ENGRI 1101 Engineering Applications of OR
Fall ’08 Homework 12
Homework 12 Solutions
1.
(a) The labor union has the following strategies available: they can demand any amount (rounded to
multiples of 10 cents) between the management’s current offer ($1.10) and their current demand
($1.60). Clearly, to demand anything outside this range does not make sense. So, labor union
strategies are to demand $1.10, $1.20, $1.30, $1.40, $1.50, or $1.60.
The management’s strategies are to offer $1.10, $1.20, $1.30, $1.40, $1.50, or $1.60.
Note that this is a 2player 0sum game, since everything that is gained by the union is lost by
the management, and vice versa. Let the union be the row player, and the management be the
column player. Then we can set up a table where the entry (
i,j
) represents the final settlement,
given that union demands according to strategy
i
, and management offers according to strategy
j
:
union
\
management
$1.10
$1.20
$1.30
$1.40
$1.50
$1.60
$1.10
$1.10
$1.15
$1.20
$1.25
$1.30
$1.35
$1.20
$1.20
$1.20
$1.25
$1.30
$1.35
$1.40
$1.30
$1.30
$1.30
$1.30
$1.35
$1.40
$1.45
$1.40
$1.40
$1.40
$1.35
$1.40
$1.45
$1.50
$1.50
$1.50
$1.35
$1.30
$1.40
$1.50
$1.55
$1.60
$1.35
$1.20
$1.30
$1.40
$1.50
$1.60
To understand how the elements of the table are calculated, let’s focus on what happens when
the union demands $1.40. Notice that this is a decrease of $0.20 from their original demand of
$1.60.
•
If management offers $1.10 or $1.20, their move from the original offer of $1.10 is less than
the move by the union, so the union’s demand of $1.40 is going to be accepted.
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 '05
 TROTTER
 Game Theory, labor union, column player

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