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There are 2 persons and two bags of oranges present in system.A bag is assigned to person.Each bag contains some oranges in range 1-10.After opening each person has been asked if they want to trade or not if they both say yes then trading will happen,if they contradict they will get whatever present in their respective bags(no exchange).What is the maximum number of oranges for which either player says yes in a Nash equilibrium?

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    I would never say yes (but I am not sure I'm in Nash equilibrium ;-)) Ok, I if have one orange in my bag I might say yes but I don't expect to get more than an orange back.2012-04-14
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    I'll say no with ten in my bag, and so will the other. So if I have nine ...2012-04-14
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    Do the players like oranges?2012-04-14
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    @Matt: It's obvious that you say "no" for $10$ only because you have nothing to gain from saying "yes". But that's not enough to say something about all Nash equilibria; you might still say "yes" for $10$ if you have nothing to lose from doing so.2012-04-14
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    How are payoffs calculated? Expected payoffs are not really defined without a prior and you need them for the definition of equilibrium.2012-04-15
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    The probability of saying yes by other person can be proportional to $(10-number\ of\ oranges\ in\ his\ bag)/10$ so in this way we can associate probability and with each player but i'm not able to get payoff matrix.2012-04-15
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    @Michael: For my answer to apply, all you need is that the prior is non-zero for every number of oranges from $1$ to $10$. Of course, if it's zero for some number, then that part of the strategy is irrelevant and either player can say "yes" for that number in equilibrium.2012-04-15

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