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Explainer: What "game theory" means for economists

Coming upon the term "game theory" this week, your first thought would likely be about the Winter Olympics in Sochi. But here we're going to discuss how game theory applies in economics, where it's widely used in topics far removed from the ski slopes and ice rinks where elite athletes compete.

For instance, microeconomists use game theory to explain how oligopolies -- industries with just a small number of firms -- make decisions as they interact strategically in the marketplace, to explain strategic interactions between bidders in auctions and to explain many other areas where the actions of individuals or firms are interdependent. Macroeconomists often employ game theory as well, for example, to explain how the government and the private sector interact in monetary policy decisions.

But what, exactly, is game theory?

Its origins can be traced to a paper by John von Neumann in the 1940s that examined the strategic interaction of two players trying to get the largest share possible share of a fixed payoff (i.e., more formally, a mixed-strategy, two-person, zero-sum game) and a subsequent book by von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior.

Game theory can be used to describe any situation where people -- the players in the game -- make strategic decisions that take account of the actions and responses of other participants. The strategic decisions result in a payoff, for example, the profit that a firm in an oligopolistic industry realizes as a result of its strategic choices. Thus, game theory involves specifying interdependencies between players, their actions, the outcomes and payoffs, and the rules of the game.

Here's an example of a simple game. Suppose two companies, firm A and firm B, compete for the same customers. The question concerns whether each firm should invest in new facilities or not. The following table shows the payoffs to each company for each set of possible actions:

                  Firm B
    Invest Don't invest
Firm A Invest   15,10      20,5
Don't invest   11,13      15,7

So, if both firms invest, then firm A will earn a profit of 15 and firm B a profit of 10 (i.e. each cell in the payoff table shows the payoffs for A,B associated with each possible outcome of the game). If neither one invests, firm A will earn 15, and firm B earns 7, and so on.

In this case, there is what's known as a dominant strategy for each firm. Firm A always earns more by investing no matter what firm B does -- it earns 15 rather than 11 if firm B invests, and it earns 20 rather than 15 if firm B doesn't invest. Therefore, firm A should invest. Similarly, firm B always earns more by investing, so it should invest no matter what firm A does. In this case, the outcome is easy to determine: both firms should invest.

Now consider a different set of payoffs:

                  Firm B
    Invest Don't invest
Firm A Invest   15,10      20,5
Don't invest   11,13      30,7

The only change is the payoff for firm A in the lower right-hand corner. It now earns 30 instead of the 15 as in the previous game if firm B chooses not to invest.

In this case, there is no dominant strategy for firm A, it depends upon what firm B does. If firm B invests, firm A should follow suit and invest too, it earns 15 rather than 11, but if firm B does not invest, firm A's optimal choice is to not invest so that it earns 30 rather than 20.

But we can still determine the outcome of the game. Firm B should invest no matter what firm A does because its payoff has not changed from above, so it always does best by investing. It still has a dominant strategy. Firm A can then ask itself what firm B will do, and knowing that firm B will invest no matter what it does, firm A can figure out that its best response is to also invest. Thus, although firm A no longer has a dominant strategy, the fact that firm B still does allows it to determine its best response, and the outcome is the same as above: both firms invest.

Games can differ across a number of dimensions, the strategy each player pursues, whether there's a dominant strategy, the number of players, the degree of interdependency among the players, the ability of players to communicate and coordinate, whether it's a one-shot or a repeated game, which player moves first and the amount of information.

For example, consider the last item, the amount of information each firm has. In the second example, firm A should invest if firm B rationally decides its best decision is to invest, i.e. if firm B follows its dominant strategy. But what if firm B is ill-informed about payoffs or irrational in its decision making, and mistakenly chooses not to invest.  In that case, firm A could earn much more, 30 instead of 15, by not investing. Thus, firm A's assumption that firm B is fully informed and rational is an important element of its decision to invest.

Game theory can get very complicated, and explaining all the various possibilities would be difficult in a short article. Nevertheless, it's an important tool for economists, particularly microeconomists, and it has been a key component of the development of microeconomic theory. For instance, in perfectly competitive markets where the actions of individual firms have no impact on market outcomes, the market outcome is fairly easy to describe. But when there are only a small number of firms and markets aren't competitive, the outcome is much more difficult to determine. In these situations, game theory is a key tool for understanding how these markets operate and evolve over time.

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