Sequential Game: Bargaining

here we've got two firms Dale and a software firms that can produce software for the Dell computers Dell can offer either $20 per contract per copy of the software or twin daughters and then in in return the software firm can either accept the offer of $30 or reject it or accept the offer of $20 or reject it here we look at the payoff for both firms in terms of their profit if their offer 3000 the copy for that software and the software firm accept the offer then they'll will make 10 million dollars and the software firms 5 million dollars and here we see four potential outcomes now how do we solve the game here the bargaining game between those two firms it's a it's a two-step game first you got there who has to make an offer and then the software firms has to accept or reject the offer so we're gonna use what we call a concept of backward induction to solve this game that is we're going to look at the last player gets to play the game here here the software firm and if there were to offer $30 per software what should the software firm do what's the best decision to make well the software firm can either make five million dollars back setting the offer or two million dollars by rejecting it so clearly if there were 12 for 30 the software firms should accept the offer familiar better than two million dollars now if there were to offer only $20 a software then the software firm should accept or reject in this case the firm will be better off by rejecting the offer in this case that from one leg two million dollars with other business ventures with other firms instead of making 1.5 million dollars in this case you should reject the offer if you're the software firm now moving back to the first stage of this game there when there has to consider offering $30 or $20 per copy of that software what should they'll do well if they're for 30 we know that there will never make 0 mean dollars because the software firm will accept the offer and there will make 10 million dollars and now what if there were to offer $20 in this case we know that will never end up here that the software firm will clean I'm sorry will never end up here the software firm will always reject the offer so they'll will either make 10 billion dollars by offering $30 a software or make zero dollars if they were to offer $20 to the software firm so here in this case Dell will offer $30 and make 10 million dollars so this is the outcome and again here the software firm will make 5 million dollars and they're telling $1 when they're offered $30 a contract per copy to the software firm and the software firm will accept it and you can see here we call those this branch in the decision tree they are connected here and this is our outcome

Channel: Michaël Bonnal

Views: 10,960

Rating: 4.9322033 out of 5

Keywords: Sequential Game, Game Theory (Field Of Study)

Id: nBtXdG-0H2E

Length: 3min 25sec (205 seconds)

Published: Fri Mar 20 2015