GU 4260 Spring 21 — Assignment 3

8.9 8 10.7 4 11.1 3

B C D E F G H I J K L

8.2 3

•i2的第二和第三最喜欢的学校； •i3最受青睐的学校排名第一和第二；

1个

Pi1 Pi2 Pi3 Pi4 s4s4 s2 s3 s3 s2 s2s1 s1 s1 s1 s4

1 1 1 1

Ps1 Ps2 Ps3 Ps4 i4 i3 i2 i1 i2 i4 i3 i4 i1 i1 i4 i2 i3 i2 i1 i3

2个

Problem 1 We consider the sequence of orders submitted by trader for the same security given in Table 1. The order of arrival is the same as in the table (i.e., A’s order is the first, then B, then C, . . . ). The book is empty before the first order arrives.

A sell

Type

limit
limit
limit
immediate or cancel
limit 8 1

limit 8.3 7

limit 8.7 4 immediate or cancel 11.4 1 limit 12 8 limit 9.1 8 immediate or cancel 11.2 5 limit 8.9 2 limit 9 3

Table 1: Submitted orders

Price Quantity

8.9 8 10.7 4 11.1 3

B C D E F G H I J K L

8.2 3

1. For each trader, give the quantity and price at which the asset is sold/bought if we use the continuous limit order book protocol. For each quantity bought/sold say whether the trader was a liquidity taker or liquidity provider.
2. For each trader, give the quantity and price at which the asset is sold/bought if we use a double auction waiting for the last trader’s order to arrive to run the auction and considering all the order (i.e., including the “immediate-or-cancel” orders).

Problem 2 We consider the following matching problem with 4 students (i1,i2,i3, and i4) and 4 schools (s1,s2,s3, and s4). Each school has a capacity equal to 1.

Students’ preferences are given by Table 2 and schools’ priorities are given by Table 3. In Table 2 some entries are missing:

The 2nd and 3rd most preferred schools for i2; The 1st and 2nd most preferred schools for i3;

1

1. Complete the students’ preferences in Table 2 such that the DA algorithm with students proposing runs in 7 steps.

Your answer should show the proposals and acceptance/rejection decisions at each step and the final maching.

2. With the complete preferences calculate the assignment when we run the Boston algo- rithm.

Your answer should show the proposals and acceptance/rejection decisions at each step and the final maching.

Pi1 Pi2 Pi3 Pi4 s4s4 s2 s3 s3 s2 s2s1 s1 s1 s1 s4

Table 2: Students’ Preferences

capacity

1 1 1 1

Ps1 Ps2 Ps3 Ps4 i4 i3 i2 i1 i2 i4 i3 i4 i1 i1 i4 i2 i3 i2 i1 i3

Table 3: Schools’ Priorities

2

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