Core and competitive equilibria: An approach from discrete convex analysis

We extend the assignment market (Shapley and Shubik, 1972; Kaneko, 1976, 1982) by utilizing discrete convex analysis. We consider the market in which buyers and sellers trade indivisible commodities for money. Each buyer demands at most one unit of commodity. Each seller produces multiple units of several types of commodities. We make the quasi-linearity assumption on the sellers, but not on the buyers. We assume that the cost function of each seller is M^♮-convex, which is a concept in discrete convex analysis. We prove that the core and the competitive equilibria exist and coincide in our market model.     

Equilibrium price and advertisement distributions

We consider an economy where many sellers sell identical goods to many buyers. Each seller has a unit supply and each buyer has a unit demand. The only possible information flow about prices is through costly advertising. We show that in equilibrium the sellers use mixed strategies in pricing which leads to price and advertisement distributions. With convex advertising costs each seller sends only one advertisement in the market. We also delineate a class of advertising costs which ensures that sellers may send multiple advertisements in equilibrium. Higher prices are advertised more than lower prices.     

Buyer–seller networks with demand shocks and intermediation

We present a model in which buyers and sellers use links to trade with each other. Each seller produces a good which can be one of two types. Buyers are ex ante identical but receive specification or valuation shocks after the links are formed. We show that efficient networks are stable and that severing a link in an efficient network results in a higher price for the buyer but a lower price for the seller. We also examine network intermediation when sellers (buyers) form links sequentially. When sellers form links sequentially, the first seller becomes an intermediary and shares links with other sellers; this makes all sellers better off. However, when buyers form links sequentially, buyers may or may not share links. If links are shared multiple intermediaries result.     

基于拍卖的垄断型产品供应链的博弈分析

论文研究了基于拍卖交易的垄断型产品供应链中卖方和买方的博弈问题,成交价格同时取决于卖方向拍卖市场的供货数量和买方向拍卖市场的竞拍数量。博弈结果显示,在垄断供应的情况下,博弈的纳什均衡将会是买卖双方都不通过拍卖渠道来进行交易,只有在非常极端的条件下可以达成供货和竞拍等量的均衡。最后,论文引入一个新卖方作为买方参与拍卖后的补货来源,得到的新均衡解能使原买卖双方的收益提高,从而说明单纯的拍卖并不总是最好的交易方式,多渠道的销售方式有时更能保障买卖双方的利益。     

Nash equilibria in a model of multiproduct price competition: an assignment problem

We study the market interaction of a finite number of single-product firms and a representative buyer, where the buyer consumes bundles of these goods. The buyers’ value function determines their willingness to pay for subsets of goods. We show that Nash-equilibrium outcomes are solutions of the linear relaxation of an integer programming assignment problem and that they always exist. The Nash-equilibrium price set is characterized by the Pareto frontier of the associated dual problem’s projection on the firms’ price vectors. We identify the Nash-equilibrium prices for monotonic buyers’ value functions and, more importantly, we show that some central solution concepts in cooperative game theory are (subgame perfect) equilibrium prices of our strategic game.     

The influence of seller learning and time constraints on sequential bargaining in an artificial perishable goods market

This paper investigates the formation of prices in a perishable goods market where agents bargain repeatedly through pair-wise interactions. After extensive field observations, we chose to focus on two aspects that seem important to actors of this market: the passage of time and update in judgement when gathering information. The main feature of the market is that a seller bargaining with a buyer has incomplete information about buyer's willingness to pay and is not sure how her trading partner will evaluate an offer or compare it with other options. On the other hand, buyers have limited time to look for goods and cannot meet all possible sellers before making a decision. Hence agents cannot calculate the best price to offer but receive information through limited interactions, and use this information to choose their actions.An agent-based model was built to represent a framework that mimics the observed market institution and where agent's possible behaviors and learning was made as consistent as possible with gathered data. Simulations were run, first for sensitivity analysis concerning main parameters, then to test the dependance of agents’ learning to (a) the time buyers can spend on the market and (b) the frequency of update in learning by sellers. To validate the model, features produced by the simulated market are compared to the stylized facts gathered for negotiation about four goods. We reproduce the main features of the data on the dynamics of offers, transaction prices and agents’ behavior during the bargaining phases.     

Neutrality of buyer and seller commissions to auction house profit

This paper presents an examination of optimal revenue management of a monopoly auction house through which a seller sells goods via a second‐price auction. The house charges commissions to both the buyer and seller. Results demonstrate that a continuum of combinations of optimal buyer and seller commission rates exists, all of which yield the same expected profit of the house. Additionally, we discuss several possible factors that lead to the prevailing custom of zero buyer commission, such as commission aversion of buyers, the house's incentive to maximize the hammer price, and seller and buyer preferences for apparently lowered commission rates.     

