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。     

No arbitrage conditions and liquidity

We extend the fundamental theorem of asset pricing to the case of markets with liquidity risk. Our results generalize, when the probability space is finite, those obtained by Kabanov et al. [Kabanov, Y., Stricker, C., 2001. The Harrison-Pliska arbitrage pricing theorem under transaction costs. Journal of Mathematical Economics 35, 185–196; Kabanov, Y., Rásonyi, M., Stricker, C., 2002. No-arbitrage criteria for financial markets with efficient friction. Finance and Stochastics 6, 371–382; Kabanov, Y., Rásonyi, M., Stricker, C., 2003. On the closedness of sums of convex cones in L⁰$L^0$ and the robust no-arbitrage property. Finance and Stochastics] and by Schachermayer [Schachermayer, W., 2004. The fundamental theorem of asset pricing under poportional transaction costs in finite discrete time. Mathematical Finance 14 (1), 19–48] for markets with proportional transaction costs. More precisely, we restate the notions of consistent and strictly consistent price systems and prove their equivalence to corresponding no arbitrage conditions. We express these results in an analytical form in terms of the subdifferential of the so-called liquidation function. We conclude the paper with a hedging theorem.     

Investment timing and efficiency in incomplete contracts

This paper considers a buyer and seller capable of making observable but nonverifiable relationship-specific investments before the parties' valuations of trade (also observable but nonverifiable) are known. Our formulation allows investments to have direct external effects and the investments to occur sequentially. We characterize an incomplete contract that implements the first-best investments and trade. This optimal contract states negotiation procedures used to determine a monetary transfer made during the investment phase and the terms of trade.     

Inflation tax in the lab: a theoretical and experimental study of competitive search equilibrium with inflation

In this paper we measure the effect of the inflation tax on economic activity and welfare within a controlled setting. To do so, we develop a model of price posting and monetary exchange with inflation and finite populations. The model, which provides a game–theoretic foundation to Rocheteau and Wright (2005)׳s competitive search monetary equilibrium, is used to derive theoretical propositions regarding the effects of inflation in this environment, which we test with a laboratory experiment that closely implements the theoretical framework. We find that the inflation tax is harmful – with cash holdings, production and welfare all falling as inflation rises – and that its effect is relatively larger at low inflation rates than at higher rates. For instance, for inflation rates between 0% and 5%, welfare in the two markets we consider (2[seller]×2[buyer] and 3×2) falls by roughly 1 percent for each percentage–point rise in inflation, compared with 0.4 percent over the range from 5% to 30%. Our findings lead us to conclude that the impact of the inflation tax should not be underestimated, even under low inflation.     

基于不完全信息动态博弈模型的报价策略研究

目前应用博弈论对价格谈判所进行的研究大多集中于讨价还价问题,而关于报价问题的研究往往依靠定性分析。因此本文建立了一个关于报价策略的三阶段不完全信息动态博弈模型,并通过求解证明：在谈判双方信息对称的条件下,无论对买方还是卖方来说,“抢先报价”都是占优策略。在买卖双方都采取“抢先报价”策略时,报价顺序博弈的结果具有不确定性。在现实中买卖双方往往会通过各种其他手段来达到抢先报价的目的。     

Inefficiency of equilibria with incomplete markets

As is well known, equilibria with incomplete markets are generically Pareto inefficient. In this paper, we demonstrate the leading role of a budget constraint in the occurrence of Pareto inefficiency of equilibria with incomplete markets. Specifically, on the basis of the classical two-period one-good pure exchange model we prove that so long as a budget constraint is met for all agents, equilibria with incomplete markets are generically Pareto inefficient in initial endowments and utility functions regardless of the optimization behavior of each agent. All we require of utility functions is a very weak hypothesis called current monotonicity. A simple unified method applicable to both a real asset case and a nominal asset case is presented, so that our claim is proved in both cases.     

