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Gry powtarzane w nieskończoność
Gra powtarzana w nieskończoność to scenariusz, w którym gracze wielokrotnie angażują się w tę samą grę bez ustalonego z góry końca. Ta koncepcja jest…
Gra powtarzana w nieskończoność to taka, w której gracze wielokrotnie angażują się w tę samą grę bez z góry określonego końca.
Przykładem mogą być firmy wielokrotnie ustalające ceny lub kraje negocjujące warunki handlowe przez wiele lat.
W tych grach firmy często przyjmują strategię "wet za wet".
Weźmy na przykład pod uwagę dwie konkurujące ze sobą firmy, Alpha i Beta, ustalające ceny swoich napojów bezalkoholowych.
Ustalają cenę na początku każdego miesiąca. Jeśli obie firmy utrzymują ceny na wysokim poziomie, cieszą się wysokimi zyskami.
Strategia "wet za wet" polega na rozpoczęciu od wspólnego działania, takiego jak ustalenie wysokiej ceny.
Beta nadal ustala wysokie ceny, o ile Alpha robi to samo.
Jeśli Alpha obniży cenę, Beta również obniży swoją cenę w następnej rundzie. Daje to Alfie przewagę zysku, a Becie niekorzyść zysku w tej jednej rundzie. Kiedy Alpha wraca do wysokiej ceny, Beta dopasowuje się do niej.
Wynikiem powtarzanej w nieskończoność gry jest trwała współpraca. Firmy zdają sobie sprawę, że krótkoterminowe zyski z obniżania cen są mniejsze niż długoterminowe straty z niskich cen.
Utrzymywanie wysokich cen staje się racjonalną strategią dla obu firm, prowadzącą z czasem do obopólnych korzyści.
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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.