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Coordination Many social interactions can be modeled as a coordination game: The players have a common interest, but as there are multiple equilibria, the desired outcomes are only achieved if they mutually adjust their actions in the right way and go for the same equilibrium.

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Ejemplos coordinación Conducir por el lado derecho. Eligir otra ruta en caso de congestión. Ancho del tren en América, ancho de las cohetes. Bank-run. Encontrarse en Barcelona.

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Peyton Young (1993) distinguishes three broad equilibrium selection theories: First, some equilibria may be a priori more reasonable than others (see, e.g., John Harsanyi and Reinhard Selten, 1988). First, some equilibria may be a priori more reasonable than others (see, e.g., John Harsanyi and Reinhard Selten, 1988). Second, it might be that "agents focus their attention on one equilibrium because it is more prominent or conspicuous than the others" (Peyton Young, 1993, p. 58). Second, it might be that "agents focus their attention on one equilibrium because it is more prominent or conspicuous than the others" (Peyton Young, 1993, p. 58). Third, expectations may converge on one equilibrium through precedent (see, e.g., Vincent Crawford and Hans Haller, 1990). Third, expectations may converge on one equilibrium through precedent (see, e.g., Vincent Crawford and Hans Haller, 1990).

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Exemple de situació amb equilibris múltiples: Heu d’escollir un número entre 1 i 7. Els guanys del jugador i depenen: tant del numero escollit pel jugador i, e i, com del mínim m = min{e j } dels números escollits per tots els jugadors, segons la formula 0,6€ + [0.2€m – 0,1€e i ]. Això queda resumit en la taula següent

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Experimento principal Van Huck, Batalio, Beil (1990, AER): Minimum effort game. 0,6€ + [0.2€m – 0,1€e i ]

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7 equilibria ranked 7 equilibria ranked Pareto dominant could be focal Pareto dominant could be focal Conflict between encouraging others to choose high number and risk of doing it. Conflict between encouraging others to choose high number and risk of doing it. Pareto-dominant is not always chosen Pareto-dominant is not always chosen With the same 2 players Pareto dominant is usually chosen. Not with random pairings, not with n large. With the same 2 players Pareto dominant is usually chosen. Not with random pairings, not with n large.

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Cómo se puede mejorar la coordinación Comunicación. Tamaño del grupo. Número de periodos. Costes de entrada. Competición.

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Horizonte con pocos vs muchos periodos

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Coordinación con 2 personas (con la misma pareja vs emparejamiento por azar)

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Battle of Sexes

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Coordinación con competición

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Localization problem You want to locate where everybody goes (BCN vs MAD) You want to locate where everybody goes (BCN vs MAD) 7 persons play 15 periods 7 persons play 15 periods

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Results: Path Dependence Results: Path Dependence Small historical accidents have large long-run impact. “Lorentz effect” Small historical accidents have large long-run impact. “Lorentz effect” Extreme sensitivity to initial conditions. Extreme sensitivity to initial conditions. Predicting in these games is like trying to prove that a joke is funny without telling it Predicting in these games is like trying to prove that a joke is funny without telling it Continental divide: two water drops fall infinetissimaly close, yet… Continental divide: two water drops fall infinetissimaly close, yet…

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Focal points as a coordination device As Thomas Schelling (1960) put it: As Thomas Schelling (1960) put it: "Most situations - perhaps every situation for people who are practiced at this kind of game - provide some clue for coordinating behavior, some focal point for each person’s expectation of what the other expects him to expect to be expected to do. Finding the key, or rather finding a key - any key that is mutually recognized as the key becomes the key - may depend on imagination more than on logic; it may depend on analogy, precedent, accidental arrangement, symmetry, aesthetic or geometric configuration, casuistic reasoning, and who the parties are and what they know about each other" (p. 57).

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Conclusión (coordinación) Reglas de selección: Precedencia (historia importante). Dominancia del riesgo. Pareto optimalidad (no siempre llegamos) Evitar pérdidas. Seguridad (maximización del mínimo de todos) Ventaja para el que elige primero.

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