Incomplete Information. This lecture shows how to analyze games that have more complicated information sets than complete information games. This requires us to apply rules, already learned in previous lectures, to more complicated settings. Incomplete information games .
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Incomplete Information
This lecture shows how to analyze games that have more complicated information sets than complete information games. This requires us to apply rules, already learned in previous lectures, to more complicated settings.
First we shall analyze two games in which one player knows more about a second player’s previous move than a third player.
This game features a corrupt government, a poorly run state enterprise and an opportunistic foreign investor wrestle for mineral and oil wealth.
A dominant strategy for the government in this game is to seize foreign assets when presented with the opportunity to do so.
But if the customer never buys the product, the retailer would always return defective ones.
In this case the manufacturer specializes in produced flawless products.
It now follows that the strategy of not buying is not a best response
Therefore the consumer follows a mixed strategy.
3r - 2(1 - r) = -1
⇒ 3r – 2 + 2r = -1
⇒ 5r = 1
⇒ r = 0.2
The producer will only mix between defective and flawless items if the benefit from both are equated:
[6r + (1 - r)]q - 3(1 - q) = [3r + (1- r)]
⇒ 2q – 3 + 3q = 1.4
⇒ 5q = 4.4
⇒ q = 0.88
9p - 10(1 - p)q = 0 ⇒ (9 +10q)p = 10q
⇒ p = 44/89
We now modify the game slightly. If the customer buys a defective product, she receives partial compensation.
Incomplete Information due to Nature
This lecture considers four games where nature is the source of the incomplete information, and discusses the costs and benefits of making players more informed.
The analysis of this game can be somewhat simplified by investigating the reduced game:
Cost of incomplete information
Air-taxi service
Often companies do not know precisely how much competition they will face before launching a new product:
Both firms have a dominant strategy to advertise the product, which determines the unique solution to this game.
Now suppose a newsletter is produced to keep firms abreast of the latest developments. The extensive form becomes: