Human Behavior and Aggregate Supply Chain Performance

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