Numeraire portfolios and utility-based price systems under proportional transaction costs

In a discrete-time incomplete financial market with proportional transaction costs and with independent and bounded returns, we prove the existence of a consistent price system that can be written as the expectation of the discounted claim under the real-world probability measure P and not just under a martingale measure. In fact, the claim is then discounted by some specific dynamic portfolio called the numeraire portfolio as in the classical case of markets without transaction costs. For that specific numeraire, P will be a martingale measure. Naturally, the concept of a numeraire portfolio has here to be adapted to the concept of consistent price systems for markets with transaction costs. Moreover, again as in the classical case, the numeraire portfolio can be chosen as log-optimal portfolio. The same analysis works for power utility functions. However, then a change of measure is necessary. This paper applies methods from stochastic dynamic programming to finance.     

The quality assurance role of seller financing: evidence from second mortgages

Quality problems that are known to the seller of a product, but will become known to the buyer only after the purchase have the potential to frustrate voluntary exchanges. Where the determination of quality after the sale is cut-and-dried, brand names and unconditional guarantees will bond contract performance. When the problem is more subtle or confounded by the extent of consumer inputs, requiring risk-sharing by the contracting parties, these bonding devices typically are not sufficient. Under the circumstances, seller financing may be an efficient contracting solution for bonding the quality dimension of the contract. This form of financing makes both the buyer and the seller share the risk that the product may not suit the buyer’s needs in the way promised by the seller. This paper provides further empirical evidence on the quality assurance role of seller financing. We consider seller-financed second mortgages in the National Association of Realtors database. Seller financing in second mortgages may be a supplement to first mortgages supplied by conventional lenders. The role of seller financing as a quality assurance mechanism in second mortgages is more complex than its role in first mortgages, but is also less subject to an alternative interpretation of credit rationing than is its role in seller-financed first mortgages. To avoid further complexities, we do not consider second seller financing transactions that supplement first assumption mortgage transactions.     

Optimal two-object auctions with synergies

We design the revenue-maximizing auction for two objects when each buyer has bi-dimensional private information and a superadditive utility function (i.e., a synergy is generated if a buyer wins both goods). In this setting the seller is likely to allocate the objects inefficiently with respect to an environment with no synergies (see Armstrong, RES (2000)). In particular, the objects may be bundled too rarely or a buyer may win the bundle even though her valuations for the goods are weakly dominated by the values of another buyer.Received: 29 October 2001, Accepted: 29 October 2002, JEL Classification: D44, D82This paper has been written while the author was a member of the Dipartimento di Statistica e Matematica Applicata alle Scienze Umane "Diego De Castro", Universitá degli Studi di Torino, Italy. Valuable comments and suggestions were provided by Antonio Cabrales, Massimo Marinacci, three anonymous referees and, especially, by Mark Armstrong. The usual disclaimer applies.     

On the informed seller problem: optimal information disclosure

We consider a revenue-maximizing seller who, before proposing a mechanism to sell her object(s), observes a vector of signals correlated with buyers’ valuations. Each buyer knows only the signal that the seller observes about him, but not the signals she observes about other buyers. The seller first chooses how to disclose her information and then chooses a revenue-maximizing mechanism. We allow for very general disclosure policies, that can be random, public, private, or any mixture of these possibilities. Through the disclosure of information privately, the seller can create correlation in buyers’ private information, which then consist of valuations plus beliefs. For the standard independent private values model, we show that information revelation is irrelevant: irrespective of the disclosure policy an optimal mechanism for this informed seller generates expected revenue that is equal to her maximal revenue under full information disclosure. For more general allocation environments that allow also for interdependent, for common values, and for multiple items, disclosure policies may matter, and the best the seller can do is to disclose no information at all.     

