Please Wait

- May 3, 2017
- Livingston
- Economics
- Economics Assignment Help
- No Comments

Internal Code: 1HAEF

**Task:**

**Problem 1**

Problem 1 continues from Problem 1 of Assignment 1. The numbering of sub-parts is kept throughout the problem, so the rst sub-part of this problem is (d).

Consider the following auction that most of you must have encountered before.

There is a prize (e.g. a chocolate rabbit). Each player buys tickets, worth 1 cent each, write his or her name on it, and put them in a box. Then a ticket is drawn at random and the person whose name is on

the ticket receives the chocolate rabbit. If no player bought any tickets (that is, the box is empty), then all players get nothing.

Assume, for all parts of this problem, that there are two players and that the rabbit is worth $1 for both. The auction I am describing is usually used for charity; ignore all aspects of charity and assume that the only thing players care about is getting the rabbit.

Note: In this problem, you may assume that (i) tickets are perfectly divisible (you can buy 0.71486 tickets) or (ii) tickets must be whole non-negative numbers (0 is included in both cases). If you assume (i),the solution would be much nicer, but you will need to deal with a small technical problem. If you assume (ii), a technical problem disappears, but solution is ugly. It’s your choice.

Suppose that the timing of the problem has changed: Player 1 buys the lottery tickets and put them in a transparent box. Player 2 observes the decision of player 1 and decides how many lottery tickets to buy.

(d) [8pt] Model this new situation as a formal game.

(e) [12pt] Find the subgame perfect Nash equilibrium of this game. (Hint: although this game may look slightly dierent to what we have seen so far, approach it in the same way as other games: nd that Player 2 will do given Player 1’s choice; then nd what Player 1 will do knowing the choice of Player 2 that will follow. You will need to write maximisation problems; pay attention what is the decision variable in these problems and what is not.)

Let us now consider a hybrid of (a) and (d). Let us suppose that Player 1 buys tickets and put them in the box, and Player 2 can observe whether the box is empty (Player 1 bought nothing) or has tickets, but cannot observe how many tickets there are inside.

(f) [10pt] Model this situation as a formal game.

(g) [7pt] Give an example of the strategy prole in this game.

(h) [4pt] Explain why the strategy prole in (g) is / is not a Nash equilibrium.

(i) [5pt] Does pure strategy Nash equilibrium exist in this game? Give an example if it does or explain if it does not.

(j) [4pt] Suppose we are looking for a subgame perfect Nash equilibrium. How does you answer to (i) changes?

**Problem 2**

Suppose there are three players (1, 2 and 3) who need to pick one of the three alternatives: a; b or c. The decision is reached as follows:

- Players rst simultaneously vote for either a or b (they cannot abstain). The alternative that collects 2 votes wins. Let us call this alternative w1.
- Then players simultaneously vote for either w1 or c (they cannot abstain). The alter-native that collects 2 votes wins. Let us call this alternative w2.
- The alternative w2 is chosen.

Suppose players’ preferences are: a 1 b 1 c; b 2 c 2 a; c 3 a 3 b. All players know the preferences of other players.

(a) [5pt] Suppose that each player votes for alternatives according to their preferences (that is, if i prefers a to b, then i votes for a). Find the chosen alternative w2.

(b) [15pt] Suppose now that each player anticipates the outcome of the second round and votes strategically. That is, players’ strategies form a subgame perfect Nash equilibrium of the overall game. Suppose also that, when player’s vote does not matter, she votes for an alternative she personally prefers. For example, when choosing between a and c, if players 2 and 3 vote for c, then the vote of player 1 does not change the outcome. In that case, we assume that player 1 votes for a.1 When player’s vote matters, the player votes so that she will get the best possible outcome (hint: it involves voting contrary to own preferences in the rst round).

Find the equilibrium strategies and the chosen alternative.

(c) [10pt] Suppose that player 1 sets the agenda; that is, player 1 picks the order in which alternatives are voted for. Can player 1 pick the order so that her favourite outcome (a) gets selected?

