Spieltheorie extensive Form erstellen

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Spieltheorie extensive Form erstellen
So ich schreibe die Aufgabe mal ab:
"Two Generals, A and B, whose armies are fortified in opposite hills have to decide whether to attack the enemy camped in a valley separating them. For the attack to be successful, General A must receive reinforcements. The arrival of these reinforcements on time has a prior probability of 1/2 and depends on wheather conditions not observed by the generals. They have reached agreement that if A receives the reinforcements he will send an emissary to B. They both know however, that in this case the emissary has only probability 1/3 of being able to cross enemy lines. The payoffs evaluated as follows:
in case of victory: 50 for each general
if they both refrain from attackin: 0 for each
if one general attacks and the other does not: -50 for the former, -10 for the latter
if both attack but are defeated (because A has not received the reinforcements): -40 for each
Represent the game described in extensive form!"
Soo ich habe wenig PLan, zunächst denke ich dass Nature als erster Spieler dran kommt mit r und nr: also reinforcements oder no reinforcements.
Dann schickt für mich A emissary im Fall r mit behavioral strategies 1/3 , nicht mit 2/3 dann entscheidet er: attack oder nicht, dann General B, aber wie schauen dies Payoffs aus, INformationsmenge etc?

Viele grüße!
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