Risk aversion and the elasticity of substitution in general dynamic portfolio theory: Consistent planning by forward looking, expected utility maximizing investors

Using the measure of risk aversion suggested by Kihlstrom and Mirman [Kihlstrom, R., Mirman, L., 1974. Risk aversion with many commodities. Journal of Economic Theory 8, 361–388; Kihlstrom, R., Mirman, L., 1981. Constant, increasing and decreasing risk aversion with many commodities. Review of Economic Studies 48, 271–280], we propose a dynamic consumption-savings–portfolio choice model in which the consumer-investor maximizes the expected value of a non-additively separable utility function of current and future consumption. Preferences for consumption streams are CES and the elasticity of substitution can be chosen independently of the risk aversion measure. The additively separable case is a special case. Because choices are not dynamically consistent, we follow the “consistent planning” approach of Strotz [Strotz, R., 1956. Myopia and inconsistency in dynamic utility maximization. Review of Economic Studies 23, 165–180] and also interpret our analysis from the game theoretic perspective taken by Peleg and Yaari [Peleg, B., Yaari, M., 1973. On the existence of a consistent course of action when tastes are changing. Review of Economic Studies 40, 391–401]. The equilibrium of the Lucas asset pricing model with i.i.d. consumption growth is obtained and the equity premium is shown to depend on the elasticity of substitution as well as the risk aversion measure. The nature of the dependence is examined. Our results are contrasted with those of the non-expected utility recursive approach of Epstein–Zin and Weil.     

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.      

Equal risk pricing under convex trading constraints

In an incomplete market model where convex trading constraints are imposed upon the underlying assets, it is no longer possible to obtain unique arbitrage-free prices for derivatives using standard replication arguments. Most existing derivative pricing approaches involve the selection of a suitable martingale measure or the optimisation of utility functions as well as risk measures from the perspective of a single trader.We propose a new and effective derivative pricing method, referred to as the equal risk pricing approach, for markets with convex trading constraints. The approach analyses the risk exposure of both the buyer and seller of the derivative, and seeks an equal risk price which evenly distributes the expected loss for both parties under optimal hedging. The existence and uniqueness of the equal risk price are established for both European and American options. Furthermore, if the trading constraints are removed, the equal risk price agrees with the standard arbitrage-free price.Finally, the equal risk pricing approach is applied to a constrained Black–Scholes market model where short-selling is banned. In particular, simple pricing formulas are derived for European calls, European puts and American puts.     

Shortfall risk minimisation versus symmetric (quadratic) hedging

Abstract We consider the seller of a contingent claim who wants to hedge against the corresponding risk by means of a self-financing strategy, endowing less initial capital than the one required for (super)hedging. Two classical criteria used in this situation are shortfall risk minimisation and symmetric hedging (a natural generalisation of the quadratic hedging problem). We show that these two problems are equivalent if the market is complete. The case when the market is incomplete is also discussed. Mathematics Subject Classification (2000): 91B28, 91B70, 93E20 Journal of Economic Literature Classification: D81, G11     

Price functionals with bid–ask spreads: an axiomatic approach

In Jouini and Kallal [Jouini, E., Kallal, H., 1995. Martinagles and arbitrage in securities markets with transaction costs. Journal of Economic Theory 66 (1) 178-197], the authors characterized the absence of arbitrage opportunities for contingent claims with cash delivery in the presence of bid–ask spreads. Other authors obtained similar results for a more general definition of the contingent claims but assuming some specific price processes and transaction costs rather than bid–ask spreads in general (see for instance, Cvitanic and Karatzas [Cvitanic, J., Karatzas, I., 1996. Hedging and portfolio optimization under transaction costs: a martinangle approach. Mathematical Finance 6, 133-166]). The main difference consists of the fact that the bid–ask ratio is constant in this last reference. This assumption does not permit to encompass situations where the prices are determined by the buying and selling limit orders or by a (resp. competitive) specialist (resp. market-makers). We derive in this paper some implications from the no-arbitrage assumption on the price functionals that generalizes all the previous results in a very general setting. Indeed, under some minimal assumptions on the price functional, we prove that the prices of the contingent claims are necessarily in some minimal interval. This result opens the way to many empirical analyses.     

Contractual solutions to hold-up problems with quality uncertainty and unobservable investments

Consider a seller and a buyer who write a contract. After that, the seller produces a good. She can influence the expected quality of the good by making unobservable investments. Only the seller learns the realized quality. Finally, trade can occur. It is always ex post efficient to trade. Yet, it may be impossible to achieve the first best, even though the risk-neutral parties are symmetrically informed at the contracting stage and complete contracts can be written. The second best is characterized by distortions that are reminiscent of adverse selection models (i.e., models with precontractual private information but without hidden actions).     

