrant, and everyone wins. The industry is said to have pricing discipline, but in fact the discipline is brought about by scarcity – a shortage of capacity. (Note: this is not a prisoner’s dilemma, since there is no dilemma).
Figure 3 – Airline Pricing Game Today
Therefore, the cooperation quadrant is a new type of Nash equilibrium – one where everyone wins.
Supply Chain Problem Definition
Let’s define a common problem with supply chain performance, one which was prominent during the pandemic and one in which human behavior played a significant role.
Most supply chains operate using shared resources, that is, resources that are also used by multiple companies and supply chains. In other words, there are very few vertically integrated supply chains, particularly in a global context. There may be simple regional supply chains that are vertically integrated, but even small companies leverage global resources. These shared resources include manufacturing, warehouses, trucks, ports, airplanes, airports, ships, and all the labor associated with these resources. A simplified picture of part of the global supply chain is shown in Figure 4.
Figure 4 – Simplified View of Global Supply Chain
In this view, a company (retailer, manufacturer, or distributor) in the United States has its products manufactured in China and then transported to their “owned” supply chain in the United States. The manufacturing is done by a sub-contractor in China; this sub-contractor may also produce products for other companies. Once the product is manufactured, it must navigate through various third-party logistics companies to make the 9,000-mile journey to someplace in the middle of the United States. This overall journey can be coordinated by the company itself, or by a third party, or by a combination.
We call these third-parties shared resources because they serve multiple company supply chains. Of course, the resources are contracted; this means that they do provide some level of dedicated capacity to their clients for some period of time. But they also provide spot-market or surge capacity for everyone; furthermore, they are scheduled in accordance with the needs of their customers.
Now consider what happens in competitive situations in business with Competitor A and Competitor B in this supply chain context, in situations in which there is “normal” demand and supply disruption. The game here is that both competitors “compete” for shared resources that are necessary for manufacturing, transporting and their products to customers (retail locations, individuals, enterprises, distributors).
In this game, cooperation may not be possible, or even legal. Both competitors follow their demand and supply strategies, which are based on winning in the market (i.e., doing better than their competitors). In this case, there are enough shared resources to go around, so it’s a matter of getting those shared resources for the most competitive price and the best service. As long as there is excess capacity, there is a “benevolent” equilibrium in which aggregate supply chain performance is maintained within a manageable band.
But what happens when the shared resources don’t run on time? The schedule of one company starts to affect the schedule of another company – and so on a thousand times over – and things rapidly unravel. The “benevolent” competition shifts to a different kind of equilibrium where everyone loses; and the greater the extent to which company shared resource schedules overlap the greater the extent to which things can devolve into chaos. Even though everyone has the same goal of keeping the trains running on time, the game devolves into a scramble for resources at any cost. The “benevolent” equilibrium rapidly transitions to a pernicious equilibrium in which aggregate supply chain performance goes in the tank, and everyone loses. This can be represented by the following game theory matrix.
Figure 5 – Supply Chain Game in the Pandemic or Other Significant Disruption
Here, if competitor A defects (starts over ordering, attempting to get a greater slice of shared resources), they clearly get an advantage at the expense of competitor B (10,-10). This makes sense; when there is a disruption, or a spike in demand, you want to take advantage of that at the earliest point of visibility. You try to secure scarce capacity and increase your orders.
However, what happens is that eventually everyone catches on; in the case of the pandemic, this was done quickly. Therefore, the entire system gravitated towards everyone defecting and ended up with all competitors losing due to a significantly clogged supply chain. This is represented by the lower right quadrant (-10,-10). The is where scrambling for inventory and significant over ordering were happening.
In these situations, invariably the larger players end up with a bigger piece of the pie. The shared resource companies have their own prisoner’s dilemma – how to best allocate constrained resources across multiple customers. In fact, how best to allocate constrained supply across customers is a classic strategy game in the field of game theory. The larger players also have the resources to bypass certain elements of the shared resources by vertically integrating. For example, several players were contracting their own ships and circumventing clogged ports.
The net result of this human behavior is that the amplitude of the bullwhip effect increases substantially. This was on full display during the pandemic. Hopefully, we don’t have to see a disruption of this depth and duration for a good long time. However, it does not take a pandemic to bring forth this behavior. Human behavior of this kind is not going away; shared resource disruptions of all kinds will manifest it.
What to Do About It?
