Zero Sum Games
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Hi Yair! I'll give it a try but I can't be absolutely sure that I'm correct :) Here goes.....
If this game is infinite (there's no deadline), and the size of the pie shrinks in each period, there will be no last-mover advantage. I suppose we can look for a symmetric equilibrium (players repeating their strategy). The equilibrium strategy will be stationary as when an offer is rejected, the game is exactly the same as before the offer was made, excluding the shrinking.
Let us assume that player one offers player two a fraction of $100 (maybe just a cent). This will be $100x. He thus keep $100(1-x) to himself. This is almost the full amount. Player 2 can accept, and get this one cent, or reject and get to hear about the second offer which will definately still be that one cent, but, now it would have to be discounted. Since one cent w/o being discounted is surely better than one cent tomorrow, player 2 will accept the offer. At the equilibrium, player one gets $100/(1+d) & player two gets $100d/(1+d). In the infinite version, it is always an adv to be able to make the 1st move. The 1st offer is always accepted. [Manage messages]
The game is identical to the classic inifinte horizon game of alternating offers (Rubinstein 1982) , 2 players, fixed discount factor etc. The only difference is that player 2 makes offer at period that are product of 3, for [View full text and thread]
|03/20/2001 03:28 AM by yair; bargaining game of alternating offers.|