Question

. Consider a two-stage bargaining bewteen one seller and two buyers. It is common knowledge that the seller’s valuation of the item is zero while buyers’ valuation of the item is, game theory, auctions,

1. Consider a two-stage bargaining bewteen one seller and two buyers. It T is common knowledge that the seller's valuation of the item is zero while buyers' valuation of the item is 1. » Stage-1: The seller writes down an ask that specifies who he would like to trade with as well as a proposed trading price. The proposed buyer can choose either to accept or reject the ask. If the ask is accepted, the game ends and the seller trades with the proposed buyer at the proposed trading price. If the ask is rejected, the game proceeds to stage-2. » Stage-2: If the stage-1 ask is rejected, the seller is allowed to make an offer to the other buyer at stage-2. If accepted, they trade at the proposed trading price; Otherwise, there is no trade. In either case, the game ends. (1) Suppose all asks are public observable, i.e., buyers are able to observe the proposed trading price in stage-1 ask even if it is not proposed to him/her. Specifify the extensive-form representation of the game (10 points) (2) Suppose all asks are made in sealed envelops such that only the receiving buyer can observe the proposed trading price. Specify the extensive-form representation of the game. (10 points)

Answer 1

1. If the asks are public observables, then it would certainly be a losing situation for the seller if the initial buyer rejects the bid because then the other buyer would know the price he rejected it at and also the fact that the first offer was n to made to him.

2. if the entries are sealed then, this game will be well in the favour of the seller only because the second buyer doesn't get egoistically hurt and also the price fall is  not guaranteed, seller will be on the driver seat again.