Bilateral trade is a fundamental economic scenario comprising a strategically acting buyer and seller, each holding valuations for the item, drawn from publicly known distributions. A mechanism is supposed to facilitate trade between these agents, if such trade is beneficial. It was recently shown that the only mechanisms that are simultaneously DSIC, SBB, and ex-post IR, are fixed price mechanisms, i.e., mechanisms that are parametrised by a price p, and trade occurs if and only if the valuation of the buyer is at least p and the valuation of the seller is at most p. The gain from trade is the increase in welfare that results from applying a mechanism; here we study the gain from trade achievable by fixed price mechanisms. We explore this question for both the bilateral trade setting, and a double auction setting where there are multiple buyers and sellers. We first identify a fixed price mechanism that achieves a gain from trade of at least 2/r times the optimum, where r is the probability that the seller's valuation does not exceed the buyer's valuation. This extends a previous result by McAfee. Subsequently, we improve this approximation factor in an asymptotic sense, by showing that a more sophisticated rule for setting the fixed price results in an expected gain from trade within a factor O(log(1/r)) of the optimal gain from trade. This is asymptotically the best approximation factor possible. Lastly, we extend our study of fixed price mechanisms to the double auction setting defined by a set of multiple i.i.d. unit demand buyers, and i.i.d. unit supply sellers. We present a fixed price mechanism that achieves a gain from trade that achieves for all epsilon > 0 a gain from trade of at least (1-epsilon) times the expected optimal gain from trade with probability 1 - 2/e^{#T epsilon^2 /2}, where #T is the expected number of trades resulting from the double auction.
翻译:双边贸易是一种基本的经济情景,它包含一个具有战略作用的买卖双方,每个货品的估价都是从公开的分销中得出的。如果这种贸易有利,一个机制应该促进这些代理商之间的贸易。最近显示,唯一同时使用DSIC、SBB和事后IR的机制是固定价格机制,即由价格p 所抵消的机制,只有买方估价至少为p2,而卖方估价最多为p2,才能进行贸易。贸易收益增加的原因是:采用机制后,福利增加;我们在这里研究贸易需求通过固定价格机制实现的收益。我们探讨这个问题,既包括双边贸易环境,也包括有多个买方和卖方的双重拍卖。我们首先确定一个固定价格机制,从交易中至少获得2倍的收益,而卖方的估价可能不会超过买方的估价。我们比McAfefe的以往结果更丰富。我们后来改进了这一近似因素,从固定价格规则中取得一个更精细的贸易收益。我们从固定的贸易成本中取得一个最精确的收益。