Game Theory Payoff Matrix Intro | AP Microeconomics

Nash equilibrium is a game theory concept where neither player has an incentive to change their decision given the other player's actions. To find it, first identify dominant strategies (actions that are always best regardless of the other player's choice). In the Coke-Pepsi example, Pepsi has a dominant strategy of low output, while Coke has no dominant strategy. The Nash equilibrium occurs when both players choose their optimal responses: Pepsi chooses low output (its dominant strategy), and Coke responds with high output (since $150 > $110 when Pepsi does low output). This creates a stable outcome where neither firm wants to change their action.

A Nash equilibrium is a set of strategies, one for each player, such that no player has incentive to change his or her strategy given what the other players are doing. In pure strategy Nash equilibrium, players are not randomizing between two or more strategies; they definitively choose one action over others.

Nash Equilibrium is a fundamental concept in game theory where each player in a strategic interaction chooses their optimal strategy given the strategies chosen by other players, such that no player has an incentive to unilaterally change their decision. In a two-player game, if Player A's best response to Player B's strategy is Strategy X, and Player B's best response to Player A's strategy is Strategy Y, then the combination (X, Y) constitutes a Nash Equilibrium. Importantly, a single game can have multiple Nash Equilibria, as demonstrated by the example where two competing companies can reach either (Build, Enter) or (Not Build, Not Enter) as stable outcomes, with neither company having an incentive to deviate from their chosen strategy given the other's choice.

Nash equilibrium, named after mathematician John Nash, is a concept in game theory where each player's strategy is optimal given the strategies of all other players. In a two-player zero-sum game at Nash equilibrium, neither player has incentive to change their strategy because any deviation would result in a worse outcome. For equal-level players, this typically results in approximately 50% chance of winning for each player when both play optimally.

Nash Equilibrium is a state in game theory where all players simultaneously maximize their outcomes given the strategies of others. In this equilibrium, no player has an incentive to unilaterally change their strategy because doing so would not improve their result.

Even when prisoners could communicate and agree to cooperate (both remaining silent), the Prisoner's Dilemma still leads to mutual confession. This is because each prisoner fears the other will defect from the agreement. If An believes Bình will remain silent, An will defect to go free. Since both think this way, both defect. This demonstrates that individually rational choices can lead to collectively irrational outcomes, even when cooperation would benefit all parties.

The prisoner's dilemma is the two-person version of market failure. Two criminals are arrested and interrogated separately. Each has an incentive to confess regardless of what the other does: if the other stays silent, confession gets a slap on the wrist; if the other confesses, confession avoids the five-year sentence. Both would be better off if neither confessed, but each acting rationally leads to both confessing and receiving three years each.

The cooperative outcome (both firms charging high prices and splitting the market) is not stable in the prisoner's dilemma because each firm has an incentive to deviate unilaterally. If both firms agree to charge high prices and split profits, each firm can increase its own profit by secretly lowering its price to capture the entire market. Since both firms face identical incentives, neither can trust the other to maintain cooperation. This demonstrates how individual rationality leads to collectively suboptimal outcomes, even when both parties would be better off through cooperation.

The Prisoner's Dilemma demonstrates how individually rational choices can produce collectively irrational outcomes. Two suspects, interrogated separately, face choices to confess or remain silent. Individual incentives drive both to confess, resulting in harsher sentences than if both had cooperated. This illustrates market failure: when individuals pursue self-interest in free markets, society often suffers. The dilemma reveals fundamental tensions between personal optimization and collective welfare, explaining why coordinated social arrangements often fail without intervention.

The Prisoner's Dilemma illustrates how individual rationality can produce collectively suboptimal outcomes. Two prisoners must decide whether to confess or remain silent, with each benefiting from confessing regardless of the other's choice. While mutual silence yields better collective outcomes, self-interest drives both to confess. This paradox applies to oligopolistic markets where firms similarly face incentives to undercut competitors despite higher collective profits from cooperation, demonstrating fundamental tensions in strategic interactions.

Game Theory explains cooperation through shared interests despite competition. The taxi licensing example shows how limited permits create scarcity, preventing market saturation and maintaining service quality. The Prisoner's Dilemma demonstrates how individual rationality leads to collective harm—confessing benefits each prisoner individually but harms both collectively. Advertising competition similarly shows how firms advertising excessively lose money while both benefit from reduced competition. These models reveal that strategic cooperation, regulation, and trust are essential for optimal outcomes in competitive environments.

Game theory studies cooperation and conflict, central to oligopolistic firm behavior. It analyzes day-to-day life examples like arms races, political party strategies for candidate selection, and vaccination policy decisions. In vaccination policy, game theory explains how consumers, private firms, opposition, and other nations respond to government decisions. It helps determine optimal policy choices: whether to regulate firms, how much to penalize non-compliance (like not wearing masks), and whether to use monetary penalties, advertising, or nudging strategies. For firms, game theory helps predict rival responses to actions, determine appropriate employee compensation during work-from-home scenarios, and analyze merger/acquisition decisions.

Game theory applications extend to advertising wars where both firms spend heavily on ads, reducing profits for both, and arms races where both nations produce weapons, increasing costs for both. In repeated games where interactions occur multiple times, cooperation becomes possible through strategies like 'tit-for-tat' (cooperate if the other cooperated, defect if the other defected). This allows firms to sustain collusive agreements over time. Antitrust laws (like the Sherman Act) prohibit collusive practices including price-fixing, aiming to promote competition and bring oligopolistic markets closer to competitive outcomes. However, the application of these laws remains controversial, with debates about whether they restrict legitimate business practices. Predatory pricing occurs when firms temporarily reduce prices below cost to drive competitors out, and tying arrangements require buyers to purchase one product as a condition for purchasing another.

Game theory analyzes strategic interactions between decision-makers whose choices affect each other's incentives; the Prisoner's Dilemma illustrates how rational self-interest can lead to collectively suboptimal outcomes, but repeated interactions with trigger strategies (where firms retaliate against deviations) can sustain collusion when the interest rate is sufficiently low, making it profitable for firms to maintain collusive agreements rather than compete aggressively.

Media concentration can be regulated through antitrust laws, which limit how much of any market a single entity can control. The 1910 antitrust law in the United States limited media concentration to 25%, creating the competitive media landscape that exists today. Media viability depends on advertising revenue, which emerged as a response to media concentration. When seven families controlled 80% of the U.S. economy before 1917, there was no need for advertising because monopolies could charge whatever they wanted. The key insight is that media concentration is a policy choice that can be regulated, and that advertising-supported media has broader reach but potentially more commercial pressures.