Write down the conditional probability

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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(I_k, II_l) = ((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 (I_k, II_l), and the vector of actions chosen is (aI, aII), the payoffs to the players are given by

u_I(I_k, II_l; a_I, a_II) = (k + l)(a_I - a_II),

u_II(I_k, II_l; a_I, a_II) = (k - l)a_Ia_II.

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.

Reference no: EM131332567

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