Nash Gleichgewicht, Pareto < Politik/Wirtschaft < Geisteswiss. < Vorhilfe
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| Aufgabe | Consider the following game
Each state is deciding on its contribution to a joint project.
The execution of the decision will be (almost completely) unobservable.
States are assumed to maximize only their pay-off.
There are 5 players (states) who can decide about how to allocate (part
of) their budget of 10 units:
Either they keep their budget for themselves or they can give it to a joint project. The project pays out half of the sum of the contribution of all the states:
Let x(i) be the contribution of player i to the joint project: then the pay-off for the player/state "i" is:
payoff(i) = 10 – x(i) + 0.5 (x(1) + x(2) + x(3) + x(4) + x(5))
a) Calculate the pay-off for all players if
x(1) = 3, x(2) = 9, x(3)= 6, x(4)= 0 , x(5) = 10 Which players are playing “best response” (= behaving optimally, given the decision of the others)? Is this situation a Nash-equilibrium?
b) What is the Nash-equilibrium?
c) Which situations are Pareto-optimal?
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Hallo!
Ich weiß nicht, wie ich das ansetzen soll?
Muss ich da für x(i) einen beliebigen Wert nehmen?
Das kann ja nicht sein, oder?
Wie soll ich da ein Nash-Gleichgewicht raussehen bzw. ein Pareto Optimum?
Bitte um Hilfe!
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(Mitteilung) Reaktion unnötig  | | Datum: | 11:20 So 01.11.2009 | | Autor: | matux |
$MATUXTEXT(ueberfaellige_frage)
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