Formulating Competitive StrategyUsing Game Theory

Microeconomics Essentials

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Course: Microeconomics Essentials

Lesson 5: Formulating Competitive Strategy Using Game Theory

Introduction to Oligopoly and Game Theory

Pepsi does not operate in isolation-it faces stiff competition in the market for soft drinks from Coca-Cola. Pepsi and Coke compete in an oligopoly market-a market that consists of a small number of firms. To formulate competitive strategy in an oligopoly market, a company needs to anticipate the moves and counter-moves of its principal competitors. Game theory is a tool for thinking carefully about competitive battles such as the cola wars between Coke and Pepsi. In this lesson, we will see how game theory can help us anticipate Coca-Cola's reactions as we formulate pricing and capacity strategies for Pepsi.

Nash Equilibrium

Now that we know how firms achieve long run equilibrium in perfectly competitive markets, we can use these principles to analyze how firms achieve long run equilibrium in markets that are less than perfectly competitive. For example, consider the soft drink market. Pepsi and Coke compete in an oligopoly market; they sell differentiated products within a market that is dominated by a small number of competitors who control the majority of the market share. And crucially, with an oligopoly, the actions of one firm significantly affect the profitability of all rivals. If Coke cuts its price, it can seize market share from Pepsi. But how much market share, and with what effect on Pepsi's profitability? Doesn't that depend upon Pepsi's response? Sure, and if this sounds like a (high stakes) game, that's because it is.

Game theory is an important tool that economists and business strategists use to analyze oligopoly markets. Game theory explores what happens when each decision maker in a competitive situation behaves rationally, i.e. each uses microeconomic analysis (the principles that we have explored thus far) to pursue a profit-maximizing path. Game theory assumes that each firm, far from operating in a vacuum, attempts to anticipate the actions and reactions of its rivals and maximize profits accordingly.

Is it possible to use game theory to predict the likely outcome of a competitive situation? Yes, and its called finding the Nash equilibrium. Let's return to Pepsi versus Coke to see how it works.

Stories

I lose? You lose: The Philippines Cola War Redux

In an earlier module, we explored the concept of economic costs as they applied to Cosmos Bottling, the Philippine bottler that, having increased its share of the local soft drink market from 10% to 25%, sold out to Coke. The economic costs to Cosmos' shareholders of remaining independent - and not selling –

were severe. And the benefit to Coke of expanding its market share from 65% to 90% - and thereby leveraging its fixed costs across a much larger-scale operation - were compelling, to say nothing of the benefit to Coke of permanently excluding Pepsi from this large and growing market.

Given the underlying microeconomics that made this deal so attractive to Coke - and to Cosmos - the outcome was preordained, right? After all, Cosmos saw the benefits of selling, and Coke was the logical buyer, yes? Probably. But there's more to the story. Let's see if we can piece this together, using some speculation and a lot of logic based on game theory.

Pretend you're an M&A advisor to Cosmos (or Coke or Pepsi; it doesn't really matter, since each party has to anticipate the actions and reactions of the other, and thereby think through to the end game). Cosmos would rather sell (at the right price) than fight on in the cat-and-mouse battle of "share versus margin" that it and Coke constantly wage in the market.

Coke realizes that it is the natural buyer of Cosmos; dominating both share and margin would be attractive, assuming that the price is right. So the issue is the price. Cosmos, with a subordinate market position, needs to find a way to motivate Coke to make a full bid. And the way to do that is to give Coke some competition.

Pepsi may appear to be the logical choice as a rival bidder, given the oligopoly structure of the industry. But Pepsi has little if any share of this local market. Undeterred, and on behalf of Cosmos, you invite Pepsi to enter the bidding, making two key observations:

• Opportunistic Rationale - First, in buying Cosmos, Pepsi could bootstrap itself into a 25% market share, which it could then expand with the Gatorade product that it has just obtained in its acquisition of Quaker Oats; and

• Defensive Rationale - Second, if Coke buys Cosmos, Pepsi may never again have a practical opportunity to penetrate this market.

Assume that, having conducted various financial analyses; you estimate that Cosmos on its own is worth 60X. Further, you estimate that Cosmos, as a part of Pepsi, could be worth as much as 85X, and as a part of Coke, could be worth as much as 100X.

Assuming that all of the players act rationally, Coke should win the bidding. But in the process, Pepsi should push Coke as hard as it can. By bidding aggressively, Pepsi might just win Cosmos on acceptable terms. And if Pepsi doesn't win, at least it will have forced Coke to pay much more than it otherwise would have. Either way, your client wins, so long as all parties play the game.

Commentary

This example illustrates how the presence of rivals can influence outcomes in a competitive situation. This dynamic changes a lot when you bring Pepsi into the picture, because now Cosmos has an alternative buyer. Simple game theory analysis would suggest that by playing one firm off against the other, Cosmos will attract a more favorable price. Cosmos needs to understand this dynamic, so that it could structure the game, to make sure that both Coke and Pepsi participate in the bidding.

