What are the extensive and strategic forms of the game if, beginning with the variation of problem 1, Beljeau must decide whether to become informed about the size of the market before learning what Jokx does, but if they decide to become informed, they learn whether Jokx chose to become informed or not?
Problem 1
Let us complicate the story of Jokx and Beljeau enormously by supposing that both Jokx and Beljeau must decide whether to commission market surveys that will reveal the size of the market. For Jokx, this survey will cost $5,000; if they choose to spend this money, Jokx can learn for sure what the market size will be before they have to decide whether to proceed with Oligopoly. And Beljeau (which previously was assumed to have this information coming) now must decide whether to commission a survey; it will cost them $5,000 as well. Both sides must decide whether to commission a survey and then whether to proceed with the respective products without learning what the other has done, both with regard to taking the survey and then to introducing their product.
(a) Draw decision trees for Jokx and Beljeau in this new situation.
(b) Draw a game tree representing the situation for the two. (This is a tedious exercise.)
(c) List all the strategies that each side has. (Depending on what you do with equivalent strategies, they have between six and sixteen apiece.)
(d) Give the reduced normal form of this game. (Again very tedious)