4.3 The Folk Theorem and Long-term Relationships
4 min read•july 22, 2024
The explains how cooperation can emerge in , even when players have short-term incentives to cheat. It shows that any payoff above each player's minimum can be sustained as an equilibrium if the game is repeated indefinitely.
In business, this applies to long-term relationships like supplier contracts or joint ventures. Companies can maintain cooperation through the threat of future punishment, like ending deals or starting price wars, if a partner cheats. This helps explain real-world business cooperation.
The Folk Theorem and Cooperation in Repeated Games
Implications of Folk Theorem
Top images from around the web for Implications of Folk Theorem
Nash equilibrium - Wikipedia View original
Is this image relevant?
Nash equilibrium - Simulace.info View original
Is this image relevant?
Nash equilibrium - Simulace.info View original
Is this image relevant?
Nash equilibrium - Wikipedia View original
Is this image relevant?
Nash equilibrium - Simulace.info View original
Is this image relevant?
1 of 3
Top images from around the web for Implications of Folk Theorem
Nash equilibrium - Wikipedia View original
Is this image relevant?
Nash equilibrium - Simulace.info View original
Is this image relevant?
Nash equilibrium - Simulace.info View original
Is this image relevant?
Nash equilibrium - Wikipedia View original
Is this image relevant?
Nash equilibrium - Simulace.info View original
Is this image relevant?
1 of 3
- Suggests any feasible, individually rational payoff can be sustained as in infinitely repeated game
- Feasible payoffs achievable through combination of strategies (price , market sharing)
- Individually rational payoffs give each player at least their minmax payoff (lowest payoff they can guarantee themselves)
- In repeated games with uncertain end points, players incentivized to cooperate and maintain reputations
- Players consider long-term consequences of actions as game end unknown (ongoing supplier relationships)
- Cooperation sustained through threat of future punishment for deviations (terminating contracts, price wars)
Folk Theorem and cooperation
- Provides framework for understanding emergence of cooperation in long-term relationships despite short-term incentives to defect
- Players use trigger strategies, cooperating as long as opponent cooperates but punishing if opponent defects ( strategy)
- Threat of future punishment discourages present defection (loss of future business)
- Shows wide range of cooperative outcomes sustainable as equilibria in repeated games
- Players coordinate on mutually beneficial outcome and maintain it through threat of punishment (industry standards, joint ventures)
- Explains cooperation emergence in business relationships, international relations, and other long-term interactions (OPEC, WTO)
Folk Theorem in business interactions
- Applies when interactions repeated indefinitely or have uncertain end point
- Business relationships often have indefinite time horizon (franchise agreements, strategic alliances)
- Players must observe and respond to each other's actions
- In business, involves monitoring compliance with agreements or contracts (audits, performance reviews)
- Players must have sufficiently low discount rates, valuing future payoffs relatively highly compared to present payoffs
- Firms with long-term orientation more likely to cooperate in repeated interactions (family businesses, Japanese keiretsu)
- Payoffs from cooperation must be individually rational for all players
- Cooperative agreements in business must provide each party with payoff exceeding their minmax payoff (profitable joint ventures, mutually beneficial trade agreements)
Communication in repeated games
- Allows players to coordinate on cooperative outcome and signal intentions to cooperate
- In business, involves explicit agreements, contracts, or informal understandings (memoranda of understanding, handshake deals)
- Helps players establish trust and build reputations for cooperation (brand loyalty, goodwill)
- Information sharing allows players to monitor each other's actions and detect deviations from cooperative agreements
- Firms share information about sales, production, or prices to facilitate collusion in repeated interactions (trade associations, price indexes)
- Helps players enforce cooperative agreements through threat of future punishment (industry blacklists, reciprocal punishments)
- However, communication and information sharing may also facilitate collusion and anti-competitive behavior
- Antitrust laws and regulations often restrict communication and information sharing among competitors to prevent collusion (Sherman Act, EU Competition Law)
- Firms must balance benefits of cooperation with legal and reputational risks of collusive behavior (price fixing scandals, boycotts)
Applying the Folk Theorem to Real-World Business Interactions
- Provides valuable insights into conditions under which cooperation can be sustained in real-world business interactions
- Long-term business relationships often involve repeated interactions with indefinite time horizon (franchising, technology licensing)
- Firms can use insights of Folk Theorem to structure relationships to promote cooperation and mutual benefit (revenue sharing, exclusive dealing)
- Highlights potential for collusive behavior in repeated business interactions
- Firms may use repeated interactions to engage in anti-competitive practices (bid rigging, territorial restrictions)
- Antitrust authorities must monitor and prevent collusive behavior, particularly in industries with few firms and high entry barriers (airlines, pharmaceuticals)
- Emphasizes importance of reputation and trust in sustaining cooperation in repeated interactions
- Firms build reputations for cooperation and trustworthiness through actions in repeated interactions (consistent quality, timely delivery)
- Cooperation reputation valuable in attracting and retaining business partners, while opportunism reputation costly in long run (negative reviews, loss of clients)
- Highlights role of institutions and legal frameworks in shaping incentives for cooperation in repeated business interactions
- Effective contract enforcement, dispute resolution mechanisms, and antitrust regulations promote cooperation and prevent collusive behavior (arbitration clauses, leniency programs)
- Firms must navigate institutional and legal frameworks to sustain cooperation and achieve long-term strategic objectives (international trade agreements, public-private partnerships)
Key Terms to Review (18)
Cartels: Cartels are formal agreements among competing firms in an industry to coordinate their actions, typically to control prices, limit production, or share markets. These arrangements can significantly affect market dynamics, as they seek to maximize collective profits at the expense of competition. By forming a cartel, firms can stabilize their market positions and deter new entrants, which can lead to higher prices and reduced consumer choice.
