For each player and each of his types write down the

Question

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.