**Problem 3**

Consider the following problem. Fisher (who is a female) has an object that is worth $1 to her and $5 to Henry. Fisher can invest into the object, at the cost of $2; the investment increases the value of the object to $2 for Fisher and to $10 for Henry. After Fisher decides whether to invest or not, Henry observes Fisher’s decision and makes her an oer to buy the object. That is, Henry oers a payment p to Fisher and Fisher can only reject (and consume the object herself) or accept (and consume the payment p for the object).

(a) [7pt] Model it as a game.

(b) [7pt] Find a subgame perfect Nash equilibrium (SPNE).

(c) [6pt] Find a Nash equilibrium (but not necessarily SPNE) where Fisher invests.

Post Views:
0

- ICT 101: Discrete Mathematics for IT – Mathematics – Report writing Assignment Help
- HAT202: The Hospitality and Tourism Management – Business Portfolio Writing Assignment Help
- 3806NRS: Nursing – Peak Professional Nursing Organisation – Portfolio Writing Assignment help
- 3806NRS: National Safety and Quality Health Service – Blood Management – Nursing Assignment Help
- BUAD 176: Professional Selling – Product Selection – Management Assignment Help

All the assignments are checked for the plagiarism and its types by our expert quality assurance team of TV Assignment Help. So, we assure you that every assignment will be 100% percent authentic and original.

The assignments are delivered much before the assignment deadline and we even work on urgent basis. Our experts work accordingly to make the delivery possible before time so that you can ask for revisions.

Please send us a Text on

+61 466 332 323

All documents prepared at TV Assignment Help are written by subject-specific experts who are certified from various renowned universities. Every assignment is checked by our “**Quality Assurance Team**” to check on the quality.

We serve you with our premium services at reasonable prices. You can even compare our prices with other assignment help services to clear your doubts. We even offer seasonal and referral discounts.

Kevin Edward

Queensland

TV391

TV Assignment Help amazed me! In order to do my assignment, I’ve read a lot of sources, but nothing helped. But, the kind of assignment help TV Assignment Help provided was beyond my request. Appreciate your hard work and would definitely recommend you to my fellow mates.
Bacar Silva Jaura

Brisbane

TV386

I approached TV Assignment Help for my dissertation paper. They helped me not only in writing my dissertation, but also to proofread it. I believe that their experts can cope up with any writing you need. The final output had all the relevant points which were mentioned by me. Thank you so much for helping me in writing my dissertation. I highly recommend TV Assignment Help!
Brayden Chan

Adelaide

TV347

I would say that TV Assignment Help has a clear view of how a good assignment should be written. As I ordered an SPSS assignment, and the final result was totally satisfying. The quality of work was really high and it met the standards of writing I needed. You guys are an A+ for me.
Nhatquyen Phan

Perth

TV338

TV Assignment Help serve students by providing high-quality assignments. It was such a relief for me as they provided me the assignment on-time and that too without any errors. I did not have to proofread it again and again, as their experts have done a quality work. Thank You, Guys!
Sagar Chettri

Melbourne

TV490

I had a management assignment due in 10 hours and had no clue what to do. TV Assignment Help turned up as a savior, as I ordered a paper with them and what I got shocked me. Their expert was able to provide the assignment despite the short deadline. The writer delivered a great assignment which got me good grade.
Vinod Mandava

Sydney

TV413

In my opinion, TV Assignment Help is doing an amazing job! I have taken assignment help from them and I like the guarantees they offer, as well as the ability to provide best-discounted offers. They provided my assignments before the deadline. I must say that TV Assignment Help provides what they promise.**Disclaimer 1.1**: The assignment delivery time by TvAssignmentHelp is contingent on the level of expertise, total word count and the technicalities involved.

**Disclaimer 1.2**: The academic papers provided by TvAssignmentHelp are for reference purpose only and not to be used as it is.

* Terms and Conditions Apply

© Copyright 2014 - 2019 TvAssignmentHelp. All Rights Reserved.