Reference no: EM131332567
Describe the following game with incomplete information as an extensive-form game. There are two players N = {I, II}. Each player has three types, TI = {I1, I2, I3} and TII = {II1, II2, II3}, with common prior:
p(Ik, IIl) = ((k(K + l))/78), 1<=k, l<=3.
The number of possible actions available to each type is given by the index of that type: the set of actions of Player I of type Ik contains k actions {1, 2,...,k}; the set of actions of Player II of type IIl contains l actions {1, 2,...,l}. When the type vector is (Ik, IIl), and the vector of actions chosen is (aI, aII), the payoffs to the players are given by
uI (Ik, IIl; aI, aII) = (k + l)(aI - aII),
uII(Ik, IIl; aI, aII) = (k - l)aIaII.
For each player, and each of his types, write down the conditional probability that the player ascribes to each of the types of the other player, given his own type.
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