Nash equilibrium, the prisoner's dilemma, and oligopoly strategic behavior concepts at college depth beyond the AP-level treatment.
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- Why must every player's strategy be a best response to others' strategies in a Nash equilibrium?
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If any player's strategy were not a best response, they could profitably deviate, violating the equilibrium condition.- Define a dominant strategy.
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A strategy that yields a higher payoff than any other strategy, regardless of what the opponent does.- In the Prisoner's Dilemma, what outcome do both players achieve when each pursues their dominant strategy?
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Mutual defection, yielding lower payoffs for both than if both had cooperated.- Why do both players choose to defect in the Prisoner's Dilemma even though mutual cooperation is better?
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Because defection is a dominant strategy for each player: they do better by defecting regardless of whether the opponent cooperates or defects.- What is Cournot competition?
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An oligopoly model where firms simultaneously choose output quantities, and market price is determined by total output.- In Cournot equilibrium, what does each firm's reaction function show?
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The firm's profit-maximizing output level as a function of its rivals' output choices.- What is Bertrand competition?
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An oligopoly model where firms simultaneously choose prices, and consumers buy from the lowest-priced firm.- In Bertrand competition with identical products, what typically happens to price and firm profit?
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Prices fall to marginal cost and firm profits approach zero, even with only two firms.- What is the Stackelberg model?
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A sequential-move oligopoly game where one firm (the leader) chooses output first, then the other firm (the follower) chooses after observing the leader's choice.- What defines an oligopoly?
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A market with a small number of firms producing homogeneous or differentiated products, where each firm's actions affect competitors' profits.- In a coordination game, what is the primary challenge?
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Players want to coordinate on the same outcome but risk unilateral deviation if they cannot guarantee others' choices.- What is the Battle of the Sexes game?
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A coordination game where a couple prefers to go out together but disagree on where: one prefers an opera, the other a soccer match.- In Matching Pennies, why does no pure strategy Nash equilibrium exist?
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Each player wants to do the opposite of what the opponent does, so any pure strategy can be exploited by the opponent switching theirs.- What is limit pricing as an entry deterrent?
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An incumbent firm prices below monopoly level to make entry unprofitable for potential competitors.- What is a mixed strategy?
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A strategy where a player randomizes over two or more pure strategies according to some probability distribution.
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