The holdout problem and urban sprawl: Experimental evidence

Conventional wisdom as well as economic theory suggests it is more costly to reassemble fragmented land due to transactions costs and strategic bargaining costs. Both costs are expected to increase with the number of sellers. Inefficient allocation of land resources may result including property entropy (Parisi, 2002), urban sprawl (Miceli and Sirmans, 2007) and deteriorating inner cities. Given the difficulty of observing actual values attached by buyers and sellers to land, little empirical evidence exists to support the conventional wisdom and theoretical work. We use experimental methods to examine transactions costs and strategic bargaining costs in a land-assembly market game with one buyer, 1-4 sellers, and complementary exchanges. The buyer’s final earnings vary inversely with the number of sellers, ceteris paribus, indicating an incentive to purchase consolidated land. Delay costs reduce holdout, but result in lower payoffs for both buyers and sellers. Competition between sellers reduces holdout and the buyer’s total purchase price.     

A mechanism for package allocation problems with gross substitutes

We consider a package allocation problem in which a seller owns many indivisible objects and the rest of the agents, buyers, are interested in packages of these objects. Buyers’ valuations satisfy monotonicity and the gross substitutes condition (Kelso and Crawford, 1982). The aim of this paper is to analyze the following mechanism: simultaneously, each buyer requests to the seller a package by announcing how much he would pay for it; once buyers have played, the seller decides the final assignment of packages and the prices, as long as this assignment makes no buyer worse off than with his initial request. The subgame perfect equilibrium outcomes of the mechanism correspond to the Vickrey outcome (Vickrey, 1961) of the market.     

First price package auction with many traders

This paper studies a first price package auction in which multiple sellers participate in addition to multiple buyers. We generalize the notion of the profit-target strategy which is first introduced as a truthful strategy in a first price package auction with a single seller by Bernheim and Whinston (1986b). We then show that the set of equilibrium payoffs in profit-target strategies is equal to the bidder-optimal core, and is also equal to the set of coalition-proof Nash equilibria. Using this result, we find that any equilibrium payoff vector is weakly Pareto-dominated by the VCG payoff vector for buyers, and that the Walrasian competitive equilibrium payoff vector is weakly Pareto-dominated by some equilibrium payoff vector for buyers, even if goods are substitutes. This contrasts with the first price package auction with a single seller, in which it is shown that if goods are substitutes, then those three outcomes are payoff-equivalent.     

Models for conflict resolution in ecosystem management

Tools developed in the fields of decision analysis and game theory that have potential for use in public sector conflict resolution are reviewed. The strengths and weaknesses, as well as the axioms defining principles of fairness, are examined for multiobjective optimization, Nash and Nash–Harsanyi solutions, voting models, and the Shapley value. The case of conflict between stakeholders over proposed oil and gas leasing on National Forest System lands is presented as a sample application. We conclude that the Shapley value is the appropriate approach for determining the “fairness” of alternative conflict solutions, at least in those situations where cardinal utilities can be estimated.     

On second-price auctions and imperfect competition

Consider two sellers each of whom has one unit of an indivisible good and two buyers each of whom is interested in buying one unit. The sellers simultaneously set reserve prices and use second-price auctions as rationing device. An equilibrium in pure strategies where each seller has a regular customer is characterized. The result is applied in order to demonstrate that not allowing sellers to use second-price auctions may enhance total surplus.     

供应链中双方供应的竞争和合作博弈研究

针对当前供应链中供应方面存在的相关局限性。构造了双方供应和制造商之间的博弈模型。该模型主要特点是双方 供应之间的二阶段博弈所形成的质量和价格策略。在此条件下制造商和供应商之间进行讨价还价。以分配整体利润。指出了供 需双方在讨价还价时存在惟一的子博彝精炼纳什均衡。     

Buyer brokerage: Experimental evidence

This paper offers an experimental investigation of two commission structures for buyer brokerage. One commission structure is the currently used structure in the industry where both the seller’s broker and the buyer’s broker each receive a percentage of the sales price as their compensation from the seller. In an alternative commission structure, while the seller’s broker still receives a percentage of the sales price from the seller, the buyer’s broker is compensated by the buyer and the compensation is inversely related to the sales price. We find that how the buyer’s broker gets compensated has significant implications. While both commission structures yield a similar probability of reaching an agreement, the alternative commission structure yields a lower price and a longer time to reach an agreement. Furthermore, the alternative commission structure achieves a better alignment of the interests of the buyer and the buyer’s broker without affecting the earnings of the players in the transaction. We also find that the improvement in the alignment of interests is more significant for female buyers than for male buyers. Furthermore, a higher listing price by the seller and a higher initial bid price by the buyer each lead to a significant increase in the negotiated price.     

