18.16
Juegos repetidos infinitamente
Un juego repetido infinitamente es un escenario en el que los jugadores participan repetidamente en el mismo juego sin un final predeterminado. Este c…
Un juego repetido infinitamente es aquel en el que los jugadores participan repetidamente en el mismo juego sin un final predeterminado.
Por ejemplo, las empresas que fijan repetidamente los precios o los países que negocian las condiciones comerciales durante muchos años.
En estos juegos, las empresas a menudo adoptan una estrategia de ojo por ojo.
Por ejemplo, considere dos empresas competidoras, Alpha y Beta, que establecen el precio de sus refrescos.
Deciden un precio a principios de cada mes. Si ambas empresas mantienen los precios altos, disfrutan de grandes ganancias.
La estrategia de ojo por ojo implica comenzar con una acción cooperativa, como establecer un precio alto.
Beta sigue fijando precios altos mientras Alpha haga lo mismo.
Si Alpha baja el precio, Beta también bajará su precio en la siguiente ronda. Esto le da a Alpha una ventaja de ganancias y le da a Beta una desventaja de ganancias para esa ronda. Cuando Alpha vuelve a un precio alto, Beta lo iguala.
El resultado de un juego repetido infinitamente es la cooperación sostenida. Las empresas reconocen que las ganancias a corto plazo de la reducción de precios son menores que las pérdidas a largo plazo de los precios bajos.
Mantener precios altos se convierte en una estrategia racional para ambas empresas, lo que genera un beneficio mutuo con el tiempo.
View the full transcript and gain access to JoVE Business videos
Q1: What is an infinitely repeated game?
An infinitely repeated game is a scenario where players repeatedly engage in the same game without a predetermined end. Examples include firms continuously adjusting prices or countries consistently negotiating trade terms over many years. Players recognize that short-term gains from non-cooperative actions are less valuable than long-term losses, making mutual cooperation a rational strategy that benefits all parties over time.
Q2: How does the tit-for-tat strategy work in repeated games?
Tit-for-tat involves starting with a cooperative action, such as setting a high price, then matching the opponent's previous action in each subsequent round. If one player lowers the price, the other follows suit in the next round but returns to cooperation when the opponent does. This strategy encourages mutual cooperation while punishing defection, creating sustained high profits for both firms.
Q3: Why do firms maintain high prices in infinitely repeated games?
Firms maintain high prices because they recognize that mutual cooperation yields better long-term benefits than short-term gains from price cutting. When both firms keep prices high, they enjoy sustained high profits. The threat of retaliation—where the opponent matches a price cut—makes defection unprofitable, so maintaining high prices becomes the rational equilibrium strategy for maximizing long-term payoffs.
Q4: What is the difference between infinitely repeated games and one-time games?
In infinitely repeated games, players interact repeatedly without a predetermined end, allowing them to build reputation and enforce cooperation through retaliation. In contrast, nash equilibrium in one period games involves single interactions where players cannot punish future defection. The repeated nature enables sustained cooperation, whereas one-time games often result in non-cooperative outcomes due to lack of future consequences.
Q5: How do infinitely repeated games apply to real-world scenarios?
Infinitely repeated games model long-term business and international interactions. Firms use pricing strategies to maintain market stability, while countries apply cooperation principles to trade negotiations and environmental agreements. In environmental agreements, nations agree to reduce emissions and maintain cooperation to avoid long-term detrimental effects, demonstrating how repeated interaction incentivizes mutual benefit over individual short-term gains.
Q6: What happens when a player deviates from cooperation in a repeated game?
When a player deviates by lowering prices or breaking cooperation, the opponent retaliates in the next round by matching that action, creating a profit disadvantage for the deviator. However, retaliation is temporary; when the deviator returns to cooperation, the opponent forgives and resumes high prices. This cycle of retaliation and forgiveness reinforces the incentive to maintain cooperation rather than pursue short-term gains.
Q7: Why is mutual cooperation the outcome of infinitely repeated games?
Mutual cooperation emerges because players recognize that the present value of long-term cooperative profits exceeds the one-time gain from defection plus subsequent losses from retaliation. The infinite time horizon makes future payoffs significant, and the threat of punishment deters deviation. Both players rationally choose to maintain high prices or other cooperative actions, achieving a stable equilibrium that maximizes collective and individual long-term benefits.