Nash Equilibrium

Consider the competitive dynamics between Pepsi and Coke in the U.S. market. Each can choose one of two strategies - a low-price strategy ("pricing for share") or a high-price strategy ("pricing for margin"). The table above assigns a profit value to the four possible outcomes, given the demand and cost fundamentals of the cola market and Coke's market dominance.

Where is the Nash equilibrium, i.e., assuming that Coke and Pepsi both act rationally, which strategy will each likely choose and with what likely outcome? In the animation above, click "next" (at the lower right-hand corner of the image) to see Pepsi's profit-maximizing response to Coke's possible strategies. When Coke opts to "Price for Share", Pepsi will choose to "Price for Share" (Pepsi will reap a profit of $90, vs. $53 if it opts to "Price for Margin"). When Coke opts to "Price for Margin", Pepsi will again choose "Price for Share" (a profit of $94 vs. $60).

Click "next" again to see Coke's response to Pepsi's choices. When Pepsi chooses the strategy "Price for Share", Coke's profit-maximizing response is to choose "Price for Share" (Coke will gain $218, vs. $213 if it "Priced for Margin"). And if Pepsi chooses to "Price for Margin," Coke would foresee higher profits with a strategy to "Price for Margin" ($264 vs. $263). Click "next" once more to see the Nash Equilibrium. You'll see that each firm responds best to the other when each chooses to "Price for Share”.

FAQ

It seems as though game theory analysis assumes that each player is out to do the best it can for itself. Does this rule out altruistic motives or for that matter, a desire to inflict punishment on ones rivals.

This is not the case. If one player gains extra utility as a result of the other player doing well, this extra utility can be explicitly "built into" the player's payoff. Similarly, if one firm benefits strategically because it inflicts harm on the other player (perhaps because it hastens the eventual exit of that firm from the market), then that feature can also be built into the payoffs that go into the game matrix.

What is the prisoner's dilemma?

The prisoner's dilemma is based on the idea that there is a conflict between the collective interest of the players in the game and their own self-interest, similar to what happens when two suspects of a crime are individually questioned about their involvement in the crime. One criminal can go free if they implicate the other, however the other may do the same and then they are both at risk of going to jail. The prisoner's dilemma arises because in pursuing its self-interest in the game, each player imposes a cost on the other player that it does not take into account. As you will see in the capacity expansion game between Pepsi and Coke that is illustrated in the next exercise, each firm's addition of extra capacity hurts the other firm because it drives down the market price. They would both be better off if they both did nothing, but individually this is not in their self-interest.

How do you determine the estimated outcome values used in determining the Nash equilibrium?

The estimated outcome values of the different pricing strategies for Pepsi and Coke are determined using net present value calculations, and other models you will learn in your finance courses. Each company would have its financial professionals perform analysis on the cost of capital and the expected return for each scenario. A firm cannot predict these values with perfect accuracy, because of potential unknown factors, but they can make reasonable assessments when they use all the financial tools and models available.

Exercise: Applying the Game Theory

Exercise: Maximizing Overall Industry Profit

Sequential Games

Using a matrix is a good way to depict the alternative outcomes when rivals make decisions simultaneously. But what happens when the game is played sequentially, i.e., when one of the competitors makes a move when the other competitor has no intention of changing its current position? Consider this scenario: Pepsi wishes to penetrate the Latin American market, which Coke currently dominates. Pepsi's alternatives are to adopt (a) a broad scope strategy, whereby it would compete head-to-head with Coke in every distribution channel (retailers, fountain syrup sales, and vending machines), or (b) narrow scope strategy whereby it would compete in discrete markets by, e.g., focusing strictly on fountain sales.

Coke is content with its current strategy and isn't considering any changes. That's what makes this game sequential and not simultaneous; Coke has the option of doing nothing, i.e., "accommodating" Pepsi's market penetration. Having said that, once Pepsi chooses its strategy and makes its move, Coke may very well respond - depending upon which strategy Pepsi chose. Coke can fight Pepsi by engaging in a price war to protect market share. Or, Coke can "accommodate" Pepsi, with a view to avoid a price war at the cost of accepting some market share erosion. To predict the outcome of a sequential game, i.e., to find the Nash equilibrium, a game tree model is useful. Let's take a closer look at how a game tree works.

FAQ

How does a business decision maker determine all the potential outcomes in a situation?

Business decision makers use many resources to determine all the potential outcomes of a situation, including logic and market research. Consulting firms have built entire practices around formulating the branches of decision trees for their clients. This is a very complicated and involved process that requires

a high level of knowledge and discipline and a great deal of analysis. However, for a decision that requires a huge capital investment, completing this exercise is well worth it. Determining potential outcomes via personal intuition can be misleading and result in poor decisions.

How does a decision maker predict the reactions of competitors so that they can map out the sequential game tree?

