Game Theory
What is Game Theory?
Game theory is a framework for analyzing strategic interactions where the outcome for each participant depends on the actions of others.
It is used to predict how firms in an oligopoly will behave when making decisions about pricing, output, or advertising, considering how rivals might respond. Payoff matrices are commonly used to illustrate possible outcomes.
Game Theory: a worked example
Two carriers, Nova and Orbit, each pick a High or Low fare. Payoffs are quarterly profits in millions with Nova listed first. Nova High and Orbit High: (60, 40). Nova High and Orbit Low: (30, 35). Nova Low and Orbit High: (70, 20). Nova Low and Orbit Low: (45, 32). Take Nova first: against Orbit High, 70 beats 60, and against Orbit Low, 45 beats 30, so Low is dominant for Nova. Orbit has no dominant strategy, preferring High when Nova plays High, 40 over 35, but Low when Nova plays Low, 32 over 20. Since Nova will certainly play Low, Orbit's best response is Low, and the Nash equilibrium is Low for both at (45, 32), where neither carrier can improve by switching alone.
The mistake students make with game theory
The equilibrium gets picked by scanning for the cell with the biggest combined total. Here High and High adds to 100, more than the 77 at the equilibrium, so it looks like the answer. Nash equilibrium says nothing about the group total. Test each player separately: sitting at High and High, Nova gains by cutting to Low, 70 rather than 60, so that cell cannot hold. Work through best responses one player at a time with the rival's choice held fixed, and never assume the outcome both firms would prefer is the outcome the game actually produces.
Game Theory questions
What is a Nash equilibrium in simple terms?
A Nash equilibrium is a combination of choices where no player can do better by changing strategy alone, given what everyone else is doing. Testing a cell means asking each player in turn whether a one sided switch would raise their own payoff, and if the answer is no for everybody, the cell is an equilibrium. A game can have one, several or none in pure strategies, and an equilibrium can leave both players worse off than an outcome they cannot reach without trust.
How do you read a payoff matrix?
The first number in each cell belongs to the row player and the second to the column player, unless the question labels them otherwise. Rows are the row player's options and columns are the column player's. To analyze it, fix the rival's choice, which means staying inside one column for the row player, then compare only that player's numbers. Marking each best response as you go makes the equilibrium easy to spot, since both marks land in the same cell.
Why is game theory used for oligopoly instead of perfect competition?
Oligopoly has few enough firms that each one's pricing or output decision noticeably changes what the others face, a condition called strategic interdependence. A perfectly competitive wheat farmer is one of thousands and takes the market price as given, so no rival needs outguessing. Game theory is the tool built for the first situation, which is why payoff matrices show up in oligopoly questions rather than in the perfectly competitive chapters.
Related terms
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