Exercise 13.3
Suppose that two mining companies, Australian Minerals Company (AMC) and South African Mines, Inc. (SAMI), control the only sources of a rare mineral used in making certain electronic components. The companies have agreed to form a cartel to set the (profit-maximizing) price of the mineral. Each company must decide whether to abide by the agreement (i.e., not offer secret price cuts to customers) or not abide (i.e., offer secret price cuts to customers).
If both companies abide by the agreement, AMC will earn an annual profit of $30 million and SAMI will earn an annual profit of $20 million from sales of the mineral. If AMC does not abide and SAMI abides by the agreement, then AMC earns $40 million and SAMI earns $5 million. If SAMI does not abide and AMC abides by the agreement, then AMC earns $10 million and SAMI earns $30 million. If both companies do not abide by the agreement, then AMC earns $15 million and SAMI earns $10 million.
Complete the following payoff matrix using the previous information.
| SAMI | |||
| Abide | Not Abide | ||
| AMC | Abide | million , million | million , million |
| Not Abide | million , million | million , million | |
In the absence of a binding and enforceable agreement, AMC’s dominant strategy is to .
SAMI’s dominant strategy is .
If the two firms can enter into a binding and enforceable agreement, AMC would chooose to and SAMI would choose to .
According to the question,
|
SAMI |
|||
|
AMC |
Abide |
Not Abide |
|
|
Abide |
$30 million, $20 million |
$10 million, $30 million |
|
|
Not Abide |
$40 million, $5 million |
$15 million, $10 million |
|
a)
In the absence of a binding and enforceable agreement, AMC’s dominant strategy is to .
SAMI’s dominant strategy is: Not Abide
Reason: Whether SAMI plays ABIDE or NOT ABIDE, the AMC gets the highest pay -off by playing NOT ABIDE.
Dominant Strategy of player 1 over player 2 is to play its strategy which gives him the highest pay-off no matter what other player is playing.
If the two firms can enter into a binding and enforceable agreement, AMC would choose to NOT ABIDE and SAMI would choose to NOT ABIDE.
Reason: SAMI also have NOT ABIDE as its dominant strategy. So they both will choose NOT ABIDE.
Exercise 13.3 Suppose that two mining companies, Australian Minerals Company (AMC) and South African Mines, Inc....
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