Collusion: Collusion refers to an agreement between competing parties to work together in a way that is intended to limit competition, often leading to higher prices or reduced output. This cooperative behavior can emerge in various business contexts, influencing strategic decision-making, affecting relationships in repeated interactions, and impacting competitive dynamics within industries. When firms collude, they often prioritize collective benefits over individual gain, which can be seen in auction settings and experimental scenarios.
Cooperative strategies: Cooperative strategies refer to approaches taken by players in a game to work together to achieve mutually beneficial outcomes rather than competing against each other. These strategies are often based on trust, communication, and the promise of future rewards, which can lead to improved long-term relationships and more favorable results for all parties involved.
Discount factor: The discount factor is a crucial concept in economics and game theory that reflects the present value of future payoffs. It essentially represents how much a player values future rewards compared to immediate ones, with a discount factor between 0 and 1 indicating the degree of time preference. This concept is important for understanding long-term relationships, cooperation strategies, and stability in collusion, as it affects decision-making in repeated interactions.
Folk Theorem: The Folk Theorem refers to a set of results in game theory that demonstrates how players in infinitely repeated games can sustain cooperation through establishing long-term relationships. It highlights that, under certain conditions, players can achieve cooperative outcomes even when they could benefit from non-cooperative behavior in a one-shot game. This theorem emphasizes the importance of future payoffs and the ability to retaliate against non-cooperative actions, fostering stable cooperation over time.
Grim trigger strategy: The grim trigger strategy is a strategy used in repeated games where a player cooperates until the opponent defects, after which the player will defect forever. This strategy acts as a deterrent against defection because the punishment is severe and permanent, thus fostering long-term cooperation in the context of games played repeatedly. By establishing this rule, players can create an environment where both sides prefer to cooperate to avoid the consequences of triggering long-term defection.
Infinite horizon games: Infinite horizon games are strategic scenarios where players engage in repeated interactions over an indefinite period, meaning there is no predetermined endpoint to the game. This concept is crucial as it allows for the development of strategies that account for the long-term consequences of actions, fostering cooperation among players through mechanisms like reputation and trust. In these settings, players can make decisions that not only impact immediate outcomes but also future interactions.
Jean Tirole: Jean Tirole is a prominent French economist known for his work on industrial organization, game theory, and regulation. His contributions have significantly shaped the understanding of how firms interact in markets, particularly in terms of collusion, reputation effects, and long-term relationships among economic agents.
Nash Equilibrium: Nash Equilibrium is a concept in game theory where players, knowing the strategies of their opponents, choose their optimal strategies resulting in a situation where no player has anything to gain by changing their own strategy unilaterally. This balance occurs when each player's strategy is the best response to the strategies chosen by others, highlighting the interdependence of player decisions and strategic decision-making.
Pareto Efficiency: Pareto efficiency refers to a state where resources are allocated in a way that no individual's situation can be improved without worsening someone else's situation. This concept highlights the importance of mutual benefit in various strategic interactions and economic environments, emphasizing that an optimal allocation exists when it is impossible to make any participant better off without making at least one other participant worse off.
Perfect Information: Perfect information refers to a situation in a game where all players have complete knowledge of the game's structure, payoffs, and the actions taken by other players at all times. This condition allows players to make fully informed decisions based on the available data, leading to more predictable outcomes. In contexts like subgame perfect equilibrium and long-term relationships, perfect information plays a crucial role in determining strategies and ensuring that players can anticipate responses from others.
Repeated games: Repeated games are strategic interactions that occur when players engage in the same game multiple times, allowing them to consider past actions and outcomes when making future decisions. This repetition introduces a dynamic element to the game, where players can build strategies based on history, fostering opportunities for cooperation or competition. The structure of repeated games has significant implications for understanding long-term relationships, strategies for cooperation, and the stability of collusion among firms.
Reputation effect: The reputation effect refers to the impact that an individual's past actions and behaviors have on their current and future interactions within a strategic environment. This effect becomes especially significant in repeated games where players care about their long-term relationships, as a positive reputation can lead to cooperation while a negative one can lead to conflict or defection.
Robert J. Aumann: Robert J. Aumann is a prominent Israeli-American mathematician known for his contributions to game theory, particularly in the areas of repeated games and the Folk Theorem. His work has significantly advanced the understanding of strategic interactions in economics and social science, illustrating how cooperation can emerge in long-term relationships among rational players.
Subgame Perfect Equilibrium: Subgame perfect equilibrium is a refinement of Nash equilibrium used in dynamic games, where players make decisions at different stages. It requires that players' strategies constitute a Nash equilibrium in every subgame of the original game, ensuring that players' strategies are optimal even when the game reaches any point in the future. This concept helps analyze decision-making processes in extensive form games and supports the evaluation of credible threats and promises in strategic interactions.
Sustained cooperation: Sustained cooperation refers to the ongoing and repeated collaboration among players in a strategic setting, where participants consistently choose cooperative actions over competitive ones to achieve mutual benefits over time. This concept highlights the importance of long-term relationships and trust in environments where decisions impact future interactions, allowing players to build reputations and foster loyalty.
Tit-for-tat: Tit-for-tat is a strategy in game theory where a player responds to an opponent's previous action with the same action, whether cooperative or uncooperative. This approach fosters mutual cooperation in repeated games by promoting reciprocity and discouraging exploitation, making it significant in understanding strategic interactions in various scenarios.
Trust-building: Trust-building is the process of establishing confidence and reliability among parties, fostering open communication and cooperation. In situations where long-term relationships are essential, trust-building becomes crucial as it encourages collaboration and supports mutually beneficial outcomes, ultimately promoting stability and reducing conflicts.