Game Theory and Strategic Rivals

Why this matters

When a market has thousands of small sellers, none of them needs to think about how the others will react. When it has three or four large ones, each company's best price, capacity, or advertising budget depends on what the others do, and the others know it. In awarding the 1994 economics prize for work on game theory, the Royal Swedish Academy of Sciences noted that such strategic interaction characterizes many economic situations, and that game theory had become a dominant tool for analyzing them.¹ For an investor in an industry with a few large players, it's a way of asking what rivals are likely to do next and why.

The basic tools

A game has players, the moves each can make, and the payoffs that result from every combination of moves. Two ideas help predict the outcome.

• A dominant strategy is a move that's best for a player whatever the others do.
• A Nash equilibrium is a set of moves in which no player can do better by changing their own move while the others keep theirs. It's named for John Nash, who developed the concept for games in which binding agreements aren't possible.¹

Competition and Market Structure showed the classic case. Two firms each choose to keep prices high or cut them. Cutting is the dominant strategy for both, so the equilibrium is that both cut and each earns 60, though both keeping prices high would have given each 100. This is the prisoner's dilemma: individually sensible choices add up to a worse result for everyone.

A game with two equilibria

	Rival enters	Rival stays out
We enter	We lose 10, rival loses 10	We earn 30, rival 0
We stay out	We earn 0, rival 30	Both earn 0

The route supports one airline, not two. Neither has a dominant strategy: entering is best only if the rival stays out. There are two equilibria, one airline in and the other out, and nothing in the table says which. In practice, being first, announcing early, or committing aircraft to the route can settle it.

Playing again and again

A one-time prisoner's dilemma tends to end in mutual defection. Rivals in a real industry, though, meet every day for years, and that changes the game. A firm that cuts its price today can be punished tomorrow.

In the early 1980s, Robert Axelrod invited game theorists to submit computer programs to play a repeated prisoner's dilemma against each other. The winner was the simplest entry, Tit for Tat, which cooperates on the first round and then copies its opponent's previous move. It won again in a second tournament, even though its 63 entrants had seen the results of the first. Axelrod attributed its success to four features: it was nice, never the first to defect; retaliatory, so it couldn't be exploited; forgiving, willing to cooperate again after a defection; and clear, so others could predict it.²

The lesson for industries is that high prices can be sustained without any agreement, if each firm expects a price cut to be matched quickly. Theory suggests this is easier when there are few firms, prices are visible, demand is steady, and the same rivals meet over and over. It's harder when a new entrant arrives, demand falls, or a firm has spare capacity it's desperate to fill, the conditions that Costs, Scale, and Profit connected with price wars. An explicit agreement to fix prices is a different matter: it's illegal under US antitrust law, as the competition lesson described.

The rest of this lesson is for members

Still to come in this lesson: Threats and commitments, The winner's curse, Questions to ask about an industry, the key takeaways, and 2 quiz questions with explanations.

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