This problem has been investigated and researched in other contexts for decades. It goes along the lines of “is there a central authority that can impose rules such that individuals don’t make decisions that are harmful to themselves and to the aggregate good?” In competition of the sort discussed here, the short answer is no. The global supply chain operates in a largely free market capitalist framework. There are rules in place to prevent the opposite problem, namely collusion, cartels, and the like. But each company makes decisions that are largely in their self-interests, namely growth and profit.
That said, there are market-moving companies like Amazon and Walmart, that can have an outsized impact on aggregate performance. The extent to which these companies maintain ordering discipline can significantly impact others. But they too, are competitive with each other. The matrix shown in Figure 5 can apply to them and by extension to the overall market.
In a previous article we discussed CONWIP (constant work in process), which is a term introduced by the book “Factory Physics,” which was published in 1996. The book uses the idea of constant WIP to describe pull systems and contrast them with push systems. In a factory, CONWIP means that you maintain a constant level of WIP between the start of operations and the end of operations; you only release new material (work) into the system when a finished product is released from the system. Early advanced planning and scheduling systems (APS) were based on this concept through pegging between orders, bills of materials, and routings.
In supply chains, this is a difficult thing to do unless you are vertically integrated and control all the resources. Let’s say you follow a CONWIP strategy for your supply chain, but your competitor releases upstream manufacturing orders into the system without regard to downstream demand. Then your performance may be negatively impacted by your competitor. As Bob Crandall said, “you may only be as good as your dumbest competitor,” since you may be forced to follow suit. The global supply chain is currently set up with a push mentality; this simply makes it worse.
S&OP and Game Theory
S&OP is a decision-rich set of processes that results in an operational plan for an enterprise. The resulting plan is intended to “operationalize” financial and other input plans (e.g., sales plans, environmental plans, capacity plans, supplier plans). These plans can then be handed to operations and supporting systems to execute.
Game theory is particularly well suited for situations where you want to compare your strategies to the potential strategies of your competitors. Demand planning software can consider competitive strategies as part of promotional programs and events based on history. However, there is never perfect information about what a competitor might do in any specific situation. Game theory is designed for these types of situations where you want to consider your strategies against potential competitor strategies, but you have limited knowledge of what those strategies are.
This is by no means an attempt to discuss the detailed use of game theory for S&OP decision making. We are merely broaching the subject. A future article will go into more detail.
Let’s take a simplified example of two competitors: Competitor A and Competitor B. They both compete with a certain product in a certain channel. Their products are similar, and their customer service levels are similar, such that they achieve the same market share (50,50). Furthermore, they employ similar supply chains with similar inventory levels, such that their costs are similar.
Competitor A wants to improve its market share through better customer service. It runs its inventory optimization system, and it tells how much incremental inventory investment is necessary to achieve the desired increase in customer service. Should it implement such a program?
Figure 6 is a simple view of what might happen between customer A and customer B, in terms of market share (note: improvement in market share will come at the expense of margin). The numbers in the matrix are market shares. The first market share is for Customer A; the second is for Customer B.
Figure 6 – Simplified Example of Comparing Strategies
Game theory would say that this scenario would evolve towards the lower right-hand quadrant, with the customer winning in all cases. But there is another key point to be made, even with this simple example: A lot of supply chain improvement programs base their paybacks on the status quo. In other words, the value proposition is based on the same competitive landscape. Or, as Clay Christenson said in Harvard Business Review, they fail to understand what the “do nothing scenario” looks like. If competitor A does nothing to improve customer service in the next three years, what will happen?
For example, companies and their consultants will develop a value proposition for Competitor A in this example. They will say “if you invest this much, you will gain 2 percentage points of market share and the discounted cash flow will be X amount over the next five years.” But most of these value propositions assume that Competitor B will stand still. Value propositions for improvement projects should include different scenarios regarding what competitors will do. Game theory can be helpful in understanding potential competitor actions and then incorporating the results in the improvement program value proposition.
Final Word
Game theory offers interesting insights into human behavior and decision making across a wide range of fields. It can be used to help understand how the bullwhip effect in supply chains can be exacerbated by human behavior, particularly under conditions of disruption. Furthermore, it can be applied for analyzing competitive strategy in several decision-making areas of supply chain, including the S&OP process and investment decisions for improvement projects. We will explore the application of game theory to these and other supply chain areas in future articles.
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