17. backward induction – ultimatums and bargaining take it or leave it offers. Two players. Split a dollar. (s,1-s) offer to 2. if accepts get (s,1-s).

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Presentation transcript:

17. backward induction – ultimatums and bargaining take it or leave it offers. Two players. Split a dollar. (s,1-s) offer to 2. if accepts get (s,1-s). Otherwise zero for both. Does backward induction permit (.99,.01), (100,0)

IN splitting the dollar Why do we see a failure of backwards induction? (see this happen in practice) – pride thing – want to be fair

Two period game. “Shrinking pie” time of making the decision enters in Dollar on the table. Make an offer Player accept/reject. If accept (s, 1-s) If reject, flip roles – but part of the money is lost. delta (90%, say) remains. If player 2 offers 2 > , player 2 will accept. Otherwise, will reject. For k stages, we get powers which determine what we need to offer to the other person:  k-1

Results of shrinking pie? We get an even split if we can potentially bargain forever. If the value of the pie and the discount is known, the first offer will be accepted. (No haggling in equilibrium) The poor will do less well in bargaining. If people's values are not known, not only are the offers not accepted immediately and not only is there some inequity in that the poor tend to be more impatient and do less well, but also you get bad inefficiency. The inefficiency occurs essentially because the sellers want to seem like they're hard bargainers and the buyers want to seem like they're hard, and you get a failure for deals to be made.

If values are not known, offers are not accepted on the first round. Get bad efficiency. Both want to seem like they are hard – failure for deals to be made.

Lecture 18 - Imperfect Information: Information Sets and Sub-Game Perfection Assume perfect recall. Can’t assume two nodes are in same information set, if those nodes have different number of choices. One reason for an information set could be that player 1 is randomizing between their choices. perfect information – all information sets have just one node. Can’t fail two distinguish between nodes that depend on YOUR prior moves. May not be true if it is a “team” that is making a decision (and others don’t know what another said).

What matters is information not time

Subgame 1.starts from a single node 2.comprises all successors to that node 3.does not break up any information sets

Are these subgames?