The beer game

In my intro class this week I had the students play the beer game.

The good news is, we got fun results.

The sad news for them is that it involved no consumption of beer. After all, the class is from 9:30 to noon.

It is true that when I lived in Plzeň in 1991-92, the workers on the early shift at the Škoda factory would have a beer on their break at 10am, but the canteen only served the reduced-alcohol variety of Plzeňský prazdroj (aka Pilsner Urquell), and the workers were only making electric locomotives and nuclear reactors, so it wasn't that important to have a clear head. Drinking while learning macroeconomics would be far more dangerous.

You have four links in a supply chain:

1. A brewery
2. A distributor
3. A wholesaler
4. A bar

Everyone starts with some inventory. They have to order new product from the company above them in the supply chain. They try to satisfy orders from below them in the chain.

There's a series of delays built into the system:

• When you place an order for more product, it takes 2 weeks for the order to reach your supplier.
• When you fulfill a customer's order, it takes 2 weeks for your shipment to reach your customer.

So if the bar orders 5 cases of beer, it'll be four weeks before they get those five cases in. (Of course, in the meantime, they've received the beer they'd ordered earlier.)

And that's if their supplier has enough beer on hand when the order comes in. Say the bar orders 5 cases. Two weeks later, the wholesaler receives the order. They fill it if they can, but if they only have 3 cases in inventory, then they only ship 3 cases.

So the bar places its order, and four weeks later it probably gets what it ordered, but it can't be sure.

The brewery has a similar delay, just without the uncertainty. Each week of the game they make a production plan; four weeks later, that amount is produced.

At the end of each "week," each team sees if they had any orders they couldn't fill. If they filled all their orders, they see how many cases they have left in inventory. Each case in inventory costs them $0.50, while each case that was ordered from them but that they couldn't ship costs them $1.00 (customer dissatisfaction is costly).

The only external input is that the person running the game (that was me) tells the bar each week how many cases of beer they've sold to their customers. Everything else that happens is merely the internal workings out of how the teams play.

The classic way to run the game is that you start off with a few weeks of telling the bar that they're selling four cases a week. Then you jump up to eight, and you keep it there for the rest of the game. (I did three weeks of four cases before making the jump to eight.)

So the external input is one abrupt change, with everything else being smooth. A naïve view of markets would suggest that the system as a whole would be relatively smooth as well—a period of adjustment, but then efficiently providing eight cases a week.

That's typically not what happens. And it's not what happened in our game.

Here's the ending inventory:

You can see the wholesaler having high inventories early on, then running to zero. The brewery, in contrast, runs low through middle of the game before building up very high inventories near the end.

Here's the count of unmet orders:

The wholesaler was getting concerned about its unmet orders, so it put in a large order in week 13, and when the distributor learned about it in week 15, they were completely unprepared.

This is the combined cost of inventories and unmet orders:

Starting in week four, the input to the system is a constant customer demand, 8 cases every week. But the system's response is fairly chaotic.

I like the beer game as a mental model for how a complex economy can generate fluctuations in demand just out of its own internal dynamics.

Of course the information structure of the game is very artificial. There's no reason that orders should take two weeks to reach suppliers—even before the internet there were telephones. And the business about shipments taking two weeks is also a stretch. (Though the four-week lag in production at the brewery makes some sense, particularly for a lager.)

Presumably if you reduced the lags, or shortened the supply chain, you'd get less instability.

But if you think of it as a model for the economy as a whole, the game's restricted flow of information is more plausible.

Think of what it takes to make cars. There's the supply chain back through the steel maker to producers of iron ore and coal. The auto maker also needs glass, plastic, electronics, rubber, ... and each of those things has its own supply chain. And the steel makers aren't only supplying the auto makers, but also the construction industry, appliance makers, kitchen wares, ...

Now consider an increase in demand for cars. First, it's going to take a while for the car makers to be confident that what they're seeing is a meaningful change and not some random noise. Once they decide to ramp up production, they put in orders for more steel, and glass, and electronics, ... And each of those suppliers is seeing orders from various customers, and is trying to decide how far to ramp up production to meet demand. And if all the suppliers are facing higher demand (and thus experiencing better profits and/or paying out more in wages), then that should contribute to higher demand in the car industry.

In the beer game, if each team could know everybody's inventories and everybody's order history, the chaos in the system would be eliminated. But they don't know that. The only information they have is some stale news from their customers, and some delayed, uncertain feedback based on their suppliers' ability to deliver what's been ordered.

In the economy, if someone could see everyone's demands, orders, and production possibilities, throughout the whole economy, they could coordinate a smooth response, eliminating internally generated instability. Hayek correctly pointed out in the 1930s how that was an impossible thing for a state to achieve. His explanation for why markets work was not that private companies can achieve the universal knowledge that eludes the state. Rather, his argument was that in a decentralized market, nobody had to know everything. Firms could simply respond to what's knowable in their corner of the world, and the market would act like a giant information-processing machine, setting prices that coordinate the miraculous ballet that is a modern economy.

There's reason to believe that in many activities, decentralized coordination by the market is preferable to centralized coordination by a state that has unavoidable limits on what it can know. But the beer game provides a useful corrective for over-enthusiastic fans of markets. Free-market economies won't necessarily respond efficiently to discrete external stimuli. And such economies are capable of generating their own instabilities, simply out of the interaction of myriad agents making decisions based on very imperfect information.

Fiscal and monetary policies have their flaws, but standing back and letting recessions just "work themselves out" probably isn't the best idea.