Auctions with different rates of patience: Evidence from the resale shoe market

Bids and asks are examined over time using auction data from a continuous auction of authentic deadstock sneakers. A theoretical analysis of a double auction over time shows that if buyers and sellers have different rates of patience, then a buyer (respectively, seller) who is patient will be more likely to set a lower initial bid (respectively, higher initial ask). This causes an increase in the unfulfilled bid–ask spread over time. These results are tested using data collected from the StockX website for two specific deadstock sneakers. Results show that the unfulfilled bid–ask spread is positively correlated with time.     

Descending price multi-item auctions

We propose a simultaneous descending price auction mechanism to sell multiple heterogeneous items, each owned by a distinct seller, to a number of buyers. Each buyer has known private valuations on items, and wants at most one item. We show that if the sellers follow a descending price offer procedure and the buyers follow a greedy strategy for accepting the offers, the auction results in a nearly efficient allocation, and terminates close to a competitive equilibrium price vector. The descending price offer strategy of the sellers is close to a Nash equilibrium. However, we show that the buyers are better off waiting in our auction. There is a maximum limit (corresponding to the minimum competitive equilibrium price vector) till which they can wait without running into the risk of not winning any item. If the buyers wait within this limit, the prices can be brought arbitrarily close to a uniquely defined competitive equilibrium price vector.     

Surplus Seeking and Rent Seeking Through Back-Door Deals in Mainland China Price Control and Central Planning Fix Prices Below Market Clearance, Creating a Contrived Surplus

Abstract . When the selling price is set below the market-clearing level through government price control, the price gap represents a contrived surplus transferred from the producer to the buyer. But, due to incomplete assignment of property rights to this contrived surplus and/or high enforcement costs, contrived surplus is often a non exclusive income subject to competitive capture. Exchange of favors between buyers and sellers to gain preferential access to rationed goods has become a dominant method of surplus seeking (cf. rent seeking) in the People's Republic of China. But since only well-placed individuals in the distribution channels for such goods and officials who control access to positional goods have favors to exchange, these exchanges sabotage government efforts to achieve fairer access to scarce goods. And since favors involve illegally diverted resources, such back-door deals threaten the integrity of government. Furthermore, exchange of favors fosters particularistic values which hinder modern economic development.     

Price experimentation with strategic buyers

A two-period model in which a monopolist endeavors to learn about the permanent demand parameter of a specific repeat buyer is investigated. The buyer may strategically reject the seller’s first-period offer for one of two reasons. First, in order to conceal information (i.e., to pool), a high-valuation buyer may reject high prices that would never be accepted by a low-valuation buyer. Second, in order to reveal information (i.e., to signal), a low-valuation buyer may reject low prices that would always be accepted by a high-valuation buyer. Given this, the seller often finds it optimal to post prices that reveal no useful information. Indeed, in the equilibrium where there is no signaling, the seller never charges an informative first-period price. Learning may occur in the equilibrium where there is maximal signaling, but the scope for learning is quite limited even in this case. Indeed, in order to preempt information transmission through signaling, the seller may be induced to set a first-period price strictly below the buyer’s lowest possible valuation.      

Endogenous mechanisms and Nash equilibrium in competitive contracting games

We model strategic competition in a market with asymmetric information as a noncooperative game in which each firm competes for the business of a buyer of unknown type by offering the buyer a catalog of products and prices. The timing in our model is Stackelberg: in the first stage, given the distribution of buyer types known to all firms and the deducible, type-dependent best responses of the agent, firms simultaneously and noncooperatively choose their catalog offers. In the second stage the buyer, knowing his type, chooses a single firm and product-price pair from that firm’s catalog. By backward induction, this Stackelberg game with asymmetric information reduces to a game over catalogs with payoff indeterminacies. In particular, due to ties within catalogs and/or across catalogs, corresponding to any catalog profile offered by firms there may be multiple possible expected firm payoffs, all consistent with the rational optimizing behavior of the agent for each of his types. The resolution of these indeterminacies depends on the tie-breaking mechanism which emerges in the market. Because each tie-breaking mechanism induces a particular game over catalogs, a reasonable candidate would be a tie-breaking mechanism which supports a Nash equilibrium in the corresponding catalog game. We call such a mechanism an endogenous Nash mechanism. The fundamental question we address in this paper is, does there exist an endogenous Nash mechanism—and therefore, does there exist a Nash equilibrium for the catalog game? We show under fairly mild conditions on primitives that catalog games naturally possess tie-breaking mechanisms which support Nash equilibria.     

Characterization of the Walrasian equilibria of the assignment model

We study the assignment model where a collection of indivisible goods are sold to a set of buyers who want to buy at most one good. We characterize the extreme and interior points of the set of Walrasian equilibrium price vectors for this model. Our characterizations are in terms of demand sets of buyers. Using these characterizations, we also give a unique characterization of the minimum and the maximum Walrasian equilibrium price vectors. Also, necessary and sufficient conditions are given under which the interior of the set of Walrasian equilibrium price vectors is non-empty. Several of the results are derived by interpreting Walrasian equilibrium price vectors as potential functions of an appropriate directed graph.