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Suppose there are two players, N = {I, II}, and four states of nature, S = {s11, s12, s21, s22}. Player I's information is the first coordinate of the state of nature, and Player II's information is the second coordinate. The beliefs of each player, given his information, about the other player's type are given by the following tables:
(a) Find a belief space describing this situation.
(b) Is this belief space consistent? If so, describe this situation as an Aumann model of incomplete information.
Describe the game as a game in strategic form and find all its Nash equilibria.- Describe the new situation as a game in strategic form and find all its Nash equilibria.
In equilibrium, what is the total number of fish caught? - What is the answer to the chief's question? What is the efficient number of fishers at each reef?
Construct a belief space in which the described situation is represented by a state of the world and indicate that state.
The Candle Company and the Wick Corporation are the only manufactures of a very sophisticated type of flammable material.
What are the states of nature in this game?- How many pure strategies does each player have in this game?- Depict this game as a game with incomplete information.
A hypothesis test for a population proportion ρ is given below: Ho: ρ = 0.10 Ha: ρ ≠ 0.10
A manufacturer of a new, less expensive type of light bulb claims that this product is very well made and even more reliable than the higher priced competitive light bulbs.
Show that the game that results if player 1 is prohibited from using one of her actions in G does not have an equilibrium in which player 1's payoff is higher than it is in an equilibrium of G.
Maxminimizers vs. Nash equilibrium actions:- The game in Figure has a unique Nash equilibrium, in which player 1's strategy is ( ¼, 3/4 ) and player 2's strategy is ( 2/3 , 1/3 ).
Imagine that there are three major network-affiliate television stations in Turlock, California: RBC, CBC, and MBC. - Find the set of rationalizable strategies in this game.
Does this game have a subgame perfect Nash equilibrium? - Do you think any one of the players has a strategy that guarantees him a win (a payoff of 2)?
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