Consider a decentralized, dynamic market with an infinite horizon and participation costs in which both buyers and sellers have private information concerning their values for the indivisible traded good. Time is discrete, each period has length δ, and, each unit of time, continuums of new buyers and sellers consider entry. Traders whose expected utility is negative choose not to enter. Within a period each buyer is matched anonymously with a seller and each seller is matched with zero, one, or more buyers. Every seller runs a first price auction with a reservation price and, if trade occurs, both the seller and the winning buyer exit the market with their realized utility. Traders who fail to trade continue in the market to be rematched. We characterize the steady-state equilibria that are perfect Bayesian. We show that, as δ converges to zero, equilibrium prices at which trades occur converge to the Walrasian price and the realized allocations converge to the competitive allocation. We also show the existence of equilibria for δ sufficiently small, provided the discount rate is small relative to the participation costs. Copyright The Econometric Society 2007.

Mark A. Satterthwaite, Hugo Sonnenschein; Strategy-Proof Allocation Mechanisms at Differentiable Points, The Review of Economic Studies, Volume 48, Issue 4

This paper shows that no nondictatorial voting procedure exists that induces each voter to choose his voting strategy solely on the basis of his preferences and independently of his beliefs concerning other voters' preferences. This necessary dependence between a voter's beliefs and his choice of strategy means that a voter can manipulate another voter's choice of strategy by misleading him into adopting inaccurate beliefs concerning other voters' beliefs. CONSIDER A VOTING SITUATION, as in a committee. Each rational member has preferences over the alternatives being considered and beliefs concerning the other members' preferences. The question we consider in this short paper is: can a voting procedure be constructed such that each member's vote depends only on his preferences, not on his beliefs concerning other individual preferences. We show, by an application of Gibbard [6] and Satterthwaite's [11] impossibility theorem for strategy-proof voting procedures, that such a voting procedure does not exist. Moreover, we show that this necessary lack of independence between a member's beliefs and his choice of voting strategy makes him vulnerable to possible manipulation by other members. Specifically, consider members one and two. Since member one partially bases his vote on what he believes member two is seeking, member two may deliberately mislead member one into adopting a false belief concerning member two's preferences. As a consequence of this inaccurate belief, member one may decide to vote in a manner that is, in fact, unfavorable to himself and favorable to member two. Derivation of these results depends critically on the possibility that members may be uncertain concerning other members' preferences. This assumption is reasonable because the purpose of legislative bodies is to reconcile conflicting preferences. If preferences were generally known with certainty, then, as Wilson [14, p. 310] has pointed out, the need for a legislative body would vanish because preferences could be aggregated directly. Therefore, a realistic analysis of voting behavior must accept that a member's true preferences are private. Our results are consistent with the work that other researchers have reported. Dummett and Farquharson [3, pp. 34-35] and, to a lesser extent, NVilson [14] assumed the validity of our results. Harsanyi [7] in discussing bargaining situations where the two opponents are uncertain concerning the other's preferences argued that the decisive element may not be the actual preferences of the two individuals involved, but rather the societal stereotypes (beliefs) concerning their preferences. Schelling (12, e.g., Ch. 3] in his insightful discussion of bargaining strategy dwells extensively on the same theme.

A trader who privately knows his preferences may misrepresent them in order to influence the market price. This strategic behaviour may prevent realization of all gains from trade. In this paper, trade in a simple market with an explicit rule for price formation is modelled as a Bayesian game. We show that the difference between a trader's bid and his reservation value is maximally O(1/m) where m is the number of traders on each side of the market. Competitive pressure as m increases thus quickly overcomes the inefficiency private information causes and forces the market towards an efficient allocation.

Strategic behavior in a finite market can cause inefficiency in the allocation, and market mechanisms differ in how successfully they limit this inefficiency. A method for ranking algorithms in computer science is adapted here to rank market mechanisms according to how quickly inefficiency diminishes as the size of the market increases. It is shown that trade at a single market-clearing price in the k-double auction is worst-case asymptotic optimal among all plausible mechanisms: evaluating mechanisms in their least favorable trading environments for each possible size of the market, the k-double auction is shown to force the worst-case inefficiency to zero at the fastest possible rate.

Health care report cards–public disclosure of patient health outcomes at the level of the individual physician and/or hospital–may address important informational asymmetries in markets for health care, but they may also give doctors and hospitals incentives to decline to treat more difficult, severely ill patients. Whether report cards are good for patients and for society depends on whether their Þnancial and health beneÞts outweigh their costs in terms of the quantity, quality, and appropriateness of medical treatment that they induce. Using national data on Medicare patients at risk for cardiac surgery, we Þnd that cardiac surgery report cards in New York and Pennsylvania led both to selection behavior by providers and to improved matching of patients with hospitals. On net, this led to higher levels of resource use and to worse health outcomes, particularly for sicker patients. We conclude that, at least in the short run, these report cards decreased patient and social welfare. 1

A model of trade with m buyers and m sellers is considered in which price is set to equate revealed demand and supply. In a Bayesian Nash equilibrium, each trader acts not as a price-taker, but instead misrepresents his true demand/supply to influence price in his favor. This causes inefficiency. We show that in any equilibrium the amount by which a trader misreports is O(1/m) and the corresponding inefficiency is O(1/m2). The indeterminacy and the inefficiency that is caused by the traders' bargaining behavior in small markets thus rapidly vanishes as the market increases in size.

We study merger policy in a dynamic computational model in which firms can reduce costs through investment or through mergers. Firms invest or propose mergers according to the profitability of these strategies. An antitrust authority can block mergers at some cost. We examine the optimal policy for an antitrust authority that cannot commit to its future policy and approves mergers as they are proposed. We find that the optimal policy can differ substantially from a policy based on static welfare. In general, antitrust policy can greatly affect firms’ investment behavior, and firms’ investment behavior can greatly affect the optimal antitrust policy.