Predicting the reactions of competitors can be tricky, and it may seem that you need to be able to read minds to determine what a competitor will do. However, as a starting point, it is often useful to assume that the competitor is making purposeful profit-maximizing decisions. With that in mind, each competitor's range of reactions can be narrowed considerably.

Sequential Games

With a game tree, we can model time, i.e., the sequences that lead to the end game outcome. The first step is to identify all of the possible outcomes, starting from the far left and building out the tree. Then, with the tree in place, we work backwards using the "fold-back" method. Doing this reveals the Nash equilibrium. Click on the graphic above to see how folding back the game tree identifies the Nash equilibrium.

Stories

I lose? You lose: The Philippines Cola War Redux

In late 1993, ValuJet the low-cost, no-frills airline, entered the Atlanta market with a niche strategy. Content with taking a small piece of Delta's regional business, ValuJet focused strictly on providing short haul flights from Atlanta to 12 Southern cities.

What makes ValuJet's strategy interesting is the way in which they used game theory masterfully to compete with Delta. ValuJet openly announced that their intention was not to "dominate the market". Where giant Delta may offer a dozen flights per day to one city, ValuJet planned on running only three or four, at greatly reduced fares.

ValuJet anticipated that Delta would not respond with a price war, because Delta would sacrifice far too much revenue; Since Delta controlled 80% of the Atlanta market, cutting fares drastically would not be a

profit-maximizing strategy. Delta would willingly sacrifice a slice of the pie and accommodate ValuJet's entry.

Given this environment, ValuJet was able to gain a strong foothold in Atlanta and was able to turn a profit because of their rock-bottom operating costs. Combined with a clever marketing campaign this proved to be a win-win strategy.

Oh, and how did the game end? Since Delta's business was slowly eroding due to ValuJet's presence, Delta eventually cut their fares - but only after ValuJet developed a strong customer base. As Delta spokesperson Bill Berry stated, "By itself, they are extremely small and minute, but there are dozens of ValuJets in our system. To fail to be price competitive with all of them is to give up an important share of the marketplace.”

Commentary

ValuJet versus Delta illustrates a very interesting game theory point. If you are ValuJet and you are thinking about entering the Atlanta Market, you realize that you are entering Delta's back yard. So you absolutely have to think about how Delta is likely to react. Now if you come in on a small scale, or if you come in as a niche play, you would probably realize, that if Delta responded aggressively to your entry, then Delta is going to be cutting price on 85% of the market, which is a very, very expensive response. And so you probably can trade on the possibility that Delta is not going to respond aggressively, and that is exactly what happened.

FAQ

Why is the Pepsi v. Coke capacity expansion in Las Vegas a simultaneous game, whereas the game in Latin America is a sequential game?

In the Las Vegas example, both firms feel compelled to act to grab the market share that has resulted from the population boom. Both firms are forming their strategic plans at the same time and need to act quickly before the other firm moves first. They are making decisions simultaneously. In the Latin American example, Coke is happy with its position as it stands. If Pepsi weren't moving in, Coke would keep the status quo and not make a move at all. Even when Pepsi does make the first move and enter the market, Coke may not move, but they will have to assess that when faced with sacrificing market share.

Why does the equilibrium of the sequential game differ significantly from the equilibrium of the simultaneous-move game that we represented in matrix form?

In a sequential-move game, the first mover has the opportunity to force the second mover into a corner. By committing to a large expansion --- a seemingly irrational act --- Coke forces Pepsi into a position in which Pepsi's best response is to back down ("Don't Expand"), and that's favorable to Coke. In the sequential-move game, Coke has the opportunity to turn a "threat" (to expand by 100%) into a

"promise". In a simultaneous-move game, neither player has the opportunity to force the other into a corner.

When the capacity expansion game is a simultaneous-move game, Coke might threaten to expand by 100%, but the threat wouldn't be credible because Pepsi would know that, at the end of the day, Coke gets a higher payoff from choosing "Expand by 50%" rather than "Expand by 100%", no matter what Pepsi does. A strategy of choosing "Expand by 100%" is only valuable to Coke as a device to force Pepsi to do something it wouldn't have already done.

Exercise: Expansion and the Nash Equilibrium

Conclusion to Microeconomics Essentials

In this course, you've learned the essential microeconomic principles that represent the foundation of business strategy. Strategy is often complicated and ambiguous - and the stakes are usually high. But formulating strategy without a solid grounding in these principles doesn't make a lot of sense and won't produce reliably effective results.

Over time you'll accumulate experience diagnosing and developing strategy. And with luck and a lot of work and careful thinking, you'll be able to apply these principles with greater and greater skill. But understanding the principles is the first step, and you've taken it in this course.

Good luck!

FAQ

Where do economists obtain the data necessary to do their analyses?

Economists obtain their data from a wide variety of sources including government data, trade association studies, scanner data from retail stores, surveys conducted by consultants, focus group studies administered by marketing professionals, and back-of-the-envelope calculations. They have a wealth of data available and their challenge is to sort through it effectively to make good strategic decisions. This is no easy task and it requires years of practice to hone these skills.