Game Theory • 31

FIGURE P.15

Effect of a Reduction in Demand on the Long-Run Perfectly

Competitive Equilibrium

When demand falls, the demand curve shifts from D0 to D1, and price would initially fall to P9. Firms would earn less than they could elsewhere and would eventually begin to leave the industry. As this happens, the supply curve shifts to the left from SS9 to SS1. The industry shakeout ends when price is again P**.

As this occurs, the industry supply curve shifts to the left, and price begins to rise. Once the “shakeout” fully unfolds, the industry supply curve will have shifted to SS9, and the market price will once again reach P**. Firms are then again optimizing on output and earning zero profit. Thus, no matter what the level of industry demand, the industry will eventually supply output at the price P**.11

This theory implies that free entry exhausts all opportunities for making profit. This implication sometimes troubles management students because it seems to suggest that firms in perfectly competitive industries would then earn zero net income. But remember the distinction between economic costs and accounting costs. Economic costs reflect the relevant opportunity costs of the financial capital that the owners have provided to the firm. Zero profits thus means zero economic profit, not zero accounting profit. Zero economic profit simply means that investors are earning returns on their investments that are commensurate with what they could earn from their next best opportunity.

That free entry dissipates economic profit is one of the most powerful insights in economics, and it has profound implications for strategy. Firms that base their strategies on products that can be easily imitated or skills and resources that can be easily acquired put themselves at risk to the forces that are highlighted by the theory of perfect competition. To attain a competitive advantage, a firm must secure a position in the market that protects itself from imitation and entry. How firms might do this is the subject of Chapters 9, 10, and 11.

GAME THEORY

The perfectly competitive firm faces many competitors, but in making its output decision, it does not consider the likely reactions of its rivals. This is because the decisions of any single firm have a negligible impact on market price. The key strategic challenge

32 • Economics Primer: Basic Principles

of a perfectly competitive firm is to anticipate the future path of prices in the industry and maximize against it.

In many strategic situations, however, there are few players. For example, four producers—Asahi, Kirin, Sapporo, and Suntory—account for well over 90 percent of sales in the Japanese beer market. In the market for transoceanic commercial aircraft, there are just two producers: Boeing and Airbus. In these “small numbers” situations, a key part of making strategic decisions—pricing, investment in new facilities, and so forth—is anticipating how rivals may react.

A natural way to incorporate the reactions of rivals into your analysis of strategic options is to assign probabilities to their likely actions or reactions and then choose the decision that maximizes the expected value of your profit, given this probability distribution. But this approach has an important drawback: How do you assign probabilities to the range of choices your rivals might make? You may end up assigning positive probabilities to decisions that, from the perspective of your competitors, would be foolish. If so, then the quality of your “decision analysis” would be seriously compromised.

A more penetrating approach would be to attempt to “get inside the minds” of your competitors, figure out what is in their self-interest, and then maximize accordingly. However, your rivals’ optimal choices will often depend on their expectations of what you intend to do, which, in turn, depend on their assessments of your assessments about them. How can one sensibly analyze decision making with this circularity?

Game theory is most valuable in precisely such contexts. It is the branch of economics concerned with the analysis of optimal decision making when all decision makers are presumed to be rational, and each is attempting to anticipate the actions and reactions of its competitors. Much of the material in Part Two on industry analysis and competitive strategy draws on game theory. In this section, we introduce these basic ideas. In particular, we discuss games in matrix and game tree form, and the concepts of a Nash equilibrium and subgame perfection.

Games in Matrix Form and the Concept of Nash Equilibrium

The easiest way to introduce the basic elements of game theory is through a simple example. Consider an industry that consists of two firms, Alpha and Beta, that produce identical products. Each must decide whether to increase its production capacity in the upcoming year. We will assume that each firm always produces at full capacity. Thus, expansion of capacity entails a trade-off. The firm may achieve a larger share of the market, but it may also put downward pressure on the market price. The consequences of each firm’s choices are described in Table P.3. The first entry is Alpha’s annual economic profit; the second entry is Beta’s annual economic profit.

TABLE P.3

Capacity Game between Alpha and Beta

All amounts are in millions per year. Alpha’s payoff is first; Beta’s is second.

Game Theory • 33

Each firm will make its capacity decision simultaneously and independently of the other firm. To identify the “likely outcome” of games like the one shown in Table P.3, game theorists use the concept of a Nash equilibrium. At a Nash equilibrium outcome, each player is doing the best it can, given the strategies of the other players. In the context of the capacity expansion game, the Nash equilibrium is that pair of strategies (one for Alpha, one for Beta) such that

•Alpha’s strategy maximizes its profit, given Beta’s strategy.

•Beta’s strategy maximizes its profit, given Alpha’s strategy.

In the capacity expansion game, the Nash equilibrium is (EXPAND, EXPAND); that is, each firm expands its capacity. Given that Alpha expands its capacity, Beta’s best choice is to expand its capacity (yielding profit of 16 rather than 15). Given that Beta expands its capacity, Alpha’s best choice is to expand its capacity.

In this example, the determination of the Nash equilibrium is fairly easy because for each firm, the strategy EXPAND maximizes profit no matter what decision its competitor makes. In this situation, we say that EXPAND is a dominant strategy. When a player has a dominant strategy, it follows (from the definition of the Nash equilibrium) that that strategy must also be the player’s Nash equilibrium strategy. However, dominant strategies are not inevitable; in many games players do not possess dominant strategies (e.g., the game in Table P.4).

Why does the Nash equilibrium represent a plausible outcome of a game? Probably its most compelling property is that it is a self-enforcing focal point: if each party expects the other party to choose its Nash equilibrium strategy, then both parties will, in fact, choose their Nash equilibrium strategies. At the Nash equilibrium, then, expectation equals outcome—expected behavior and actual behavior converge. This would not be true at non-Nash equilibrium outcomes, as the game in Table P.4 illustrates. Suppose Alpha (perhaps foolishly) expects Beta not to expand capacity and refrains from expanding its own capacity to prevent a drop in the industry price level. Beta—pursuing its own self-interest—would confound Alpha’s expectations, expand its capacity, and make Alpha worse off than it expected to be.

The “capacity expansion” game illustrates a noteworthy aspect of a Nash equilibrium. The Nash equilibrium does not necessarily correspond to the outcome that maximizes the aggregate profit of the players. Alpha and Beta would be collectively better off by refraining from the expansion of their capacities. However, the rational pursuit of self-interest leads each party to take an action that is ultimately detrimental to their collective interest.

TABLE P.4

Modified Capacity Game between Alpha and Beta

All amounts are in millions per year. Alpha’s payoff is first; Beta’s is second.