Incentive compatibility

Second, there are major differences between the United States and Europe in the extent of pre-regulatory studies undertaken. Because of the U.S. requirement on agencies like the U.S. Environmental Protection Agency to conduct a Regulatory Impact Analysis before taking action, substantially more information was available about the hoped-for benefits of U.S. policies. A further issue concerns the greater reliance on taxes for regulatory purposes in Europe compared to the United States. A number of European nations use such taxes—sometimes combined with incentive compatible rebate schemes—to achieve environmental objectives. 

In bilateral bargaining with incomplete information (Figure 3. l-(b)), the supplier and the buyer hold private information s G [si,S2],v G [vi V2] as defined above with ex ante distributions F s) and G(v), respectively. The intermediary decides if the trade is to take place (/ (5, v)). If so, she collects p(s, v) from the buyer and pay w s, v) to the supplier. The intermediary determines P, p, w to maximize a certain function sub-ject to incentive compatibility, individual rationality, and ex post efficiency (see Section 5). 

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 ... 

The direct mechanism F is said to be incentive compatible if reporting the truthful valuation is the preferred strategy for the players ... 

Theorem 2 For any incentive compatible mechanism with an intermediary, is nonincreasing, Ph(v) is nondecreasing, and... 

To streamline the discussion we will only outline the main component of the proof as follows. First of all, by incentive compatibility (3.25) and (3.26), it is straightforward to show that Ps s) is nonincreasing, PbM is nondecreasing. Furthermore, from relationship (3.32), we have... 

Based on the supply chain intermediation framework outlined above, the intermediary devises a direct mechanism T P p,w) to maximize her profit (3.35), subject to incentive compatibility and individual rationality. First, the intermediary must determine P s, v) which specifies whether the trade is to take place given the reported s, v and her knowledge of their virtual opportunity costs and virtual willingness to pay. Given the simple form of the profit function (3.35) it is straightforward to find a profit maximizing P subject to individual rationality as follows ... 

The reader will observe that in this formulation, the incentive compatibility constraint has been incorporated into the objective function (4.8), and the only constraint left is the participation constraint. 

Before we conclude this section, it is also worthwhile to introduce and summarize the terminology we will be using in the remainder of this chapter. A compensation system is said to induce or implement an action if that action represents the agent s optimal choice. Such action is called incentive compatible. A pair that consists of a compensation system and an action is called a contract. Such a contract is feasible if the prescribed action is incentive compatible and if the compensation system satisfies the participation constraint. The optimal contract is the pair (not necessarily unique) of a compensation system and incentive compatible action that maximizes the principal s expected payoff and satisfies the participation constraint. The action prescribed in the optimal contract is called second-best as opposed to the so-called first-best action that is optimal when the agent s action is observable by the principal. 

The incentive compatibility constraints (4.29)-(4.30) state that the pair (a, a ) is a Nash equilibrium for the single-period game in which each agent receives a terminal payoff equal to his reservation utility at the end of the period. 

George, J. 1999. A Queue with Controllable Service Rates Optimization and Incentive Compatibility. Stanford University Graduate School of Business, unpublished Ph.D. thesis. 

In settings where the allocation problem itself is hard even if the decision maker knows the true utility function of each agent, the issues of incentive compatibility makes the design of an appropriate auction mechanism even more challenging. 

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 goal of efficiency, combined with incentive-compatibility, pins down the allocation rule ... 

We can also consider relaxed strategic models, in which the goal of complete incentive-compatibility is relaxed. We briefly outline a taxonomy of strategic relaxations [41], and provide some examples of their use in the literature. 

Properties a) and b) together would provide for an efficient and balanced DA, and violate the Myerson-Satterthwaite result. Notice that the TR-DA [8] and McAfee-DA [62] are truthful (in a dominant strategy), but deliberately clear the exchange to implement an inefficient trade. In comparison, the A -DA auction [104, 24, 95] clears to maximize reported surplus but is not incentive-compatible. Of course, we know that the VCG mechanism is efficient but not balanced. The parameter k G [0,1] in fc-DA is chosen before the auction begins, with the clearing price faced by all agents calculated as kAi+(1—fc). 

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