On axiomatizations of the Shapley value for assignment games

We consider the problem of axiomatizing the Shapley value on the class of assignment games. It turns out that several axiomatizations of the Shapley value on the class of all TU-games do not characterize this solution on the class of assignment games. However, when considering an assignment game as a (communication) graph game where the game is simply the assignment game and the graph is a corresponding bipartite graph where buyers (sellers) are connected with sellers (buyers) only, we show that Myerson’s component efficiency and fairness axioms do characterize the Shapley value on the class of assignment games. Moreover, these two axioms have a natural interpretation for assignment games. Component efficiency yields submarket efficiency stating that the sum of the payoffs of all players in a submarket equals the worth of that submarket, where a submarket is a set of buyers and sellers such that all buyers in this set have zero valuation for the goods offered by the sellers outside the set, and all buyers outside the set have zero valuations for the goods offered by sellers inside the set. Fairness of the graph game solution boils down to valuation fairness stating that only changing the valuation of one particular buyer for the good offered by a particular seller changes the payoffs of this buyer and seller by the same amount.     

Consumer surplus analysis under uncertainty: A general equilibrium perspective

This paper derives an exact form of partial equilibrium efficiency measure under uncertainty which is consistent with expected utility maximization in a general equilibrium situation with ex-post spot markets for many goods and asset markets which are in general incomplete.We consider that the good under consideration tends to be negligibly small compared to the entire set of commodity characteristics which is assumed to be a continuum, and look into the limit property of preferences over state-contingent consumption of the good and state-contingent income transfer associated to it. We show that the limit preference exhibits risk neutrality, not only that it exhibits no income effect, meaning that the two conditions are tied together. We also show that the marginal rate of substitution between extra income transfers at different states of the world converges to the ratio between the Lagrange multipliers associated to those states. When the asset markets are complete such ratios are equalized between consumers, but it is not the case in general when the asset markets are incomplete. This means that using the aggregate expected consumer surplus as the welfare measure will be in general inconsistent with individuals’ expected utility maximization in the general equilibrium environment or with ex-ante Pareto efficiency.     

Estimating the structural credit risk model when equity prices are contaminated by trading noises

The transformed-data maximum likelihood estimation (MLE) method for structural credit risk models developed by Duan [Duan, J.-C., 1994. Maximum likelihood estimation using price data of the derivative contract. Mathematical Finance 4, 155–167] is extended to account for the fact that observed equity prices may have been contaminated by trading noises. With the presence of trading noises, the likelihood function based on the observed equity prices can only be evaluated via some nonlinear filtering scheme. We devise a particle filtering algorithm that is practical for conducting the MLE estimation of the structural credit risk model of Merton [Merton, R.C., 1974. On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance 29, 449–470]. We implement the method on the Dow Jones 30 firms and on 100 randomly selected firms, and find that ignoring trading noises can lead to significantly over-estimating the firm’s asset volatility. The estimated magnitude of trading noise is in line with the direction that a firm’s liquidity will predict based on three common liquidity proxies. A simulation study is then conducted to ascertain the performance of the estimation method.     

Price discrimination in the housing market

There is little credible evidence on whether price discrimination exists in the housing market. Using a large sample of single-family home sales from Florida where both the race of the seller and buyer are known, we present evidence using the traditional and Harding et al. [HRS, Harding, J.P., Rosenthal, S., Sirmans, D.F., 2003. Establishing bargaining power in the market for existing homes. The Review of Economics and Statistics 85, (1) 178–188] approaches to empirical estimation. Omitted variable bias is found to plague the traditional approach. Results from following the HRS approach indicate that price discrimination exists by whites and Hispanics against blacks and Asians. Price discrimination against blacks is restricted to non-majority black neighborhoods and is smaller in magnitude in neighborhoods containing younger and more educated homeowners.