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Game theory studies strategic interactions where each player's payoff depends on the choices of all players. A game in normal form specifies players, strategies, and payoffs in a matrix. A dominant strategy is one that is optimal regardless of what the opponent does. The Prisoner's Dilemma is the canonical example where individual dominant strategies lead to a mutually inferior outcome, illustrating why coordination problems and market failures arise even among rational agents.
Work through the Prisoner's Dilemma payoff matrix by hand, identifying dominant strategies before defining Nash equilibrium. Then apply the framework to advertising decisions, pricing, and arms-race scenarios.
Game theory studies decision-making in strategic interactions — situations where your payoff depends not just on your own choice but on the choices of others. This distinguishes it from the optimization problems you've seen elsewhere in microeconomics, where you simply maximize utility or profit given fixed prices and constraints. In strategic situations, your best action depends on what others do, and their best action depends on what you do. Game theory provides the tools to analyze this mutual dependence precisely.
Every game in normal form has three elements: players, strategies, and payoffs. A payoff matrix displays this information visually. Each row is a strategy for player 1, each column is a strategy for player 2, and each cell shows what both players earn for that combination of choices. Reading the matrix is itself a skill — by convention, the row player's payoff is listed first. Before solving any game, spend a moment mapping out what each cell means in terms of the actual situation being modeled.
A dominant strategy is one that is optimal regardless of what the opponent does. To identify it: compare each strategy of player 1 across all columns. If one row always gives a payoff at least as high as every other row, that row dominates. When a dominant strategy exists, a rational player should always choose it — no prediction about the opponent is needed. This makes dominant-strategy reasoning especially robust. Most games, however, do not have dominant strategies for all players, which is why Nash equilibrium (a concept you'll study next) is the more general solution concept.
The Prisoner's Dilemma is the most important example in introductory game theory precisely because it exposes the limits of individual rationality. Each player has a dominant strategy — defect. Both play it. But the result (mutual defection) is worse for both than if they had cooperated. The core insight: individual rationality does not guarantee collective optimality. You've already seen this idea in the context of market failures and public goods: the rational choice for each individual (free-ride, pollute, defect) undermines the outcome for everyone. The Prisoner's Dilemma gives that intuition mathematical precision.
This framework applies far beyond stylized examples. Firms deciding whether to advertise, countries choosing military spending levels, and commuters choosing routes all face Prisoner's Dilemma-style structures. In each case, the temptation to defect is individually rational but collectively costly. Understanding this structure tells you when regulation, contracts, or repeated interaction might enable better outcomes — because when the game is played repeatedly, the calculus changes and cooperation can become self-sustaining. That extension is where the analysis gets richer.