5. Consider a setting with a buyer (player 1) and seller (player 2) who may trade one unit of a good for money. Player l's valuation of the good is denoted by v and is privately known to this player. Likewise, player 2's cost of production is denoted by c and is privately known to this player. Assume that Nature chooses v and c independently from a uniform distribution on the interval (0, 1]. If the players trade at price p, then player 1 gets a payoff of v-p and player 2's payoff is p-c. If the players do not trade, then they both get a payoff of 0. (a) Suppose that the parties interact as follows. First Nature draws v and e, player 1 observes v, and player 2 observes c. Then simultaneously player 1 makes an offer rE (0, 1] and player 2 makes an offer y E (0, 1). If a a Do this by showing that these strategies are best responses to each other (you can evaluate each type individually). For what values of a is this strategy profile a Bayesian Nash equilibrium?
5. Consider a setting with a buyer (player 1) and seller (player 2) who may trade one unit of a good for money. Player l's valuation of the good is denoted by v and is privately known to this player. Likewise, player 2's cost of production is denoted by c and is privately known to this player. Assume that Nature chooses v and c independently from a uniform distribution on the interval (0, 1]. If the players trade at price p, then player 1 gets a payoff of v-p and player 2's payoff is p-c. If the players do not trade, then they both get a payoff of 0. (a) Suppose that the parties interact as follows. First Nature draws v and e, player 1 observes v, and player 2 observes c. Then simultaneously player 1 makes an offer rE (0, 1] and player 2 makes an offer y E (0, 1). If a a Do this by showing that these strategies are best responses to each other (you can evaluate each type individually). For what values of a is this strategy profile a Bayesian Nash equilibrium?
Oh no! Our experts couldn't answer your question.
Don't worry! We won't leave you hanging. Plus, we're giving you back one question for the inconvenience.
Submit your question and receive a step-by-step explanation from our experts in as fast as 30 minutes.
You have no more questions left.
Message from our expert:
Hi and thanks for your question! Unfortunately we cannot answer this particular question due to its complexity.
We've credited a question back to your account. Apologies for the inconvenience.
Your Question:
None
![5. Consider a setting with a buyer (player 1) and seller (player 2) who may trade one
unit of a good for money. Player l's valuation of the good is denoted by v and is privately
known to this player. Likewise, player 2's cost of production is denoted by c and is privately
known to this player. Assume that Nature chooses v and c independently from a uniform
distribution on the interval (0, 1].
If the players trade at price p, then player 1 gets a payoff of v-p and player 2's payoff is
p-c. If the players do not trade, then they both get a payoff of 0.
(a) Suppose that the parties interact as follows. First Nature draws v and e, player 1
observes v, and player 2 observes c. Then simultaneously player 1 makes an offer rE (0, 1]
and player 2 makes an offer y E (0, 1). If a <y then the game ends with no trade and both
players get 0. If r y then the game ends with trade at price p y, so that player l's
payoff is v – y and player 2's payoff is y-c.
Find and report the Bayesian Nash equilibrium of this game. Note that player l's strategy
is a function s: (0, 1] [0, 1] that maps this player's type v to this player's choice of r,
and player 2's strategy is a function s2: (0, 1] → (0, 1] that maps this player's type e to
this player's choice of y. (Hint: Start by observing that player 1 has a weakly dominant
strategy, which is used in the equilibrium.)
(b) Now consider a slightly different game in which the players simultancously select r
and y, as before, and trade occurs if and only if r 2 y, but now assume that the price is
p (r+y)/2.
Show that there is a Bayesian Nash equilibrium in which, for some number a,
La if v 2a
s1(v) =0 if v < a
and
a if c<a
s2(c) =1 if c> a
Do this by showing that these strategies are best responses to each other (you can evaluate
each type individually). For what values of a is this strategy profile a Bayesian Nash
equilibrium?](https://content.bartleby.com/qna-images/question/06c9b939-bc12-440c-9f34-b9580c5484d2/893455da-c1dd-4e3f-8a95-b81146f20b8c/lbvslg_processed.jpeg)
Transcribed Image Text:5. Consider a setting with a buyer (player 1) and seller (player 2) who may trade one
unit of a good for money. Player l's valuation of the good is denoted by v and is privately
known to this player. Likewise, player 2's cost of production is denoted by c and is privately
known to this player. Assume that Nature chooses v and c independently from a uniform
distribution on the interval (0, 1].
If the players trade at price p, then player 1 gets a payoff of v-p and player 2's payoff is
p-c. If the players do not trade, then they both get a payoff of 0.
(a) Suppose that the parties interact as follows. First Nature draws v and e, player 1
observes v, and player 2 observes c. Then simultaneously player 1 makes an offer rE (0, 1]
and player 2 makes an offer y E (0, 1). If a <y then the game ends with no trade and both
players get 0. If r y then the game ends with trade at price p y, so that player l's
payoff is v – y and player 2's payoff is y-c.
Find and report the Bayesian Nash equilibrium of this game. Note that player l's strategy
is a function s: (0, 1] [0, 1] that maps this player's type v to this player's choice of r,
and player 2's strategy is a function s2: (0, 1] → (0, 1] that maps this player's type e to
this player's choice of y. (Hint: Start by observing that player 1 has a weakly dominant
strategy, which is used in the equilibrium.)
(b) Now consider a slightly different game in which the players simultancously select r
and y, as before, and trade occurs if and only if r 2 y, but now assume that the price is
p (r+y)/2.
Show that there is a Bayesian Nash equilibrium in which, for some number a,
La if v 2a
s1(v) =0 if v < a
and
a if c<a
s2(c) =1 if c> a
Do this by showing that these strategies are best responses to each other (you can evaluate
each type individually). For what values of a is this strategy profile a Bayesian Nash
equilibrium?
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Recommended textbooks for you
