Bid Double Auction Research Articles

Price discovery using a double auction

We investigate equilibrium in the buyer's bid double auction (BBDA) in a model with correlated private values/costs. Using a combination of theorems and computed examples, we demonstrate that simple equilibria exist even in small markets. Moreover, we bound traders' strategic behavior as a function of market size and derive rates of convergence to zero of (i) inefficiency in the allocation caused by strategic behavior and (ii) the error in the market price as an estimate of the rational expectations price. These rates together with computed examples suggest that strategic behavior can be inconsequential even in small markets in its effect on allocational efficiency and information aggregation. The BBDA thus simultaneously accomplishes both the informational and allocational goals that markets ideally fulfill; it does this perfectly in large markets and approximately in small markets, with the error due mainly to the smallness itself and not the strategic behavior of traders.

Minimax regret and failure to converge to efficiency in large markets

This paper studies minimax regret traders in a sealed bid double auction. Unlike the expected utility maximizers that populate typical market models, these traders do not determine their actions using a single prior. The analysis proves that, with no restrictions on beliefs about others' types and strategies, minimax regret traders will not converge to price-taking as the size of the market increases, contrary to standard economic intuition. In fact, minimax regret traders' bids and asks are invariant to the number of traders in the market. Thus, the robustness of the sealed bid double auction is sensitive to traders' preferences.

The Asymptotics of Price and Strategy in the Buyer's Bid Double Auction

The analysis of equilibrium in double auctions is complicated, with almost no closed-form examples and with formal results limited to bounds on bidding behavior. We consider the buyer's bid double auction in a correlated, private values model. Sellers have the incentive to submit their costs as their asks while buyers strategically underbid. We determine (i) the asymptotic distribution of the equilibrium market price and (ii) the asymptotic limits of terms in the first order condition for a buyer's selection of his bid. Part (i) reveals the properties of the strategically determined market price as an estimator of the rational expectations equilibrium price. Part (ii) provides a simple formula for a buyer's bid that is shown numerically to closely approximate his equilibrium bid even in relatively small markets. This formula reveals how equilibrium varies with the numbers of buyers and sellers and the distribution of their values/costs.

Price Discovery

We investigate equilibrium in the buyer's bid double auction (BBDA) in a model with correlated signals and either private or interdependent values. Using a combination of theorems and numerical experiments, we demonstrate that simple equilibria exist even in small markets. Moreover, we bound traders' strategic behavior as a function of market size and derive rates of convergence to zero of (i) inefficiency in the allocation caused by strategic behavior and (ii) the error in the market price as an estimate of the rational expectations price. These rates together with numerical experiments suggest that strategic behavior is inconsequential even in small markets in its effect on allocational efficiency and information aggregation. The BBDA thus simultaneously accomplishes both the informational and allocational goals that markets ideally fulfill; it does this perfectly in large markets and approximately in small markets, with the error attributable mainly to the smallness itself and not the strategic behavior of traders.

Optimality versus practicality in market design: A comparison of two double auctions

We consider a market for indivisible items with m buyers and m sellers. Traders privately know their values/costs, which are statistically dependent. Two mechanisms are considered. The buyer's bid double auction collects bids and asks from traders and determines the allocation by selecting a market-clearing price. It fails to achieve all possible gains from trade because of strategic bidding. The designed mechanism is a revelation mechanism in which honest reporting of values/costs is incentive compatible and all gains from trade are achieved. This optimality, however, comes at the expense of plausibility: (i) the monetary transfers among the traders are defined in terms of the traders' beliefs about each other's value/cost; (ii) a trader may suffer a loss ex post; (iii) the mechanism may run a surplus/deficit ex post. We compare the virtues of the simple yet mildly inefficient buyer's bid double auction to the flawed yet perfectly efficient designed mechanism.

Combination Exchange Mechanisms for Efficient Bandwidth Allocation

The size, scale and multiple ownership of communication network resources makes it important to consider an economic framework wherein we can investigate the efficiency of network operation taking agents' incentives into account. Such a framework has been considered in the design and analysis of pricing mechanisms to regulate congestion and share bandwidth over short time scales. We consider time scales of a few months over which owners of communication links lease bandwidth to network service providers. As is well-known, economic efficiency is related to how close an allocation is to a competitive equilibrium. We first show that achieving economic efficiency through a market mechanism depends on network topology. We then show that in finite networks a competitive equilibrium may not exist. But a competitive equilibrium does exist in an idealized continuum model, in which all agents are infinitesimal compared with the size of the network. This suggests that approximate competitive equilibria with good performance may be attainable in real networks. We finally introduce a market mechanism called the combinatorial seller's bid double auction whose outcome, in the continuum model, is a competitive equilibrium. 1. Introduction. Communication networks have increased in scale and hetero- geneity. There are multiple network owners and operators, each with their own hetero- geneous endowments and privately known cost and revenue models. So, an allocation of network resources efficient from an engineering perspective need not be realized in the market. Hence, it is useful to find economic mechanisms that result in efficient resource allocations among selfish agents. The efficiency of bandwidth allocation among competing users in a communica- tion network has been studied within an economic framework before. The previous research literature focuses attention on congestion that results when aggregate user demand exceeds capacity, and proposes usage-dependent pricing as a method for con- trolling congestion (23, 24). However, several difficulties must be faced in coming up with a good price-adjustment mechanism. First, congestion occurs over a very short time scale: Aggregate traffic is bursty and exceeds nominal capacity for periods of a few seconds (10). So the pricing mechanism must react very quickly to changes in aggregate demand. Second, the 'correct' congestion price depends on how much users are willing to pay for the service, which is not known. This has prompted invention of distributed price iteration algorithms that converge to the 'correct' price (16, 22). These algorithms are not practical but permit a re-interpretation of TCP-like proto-

