Game theory

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winw

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Sep 28, 2011
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Hi, I have a question about game theory.

An incumbent firm (firm 1) earns a profit of 1 million in an industry. A second firm (firm 2) is considering entering the industry. The decision of firm 2 to enter is reversible. After firm 2 enters the market, firm 1 will decide to accommodation or not, firm 2 can choose to remain or exit. If firm 2 enters and firm 1 accommodates then each will earn a profit of 0.5million. However, if firm 1 does not accommodate, then both will loose 0.5 million. If firm two decides to exit that market they will suffer a loss of 0.2 million, while firm 1 will make 1 million in profit.

Firm two enters, firm 1 accommodates 0.5, 0.5
Firm two enters, firm 1 does not accommodates -0.5, -0.5
Firm two does not enter, firm 1 accommodates 1,0
Firm two does not enter, firm 1 does not accommodates 1,0

Firm two enters, firm 1 does not accommodates, Firm two exits 1, -0.2

like that??

Thanks
 
oh :oops: we are supposed to find the Nash equilibrium, but the part about the entry decision being reversible confuses me
 
Could you start with the observation that "does not enter" dominates "enters" for company #2?
 
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I think I am supposed to assume that firm 2 will enter...so maybe the problem is to do with

Firm one accommodates and firm 2 exits 1, -0.2
Firm one accommodates and firm 2 does not exit 0.5, 0.5
Firm one does not accommodate and firm 2 exits 1, -0.2
Firm one does not accommodate and firm 2 does not exit -0.5, -0.5

so then the nash equilibrium would be...

Firm 1 does not accommodate and firm 2 exits

and

Firm one accommodate and firm two does not exit??
 
Okay, now prove it. Make each company change its mind unilaterally and see if the individual position can be improved.
 
so If firm one declides to accommodate the best responce for firm two would be to stay in the market so do not exit

if firm one decides not to accommodate , then firm two will choose to exit

If firm two decided to exit, then firm one will decide to accommodate or not to accommodate , they will be indifferent

if firm two decides to stay, then firm one will accommodate


so the 2 solutions about would be correct right?
 
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