Market Entry with Game Theory and Backward Induction

Hello! Welcome to the first lesson in our new module, "Market Entry and Positioning."

In the previous module, we focused on simultaneous-move games, where you and your competitors make decisions without knowing the other's choice. The Prisoner's Dilemma showed us why a mutually destructive price war can be the logical outcome, even when cooperation would be better for everyone.

Today, we shift our focus to situations where timing is everything. Many crucial business decisions, especially your decision to launch your woodworking business, are not made in a vacuum. They are sequential moves, where you act, and others react. Our goal for this lesson is to apply a game tree and backward induction to analyze your market entry decision. This powerful framework will help you move from simply guessing how a competitor might react to logically predicting their most likely response.

From Simultaneous to Sequential Decisions

The pricing games we analyzed before were like playing "Rock, Paper, Scissors"—you choose at the same time. Sequential games are more like chess—one player moves, the other observes, and then decides their counter-move.

Your decision to launch your business is a perfect example. You are the first mover, the entrant. The established local players are the incumbents. They will see you enter the market and then decide how to react. To analyze this, we need a new tool: the game tree.

A game tree, also known as the "extensive form" of a game, is a diagram that maps out the sequence of moves.

• Nodes are points where a player makes a decision.
• Branches are the possible actions a player can take.
• Payoffs at the end of the branches show the outcome for each player.

Let's watch a quick video that introduces the classic market entry game and visualizes it as a game tree.

As you saw, the game tree makes the order of decisions explicit. Here's a typical representation of that scenario:

The Power of Thinking Forward and Reasoning Backward

In a sequential game, a competitor might threaten a certain action to scare you off. For example, an established local cabinet maker might say, "If any new premium CNC business starts up here, I'll slash my prices and drive them out of business!"

Should you believe this threat? Not necessarily. Game theory teaches us to analyze whether the threat is credible. A threat is only credible if, when the time comes to act, it is in the player's best interest to carry it out.

The technique to systematically sort credible actions from non-credible bluffs is called backward induction. The logic is simple but incredibly powerful: to figure out the best first move, you must first figure out what the last move will be.

How to Use Backward Induction

Backward induction involves starting at the final decision points in the game and working your way back to the beginning. At each node, you find the optimal choice for the player whose turn it is. Since you assume your competitors are rational, you can predict their moves and "prune" the branches of the tree they won't choose.

The following video provides an excellent step-by-step demonstration of this process. While the example is whimsical (involving characters from Harry Potter), the logical process is exactly what we need.

Applying Backward Induction to Your Woodworking Business

Now, let's apply this to your situation. You are considering entering the premium cabinet market. Your main competitor is an established local company, let's call them "Heritage Kitchens".

Here is the game tree for your decision. We'll estimate the monthly profits (in thousands of dollars) for each outcome. The payoffs are listed as (Your Profit, Heritage's Profit).

1. Your Decision: You can Enter the market or Stay Out.
   • If you Stay Out, the game ends. You make $0, and Heritage Kitchens keeps its monopoly profit of $40k. Payoff: ($0, $40k).
2. Heritage's Decision: If you Enter, Heritage Kitchens sees your new business and must respond. They can either Accommodate you or Fight you with a price war.
   • If they Accommodate, they accept the new competition. The market is shared. You both make a decent profit. Payoff: ($15k, $25k).
   • If they Fight, they drastically cut their prices on similar products to try and drive you out. The price war hurts everyone. Payoff: (-$10k, $5k).

Let's solve this using backward induction:

Step 1: Start at the end. Look at Heritage Kitchens' decision node. This decision only happens if you enter. They have two choices:

• Accommodate and get a profit of $25k.
• Fight and get a profit of $5k.

A rational Heritage Kitchens will choose the action that gives them a higher payoff. Since $25k > $5k, they will choose to Accommodate. Their threat to fight is not credible. We can effectively cross out the "Fight" branch.

Step 2: Work backward to the previous decision. Now, look at your initial decision to Enter or Stay Out. You are a rational player, and you've already figured out what Heritage will do if you enter.

• If you Stay Out, your payoff is $0.
• If you Enter, you know that Heritage will Accommodate, leading to a payoff of $15k for you.

Comparing your two options, $15k > $0. Therefore, your best move is to Enter.

The predicted outcome of the game is: You Enter, and Heritage Kitchens Accommodates. This outcome, found through backward induction, is called a Subgame Perfect Equilibrium. It's the most likely result because it's built entirely on credible choices.

Test your understanding!

Imagine the market is tougher than we thought. A price war would hurt Heritage Kitchens, but not as badly, because their scale gives them lower material costs. The payoffs for fighting are now different:

• Stay Out: ($0, $40k)
• Enter -> Accommodate: ($15k, $25k)
• Enter -> Fight: (-$10k, $30k)

Using backward induction, what is the predicted outcome of the game now? What should you do?

Show answer

Let's apply backward induction again.

1. Start with Heritage's decision: If you enter, they now compare Accommodating (payoff of $25k) to Fighting (payoff of $30k). Since $30k > $25k, their rational move is now to Fight. The threat has become credible.

2. Work backward to your decision: You anticipate their response. If you Stay Out, you get $0. If you Enter, you know they will Fight, and your payoff will be -$10k. Since $0 > -$10k, your best move is to Stay Out.

The predicted outcome has completely changed. This shows how crucial it is to accurately estimate the payoffs—not just for yourself, but for your competitors as well.

Conclusion

Today we've added a vital tool to your strategic toolkit. By modeling sequential decisions with a game tree and solving them with backward induction, you can cut through the noise of bluffs and threats to see the logical path a competitive interaction will likely take.

Key Takeaways:

• Sequential games are where players move in order, observing and reacting to one another's actions. Market entry is a classic example.
• Game trees are the visual tool used to map out the players, actions, and payoffs in a sequential game.
• Backward induction is the method for solving these games. By starting at the end and working backward, you can determine each player's best move at every stage.
• This process reveals which threats are credible (in the player's self-interest) and which are non-credible bluffs that should be ignored.
• The solution found through backward induction is the Subgame Perfect Equilibrium, representing the most plausible outcome of the game.

Preview of the Next Lesson:

We've established how to analyze an entry decision. But this raises a new question: is it always best to be the first to enter a market? In our next lesson, we will evaluate first-mover advantages and disadvantages for your woodworking business. We'll explore the strategic pros and cons of being a pioneer versus a follower.