Question

Draw the extensive-form diagram of the Monty Hall three-door game demonstrated in class on Tuesday. In this game, the host (player 1) privately selects an envelope in which to put the prize money (A, B or C). The contestant (player 2) does not observe the host's choice but then must select an envelope. The host must open one of the envelopes that the contestant did not select, but the host is not allowed to open the envelop containing the prize. Finally, the contestant chooses whether to stay with his/her originally selected envelope or switch to the other unopened one. If the contestant's envelope contains the prize then he/she wins the money. Otherwise, the money goes back to the host.

Answer 1

This case includes two players 1 and 2 who are given the option of selecting the envelope to find out whether he or she has won the prize in the Monty Hall three door-games.

The envelop a,b,c can be selected by player 2 and in simultaneously form since a, b and c are related as shown in the figure above. Name the tree from the above as L,M,N,O,P,R,S,T,U,V.

The below can be represented in the normal form representation