Over the last decade, preschool education has become a popular topic of conversation. Many public schools now offer “education” for kids before kindergarten. An overlooked aspect of this is the strategic implications. By offering pre-kindergarten education, the public schools are channeling students into their K-12 system. Effectively, they are preventing charter school boards from access to these students. We can use game theory to analyze how public school boards use preschool to prevent entry by charter school boards.

Now, of course, parents still have a choice. They could enroll their kids in public preschool then move them to kindergarten in a charter school board. But that takes time and, perhaps, money. Thus, public preschool imposes a cost on parents who want to have their kids educated in a charter school board.

It is an axiom of economics that when you increase the cost of an activity, the volume of that activity will decrease. It’s easy to predict that some parents who like charter school boards will be unwilling or unable to bear the cost of transferring their kids to charters.

The astute reader will wonder why charters don’t just offer preschool. And, eventually, many will. But changes to their curriculum must be approved by the chartering agency. Often this is a hostile public school board. It may take years for the charter to finally be allowed to offer pre-kindergarten classes.

Why has preschool become so popular? The best available evidence shows that the benefits vanish by about third or fourth grade. There appear to be two reasons for the substantial support for preschool. The first is preventing entry by charters. The second is low-cost babysitting services.

This article focuses on economic analysis. A companion piece delves into the details specific to California. As always, a pdf version is available at the bottom of this article.

Game Theory and Preschool

Game theory teaches us that there are a variety of strategies available to deter entry to a market. In this case, the market is pre-kindergarten education. Potential suppliers include public schools, private schools, chartered schools and not-for-profit organizations (often religious). Public schools have a competitive edge because parents can send their children to these programs for very low prices, often zero. Let’s explore some of the game theory results to see how they apply to this market.

First, it’s important to note that entry deterrence is time dependent. It’s very costly to deter entry forever. Let’s take it as given that the planning horizon is five years. Why five years? Why not? It’s a convenient number between zero and forever. In the following examples, the numbers I use do not represent dollar payoffs. Think of them as the increase in power of each entity.

Paying to Deter Entry

One strategy is paying to deter entry. For this example assume the public school board makes the first move. The charter school board then chooses its best response to the public school board’s decision. The public school board is facing the decision tree shown in Figure 1.

Paying to deter entry

Here’s how to interpret this tree. Suppose the public school board decides not to enter. If the charter also doesn’t enter, the payoff to both will be 0. In other words, the status quo will be sustained. If the public school board does not enter and the charter enters, the school district will lose -2. That reflects parents selecting the charter, the only entity offering preschool. The payoff to the charter will be +5. But if the public school board pays to deter entry and the deterrence is effective, the payoff to the public school board will be +5 and the charter will lose -2.

When analyzing any decision tree, always start at the right edge. In this case, that means looking at the decisions faced by charter school board. If the public school decides not to enter and the charter also does not enter, the payoff to the charter is 0. But if the public school decides not to enter and the charter does enter, the payoff to the charter is +5. The charter will choose to enter. The notation for this decision is to “prune” the upper branch by putting || through it. That implies the payoff to the public school is -2. Figure 2 summarizes this outcome.

The charter school board’s decision

Now the public school board faces a decision knowing that if they choose not to pay the charter will enter the preschool market. Thus the payoff to the public school in that case will be -2. But if they pay (begin offering preschool) their payoff will be +5. We cut off the upper branch of the decision tree. The public school will offer preschool and the charter will not. At least not during the planning horizon of five years. Figure 3 shows the final outcome.

The public school board’s decision

The public school board will offer preschool. And the charter school board will start filing plans for preschool with the public school board. Having watched a number of similar situations over the years, it’s easy for me to predict that the charter’s application will be held up for at least five years, with multiple lawsuits along the way.

Raising the Charter School’s Costs to Deter Entry

A second strategy is to raise your competitor’s costs. For this example, assume the charter school board makes the first move by announcing their intention to start a preschool. The public school board has a variety of ways to raise the cost to the charter school. They can reject the application. The charter school board may revise and resubmit the application. After a few iterations of this, the charter school board will probably sue the public school board. Lawsuits are time-consuming and expensive. But there are costs to the public school if the charter offers preschool first. Students will be channeled into the charter school’s enrollment stream. Let’s see how that works. Figure 4 summarizes this situation.

Increasing costs to deter entry

If the charter decides to enter, the public school can either raise the cost of entry (denoted as “file lawsuit) or not raise cost. If the public school files a lawsuit, the cost to them will be -2. But the charter will lose -5 because their entry into the preschool will be delayed. Adding to the cost will be defending the lawsuit and filing repeated applications. If the public school decides not to file a lawsuit, the charter will benefit with a payoff of +5. But the public school will lose students as they are channeled into the charter’s K-12 system.

If the charter does not enter, let’s assume the public school offers preschool. In that case the payoff to them will be +5. The charter will lose -2 since they will lose students.

As before, we will start with the public school board’s decision. If they file a lawsuit, they will lose -2. But if they don’t file, they will lose -5. The public school board will file the lawsuit. Figure 5 summarizes this result. We prune the lower branch on the tree and make the payoff to the charter school -5.

The public school board’s decision

Now we can analyze the charter school board’s decision. If they enter the market, their payoff will be -5. But if they don’t enter, they avoid the cost of the lawsuit. The only remaining cost is the students they lose to the public school. Their payoff is -2.

The charter school board’s decision

The charter school board will not enter the market. This happened because of the threat of the public school board taking actions to raise the cost of entry.

Conclusion

In this article I’ve shown two techniques a public school can use to deter entry to the pre-kindergarten education market. The first method is a pre-emptive first move. Note that the success of this strategy depends on the ability of the public school board to delay the charter’s entry for several years. In this case, there is first-mover advantage.

The second method assumes the charter school board makes the first move. The public school board can take actions that will increase the cost of this attempted entry. By raising the cost sufficiently, the public school board can again deter entry. In this case, there is first-mover disadvantage (second-mover advantage).

In case you think these scenarios are unlikely, I have watched both strategies being used in Bay Area schools. It is not a nice experience.