The Evolution of Conventions under Incomplete Information

We formulate an evolutionary learning process in the spirit of Young (1993a) for games of incomplete information. The process involves trembles. For many games, if the amount of trembling is small, play will be in accordance with the games' (semi-strict) Bayesian equilibria most of the time. This supports the notion of Bayesian equilibrium. Further, often play will most of the time be in accordance with exactly one Bayesian equilibrium. This gives a selection among the Bayesian equilibria. For two specific games of economic interest we characterize this selection. The first is an extension to incomplete information of the prototype strategic conflict known as Chicken. The second is an incomplete information bilateral monopoly, which is also an extension to incomplete information of Nash's demand game, or a simple version of the so-called sealed bid double auction. For both games selection by evolutionary learning is in favor of Bayesian equilibria where some types of players fail to coordinate, such that the outcome is inefficient.

On the convergence of genetic learning in a double auction market

Abstract We study the learning behavior of a population of buyers and a population of sellers whose members are repeatedly randomly matched to engage in a sealed bid double auction. The agents are assumed to be boundedly rational and choose their strategies by imitating successful behavior and adding innovations triggered by random errors or communication with other agents. This process is modelled by a two-population genetic algorithm. A general characterization of the equilibria in mixed population distributions is given and it is shown analytically that only one price equilibria are attractive for the GA dynamics. Simulation results confirm these findings and imply that in cases with random initialization with high probability the gain of trade is equally split between buyers and sellers.

Game theory and applications

Contributed Papers: Refinement of Nash Equilibrium: The Main Ideas. Supergames. Infinitely Repeated Games with Incomplete Information. Repeated Games. Bounded Rationality and Strategic Complexity in Repeated Games. The Shapley Value. Advances in Value Theory. Axiomatizations of the Core, The Nucleolus, And the Prekernel. Consistency Principle. Discrete Concepts in N-Person Game Theory: Nondegeneracy and Homogeneity. Two-Sided Matching Markets: An Overview of Some Theory and Empirical Evidence. Strategic Market Game Models of Exchange Economies. Information Transmission. Monotonic Surplus Sharing and the Utilization of Common Property Resources. Developments in Stable Set Theory. Game Theoretic Models of Voting in Multidimensional Issue Spaces. Israel and the PLO: A Game with Differential Information . A Survey of Some Results Closely Related to the Knaster-Kuratowski-Mazurkiewz Theorem. Selected Abstracts: On the Core of the Assignment Game. The Second Welfare Theorem in Nonconvex Economies. An Evolutionary Game Theory Model for Risk-Taking. Values of Nonatomic Vector Measure Games: Are They Linear Combinations of the Measures? Subgame-Perfect Equilibria in Discrete and Continous Games-Does Discretization Matter? To Vote or Not to Vote: What Is the Quota? Some Bounds for the Banzhaf Index and Other Semivalues. Comparative Cooperative Games Theory. Escalation and Cooperation in International Conflicts-The Dollar-Auction Revisited. An Axiomatization of the Nonsymmetric Nontransferable Utility Value. A Milnor Condition for Nonatomic Lipschitz Games and Its Applications. Zero-Sum Nonstationary Stochastic Games with General State Space. Perfect Equilibrium Points and Lexicographic Domination. A Two-Person Repeated Bargaining Game with Long-Term Contracts. Independence of Irrelevant Alternative and Revealed Group Preferences. The Sealed-Bid Mechanism: An Experimental Study. Rate of Convergence to Full Efficiency in the Buyers' Bid Double Auction as the Market Becomes Large Stationary Strategies in Deterministic Games. Big Boss Games, Clan Games, And Information Market Games. Large Games and Economics with Near-Exhaustion of Gains to Coalition Formation. Values of Large Finite Games. Index.

Asymptotic Efficiency in Large Exchange Economies With Asymmetric Information

The authors provide conditions on an exchange economy with asymmetric information that guarantee that when the economy is replicated sufficiently often, there will be an allocation that is incentive compatible, individually rational, and nearly efficient. The main theorem covers both the case in which aggregate uncertainty remains when the economy is replicated and the case in which replication eliminates aggregate uncertainty. In addition, the authors demonstrate how their theorem does or does not apply to standard asymmetric information problems such as the buyer's bid double auction problem, Akerlof's lemons problem, and insurance with asymmetric information. Copyright 1992 by The Econometric Society.

A dominant strategy double auction

A double auction mechanism that provides dominant strategies for both buyers and sellers is analyzed. This mechanism satisfies the 1 n convergence to efficiency of the buyer's bid double auction. In addition, the mechanism always produces full information first best prices; the inefficiency arises because the least valuable profitable trade may be prohibited by the mechanism. The mechanism has an oral implementation utilizing bid and asked prices.

Existence and Convergence of Equilibria in the Buyer's Bid Double Auction

This paper concerns a Bayesian game model of the Buyer's Bid Double Auction, which is a procedure for organizing trade that selects a market-clearing price from a list of offers/bids. Strategic misrepresentation by traders may make the outcome of trade inefficient. Satterthwaite and Williams (1989) showed that misrepresentation and inefficiency quickly converge to zero as the number of traders on each side of the market increases. This is extended here to cases in which the number of buyers may differ from the number of sellers. The existence of equilibria in a generic instance of the model is also proven.

The Rate of Convergence to Efficiency in the Buyer's Bid Double Auction as the Market Becomes Large

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.