Consider the following 2-player, seller-buyer signaling game. The game starts with a random move by nature...

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Consider the following 2-player, seller-buyer signaling game. The game starts with a random move by nature to determine whether the item the seller has is good or bad (think used car). The seller knows whether his item is good or bad. All the buyer knows is there is some probability q that the item is good, and so 1-q is the probability the item is bad. After being informed of the quality of the good, the seller has to decide whether to offer it for sale or withhold it from the market. If the seller withholds the item, the game ends with the status quo payoff of 0 for both seller and buyer. If the seller offers the item for sale and it is good, it can be sold as is, but if it is bad and the seller offers it for sale, the item has to be cleaned up at a cost c. After cleanup, a bad item looks just like a good item and the buyer can't tell the difference (the buyer does not see whether or not a cleanup has occurred). Moreover, the price of the item if sold is p, regardless of whether it is good or bad, so the price does not reveal the quality either. If the item is offered for sale, the buyer has to decide whether to buy it or not, but he does not know whether the item is good or bad. The buyer can say either yes or no to the seller's item at price p. If he says no, there is no deal and he receives a payoff of 0. The seller receives a payoff of 0 if the item is good and -c if the item is bad. If the buyer says yes, the item is exchanged for price p. The value a buyer receives from a good item is V and from a bad item is W. His payoff is V-p if the item is good and W-p if the item is bad. Assume that V > p > W > 0, so the buyer has a positive payoff only if he buys the good item. The seller's payoff is the price p if the item is good and p-c if the item is bad. Consider the following 2-player, seller-buyer signaling game. The game starts with a random move by nature to determine whether the item the seller has is good or bad (think used car). The seller knows whether his item is good or bad. All the buyer knows is there is some probability q that the item is good, and so 1-q is the probability the item is bad. After being informed of the quality of the good, the seller has to decide whether to offer it for sale or withhold it from the market. If the seller withholds the item, the game ends with the status quo payoff of 0 for both seller and buyer. If the seller offers the item for sale and it is good, it can be sold as is, but if it is bad and the seller offers it for sale, the item has to be cleaned up at a cost c. After cleanup, a bad item looks just like a good item and the buyer can't tell the difference (the buyer does not see whether or not a cleanup has occurred). Moreover, the price of the item if sold is p, regardless of whether it is good or bad, so the price does not reveal the quality either. If the item is offered for sale, the buyer has to decide whether to buy it or not, but he does not know whether the item is good or bad. The buyer can say either yes or no to the seller's item at price p. If he says no, there is no deal and he receives a payoff of 0. The seller receives a payoff of 0 if the item is good and -c if the item is bad. If the buyer says yes, the item is exchanged for price p. The value a buyer receives from a good item is V and from a bad item is W. His payoff is V-p if the item is good and W-p if the item is bad. Assume that V > p > W > 0, so the buyer has a positive payoff only if he buys the good item. The seller's payoff is the price p if the item is good and p-c if the item is bad.