TEORIA DE JUEGOS

 Análisis de Decisión y Juegos Investigación Operativa I

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Teoría 







de Juegos

La Teoría de los Juegos es una rama de la matemática que se dedi de dica ca al estu tudi dio o de sit itua uaci cio one ness lla lama mad das de co conf nfllict cto. o.

En ella dos o más partes o decididores deben tomar cada una decisiones cuya efectividad depende de las decisiones tomadas por lass de la demá más. s. El objetivo del estudio es encontrar la forma en que un decididor pue pu eda to tom mar las de deci cission one es lo más efe fect ctiv iva ament nte e qu que e sea po posi sibl ble e. Se dirá entonces que cada decididor buscará maximizar el beneficio 

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Teoría

de Juegos

D efinicione efinicioness ele element mentale aless Juego: situ  ación de conflicto en la q ue dos o más j ugadores inte in tent ntan an al alca canz nza ar un objetivo seleccionando c ursos de acción de entre todos los que sean perm rmiitidos por las re reg glas. 





Reglas: posibles c ursos de acción que pueden ser elegidos. Conocidas por todos los j ugadores. Resultados: asociados a cada posib le combinación de elec ecci cion ones es so son n defi de fini nido doss po porr adelantado y conocidos por todos los jugad ores.

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Teoría

de Juegos

Estrategia:



Mét odo odo predeterminado que permita a un jugador elegir cada una de las movidas que conf orman a una partida, ante el análisis de t od iera ran n ha habe berr odas las movidas que pudie hecho t odo odos los demás jugadores. Tambi bié én se llamará est strrat ate egia a la secuencia de movidas resultante. Estrategia pura a aquella en la cual cada una de las movidas hechas por un jugador a lo largo de una partida

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Teoría 





de Juegos

Valor

del juego: resultado de jugar una part rtiida, cada jugador con su estrategia estrategi a. Indica cual es el beneficio o perjuicio que recibe cada  jugador.

Solución del  juego: conjunt o de estrategias óptimas para cada  jugador y valor del  juego resultante de la aplicación de esas estrategias. Técn cniica ca:: conjunt o de reglas mediante las cuales se intenta hallar la est stra rate teg gia óp ópttim ima a pa para ra cada jugador.

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Teoría

de Juegos

En Resumen: La teoría de juegos trata con sit uaciones de decisión en las que dos oponentes inteligentes tienen objetivos en conf lict o. Dos oponentes, conocidos como jugadores res,, tendrá cada uno un número de alternativas o estrategias.. estrategias  Asociada con cada par de estrategias hay una nj do l tr . Tal 

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

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Teoría 

de Juegos

Representación mediante matrices de pago: si A usa la estrategia i y B la estrategia j, el pago a A es aij, lo que significa que el pago a B es aij aij (es decir B paga a A)

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Teoría

de Juegos

odos para resolución de Juegos Distint os Mét odo

S bmatrices

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Teoría

de Juegos

S ubmatrices ubmatrices

matr  tr i i z de pa gos  es  una matr i iz  de tr es  por Si  la ma t i il  i zars e el m étodo de r esoluci ón ic es . u t  ón por s ub ubmatr ic 

tr es , puede

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Teoría

de Juegos

Si la suma de los resultados en la última fila es igual a la suma de los resultados en la última columna, ent onces el  juego tiene solución por este método   . Si no debe buscarse un método   alternativo para re ressolverlo.

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Teoría  A A B B B1B1 B2  A1 A1

--1 1

2

de Juegos

B3

B1B1-B2 -B B2 2

B2B2-B3 -B3

1

-3

1

3

--4 4

-1 -1

7

17

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