Revelation principle

The space of potential contract menus is quite large, so large that it is not immediately obvious how to begin to find the supplier s optimal menu. For example, how many contracts should be offered and what form should they take Furthermore, for any given menu the supplier needs to infer for each manufacturer type which contract the type will choose. Fortunately, the revelation principle (Kreps 1990) provides some guidance. 

The revelation principle begins with the presumption that a set of optimal mechanisms exists. Associated with each of these mechanisms is a NE that specifies which contract each manufacturer type chooses and the supplier s action given the chosen contract. With some of these equilibria it is possible that some manufacturer type chooses a contract that is not designated for that type. For example, the supplier intends the low demand manufacturer to choose one of the menu options, but instead the high demand manufacturer chooses that option. Even though this does not seem desirable, it is possible that this mechanism is still optimal in the sense that the supplier can do no better on average. The supplier ultimately cares only about expected profit, not the means by which that profit is achieved. Nevertheless, the revelation... 

There have been a number of applications of the revelation principle in the supply chain literature e.g., Chen (2001) studies auction design in the context of supplier procurement contracts Corbett (2001) studies inventory contract design Baiman et al. (2003) study procurement of quality in a supply chain. 

We will introduce an analytical model for each of cases listed above. The models help to characterize the role of intermediation, to determine when should they exist, and to understand how could they extract profit while sustaining the trade efficiency. For the incomplete information cases we need to make use of the mechanism design framework and the revelation principle which we will briefly summarize in the following section. In Section 3.3 we will summarize the settings of the four supply chain intermediation models. 

By the revelation principle (Section 3.2), it is sufficient to consider an incentive compatible direct mechanism. In other words, regardless of the mechanism constructed by the intermediary, given the equilibrium of the mechanism, we can construct an equivalent incentive compatible direct mechanism, where the buyer and the supplier report their respective valuations to the intermediary, and the intermediary determines if the trade is to take place. If so, she determines the buyer s payment and the suppliers revenue. Otherwise, the players take their outside options in a direct matching market. Let T(/3,p, w) represents the direct revelation mechanism, where /3(s, v) is the probability that the trade will take place, p(s, v) is the expected payment to be made by the buyer to the intermediary (the asked price), and w(s, v) is the expected payment from the intermediary to the supplier (the bid price), where s and v are the valuations given by the supplier and buyer, respectively. As mentioned above, the intermediary is aware of the buyer and the supplier s outside options as random variables characterized by distributions G and F, respectively. Based on this information the intermediary establishes the buyer s virtual willingness to pay follows ... 

In the general framework of supply chain intermediation (Section 3.2), an intermediary can be characterized in a mechanism design fi mework using the revelation principle, requiring the specification of a direct revelation mecha-... 

Care should be taken in interpreting the revelation principle. First, the revelation principle does not imply that incentive-compatibility comes for free . In fact, a central theme of mechanism design is that there is a cost to the elicitation of private information. The mechanism design literature is peppered with impossibility results that characterize sets of desiderata that are impossible to achieve simultaneously because it is necessary to incent agents to participate in a mechanism [53]. Rather, the revelation principle states that if a particular set of properties can be implemented in the equilibrium of some mechanism. 

The beauty of the revelation principle is that it allows theoretical impossibility and possibility results to be established in the space of direct mechanisms, and carried over to apply to all mechanisms. For example, an indirect mechanism can be constructed with a particular set of properties only if a direct mechanism can also be constructed with the same set of properties. 

By the revelation principle we can restrict attention to IC DRMs, and immediately express the optimal mechanism design problem [OPT] as... 

The communication complexity of a mechanism considers the size of messages that must be sent between agents and the mechanism to implement the outcome of a mechanism. To motivate this problem, recall that mechanism design often makes an appeal to the revelation-principle and considers direct mechanisms. However, direct mechanisms require agents to report complete and exact information about their type, which is often unreasonable in problems such as combinatorial auctions. In the worst-case the VCG mechanism for a combinatorial auction requires each agent to submit 2 numbers, given M items, to report its complete valuation function. 

There are a multitude of auction design parameters to play with. Once one specifies the objectives of the auction how is one to search through all these parameters to find the setting that best achieves them This is where the revelation principle of mechanism design comes in. 

One can imagine a mechanism that is not direct . Consider one that involves multiple rounds where participation in one round is conditional on bids or other information revealed in previous rounds. These indirect mechanisms can be quite baroque. It is here that the revelation principle comes to our aid. 

Given any mechanism, there is a corresponding direct revelation mechanism which will produce the same outcome as the given mechanism. Thus, for the purposes of analysis, one can restrict attention to direct revelation mechanisms. The revelation principle does pose a problem. If a direct mechanism suffices why do we observe indirect mechanisms in practice We defer a discussion of this to sections 5.3 and 6. 

We now put the revelation principle to work to identify auctions that meet two obvious and popular goals. The first is revenue maximization, the second is economic efficiency. For a more detailed treatment of the mechanism design perspective see 2.2 of Chapter 5 by Kalagnanam and Parkes. 

Yet it is on the issues of reproducibility and instrumentation that Occult Chemistry failed to persuade, at least outside of Theosophical circles and the small group of scientists in recent years who have been willing to work entirely at the level of theory. Besant and Leadbeater could move beyond older models of science, which based themselves upon deductions from revealed principles (alchemical or scientific deductions from the writings of the Hermetic tradition, for instance, or from the revelations of H. P. Blavatsky), by turning to experimentation. Not surprisingly, their form of experimentation did not admit of reproducibility. In spite of efforts by Stephen Phillips to conduct blind trials using a Buddhist clairvoyant to confirm Besant and Lead-beater s micro-psi visions (1996,48), direct experience is neither convincingly verifiable nor falsifiable. 

As mentioned in Chapter 4, experiments have determined that the distribution of ASOs into tissues is nonlinear. This revelation invalidates the above BAV equation in that it is dependent on linear pharmacokinetics and the principle of superposition. A way to circumvent this problem is to decrease the drag input function (i.e., systemic presentation of the ASO) such that ASO plasma concentrations are maintained below the level at which saturation, and thus nonlinearity of the distribution processes, occurs. Drug administration by SC rather than IV administration has a reduced drug input rate and can produce such a scenario. The corresponding plasma-derived data are then suitable for the determination of absolute bioavailability - consistent with linear pharmacokinetic principles and the following equation ... 

The Aurora, as it has come down to us, is the description of a life-shattering experience that could very well be Aquinas s revelations ofDecember 1273. Itis certainly possible that it was a transcription of Aquinas s final talk, as other of his works as we know them today were also transcribed by pupils. The work describes a vision of Sophia, the Wisdom of God. Aquinas realises he has neglected the Feminine Principle all his life, and she has revealed herself to him in all Her Glory. Perhaps this is what he meant when he said that everything he d done seemed worthless, like straw in comparison. Her wisdom is equated with the Philosopher s Stone, and links alchemy with the Feminine face of God. Had he lived, Aquinas may well have found himself in trouble for his views his work was denounced in the Paris Condemnations of 1277, which also attacked Bacon. 

Our denial of the truth of what is issuing from the pharmaceutical and chemical companies will perhaps bury our race for not only are they sucking the health out of people but they are polluting the environment to the point where the ice will melt and the temperatures will sore. Denial is the principle weapon of evil and is essentially the attitude that takes us away from life. On all levels denial works powerfully in our minds and the cost is usually high in personal terms but in social terms it spells disaster. There have already been many revelations and scandals about the darker side of medical science that should have seriously damaged our trust in scientists and government institutions. It is my hope that the information provided herein will destroy all trust and... 

---