Optimal mechanisms with simple menus

We consider revenue-optimal mechanism design for the case with one buyer and two items, when the buyer’s valuations are independent and additive. We obtain two sets of structural results of the optimal mechanisms, which can be summarized in one conclusion: under certain distributional conditions, the optimal mechanisms have simple menus.The first set of results states that, under a condition that requires that the types are concentrated on lower values, the optimal menu can be sorted in ascending order. Applying the theorem, we derive a revenue-monotonicity theorem which states that stochastically dominated distributions yield less revenue.The second set of results states that, under certain conditions which require that types are distributed more evenly or are concentrated on higher values, the optimal mechanisms have a few menu items. Our first result states that, for certain such distributions, the optimal menu contains at most 4 menu items. The condition admits power density functions. Our second result works for a weaker condition, under which the optimal menu contains at most 6 menu items. Our last result in this set works for the unit-demand setting, it states for uniform distributions, the optimal menu contains at most 5 items.     

Optimal auctions with multidimensional types and the desirability of exclusion

Within the context of a single-unit, independent private values auction model, we show that if bidder types are multidimensional, then under the optimal auction exclusion of a positive measure of bidder types occur. The results complements Armstrong’s (1996) exclusion of types result.     

A pragmatic decision model for inventory management with heterogeneous suppliers

For enterprises, it is imperative that the trade-off between the cost of inventory and risk implications is managed in the most efficient manner. To explore this, we use the common example of a wholesaler operating in an environment where suppliers demonstrate heterogeneous reliability. The wholesaler has partial orders with dual suppliers and uses lateral transshipments. While supplier reliability is a key concern in inventory management, reliable suppliers are more expensive and investment in strategic approaches that improve supplier performance carries a high cost. Here we consider the operational strategy of dual sourcing with reliable and unreliable suppliers and model the total inventory cost where the likely scenario lead-time of the unreliable suppliers extends beyond the scheduling period. We then develop a Customized Integer Programming Optimization Model to determine the optimum size of partial orders with multiple suppliers. In addition to the objective of total cost optimization, this study takes into account the volatility of the cost associated with the uncertainty of an inventory system.     

Optimal selling mechanisms for multiproduct monopolists: incentive compatibility in the presence of budget constraints

We analyze the nonlinear pricing problem faced by an incomplete information monopolist operating in a market populated by agents with budget constraints. We show that if other goods are available and if the monopolist's goods are nonessential relative to other goods, then there exists an optimal, individually rational, and incentive compatible selling mechanism for the monopolist (Theorem 1). Moreover, we show that a solution to all such nonlinear pricing problems exists if and only if the monopolist's goods are nonessential (Theorem 2). In the absence of nonessentiality, we show that if the monopolist's profit function is independent of quantity (e.g., if all costs are fixed), then an optimal selling mechanism exists (Theorem 3). Finally, we show that if there is reporting (of types by agents) and partial recognition of types (by the monopolist), then an optimal selling mechanism exists, even in the absence of nonessentiality, provided agents' utility functions are affine and continuous in goods (Theorem 4).     

Optimal investment and reinsurance policies for an insurer with ambiguity aversion

In this paper, we study the optimal investment and reinsurance problem for an insurer based on the variance premium principle, in which three cases are considered. First, we assume that the financial market does not exist. The insurer only holds an insurance business, and the optimal reinsurance problem is studied. Subsequently, we assume that there exists a financial market with an accurately modeled risky asset. The optimal investment and reinsurance problem is investigated under these conditions. Finally, we consider the general case in which the insurer is concerned about the model ambiguity of both the insurance market and the financial market. In all three cases, the value function is set to maximize the expected utility of terminal wealth. By employing the dynamic programming principle, we derive the Hamilton–Jacobi–Bellman (HJB) equations, which are satisfied by the value functions and obtain closed-form solutions for optimal reinsurance and investment policies and the value functions in all three cases. Most interestingly, we elucidate how investment improves the insurer’s utility and find that the existence of ambiguity can significantly affect the optimal policies and value functions. We also compare the ambiguities in the two markets and find that ambiguity in the insurance market has much more significant impact on the value function than the ambiguity in the financial market. It implies that it is more valuable for insurer to precisely evaluate the insurance risk. We also provide some numerical examples and economic explanations to illustrate our results.     

Optimal designs for generalized linear models with biased response

This paper is concerned with the search for locally optimal designs when the observations of the response variable arise from a weighted distribution in the exponential family. Locally optimal designs are derived for regression models in which the response follows a weighted version of Normal, Gamma, Inverse Gaussian, Poisson or Binomial distributions. Some conditions are given under which the optimal designs for the weighted and original (non-weighted) distributions are the same. An efficiency study is performed to find out the behavior of the D-optimal designs for the original distribution when they are used to estimate models with weighted distributions.     

Optimal Designs for Asymmetric Linear Paired Comparisons with a Profile Strength Constraint

Within the linear model framework the problem of determining optimal designs for paired comparisons of alternatives which are described by a set of discrete attributes is considered under the constraint that the alternatives in a pair are only allowed to differ with regard to a certain number of attributes. Whereas in previous treatments of this problem it was assumed that all attributes possess the same number of levels, here the general asymmetric case is discussed. We provide a characterization of optimal designs and demonstrate how this can be used to derive a solution of the design problem for many situations of interest.     

Optimal designs for models with block-block resp. treatment-treatment correlations

Summary In this paper we study optimal designs assuming two special covariance structures of the observations, namely that the covariance between the observations depends only on the blocks resp. the treatments. We show that the weighted least squares estimator equals the ordinary least squares estimator. Then we prove that block-block correlations resp. treatment-treatment correlations do not have any influence on the A- and MV-optimality resp. A-optimality. For the study of the MV-optimality in the case of treatment-treatment correlations we use the idea of invariance to find optimal C-matrices.     

Impossibilities for strategy-proof committee selection mechanisms with vetoers

When a group of voters selects a committee out of a set of candidates, it is common and often desirable to endow these voters with some veto power. I present impossibility results showing that even limited veto power makes many mechanisms of interest manipulable. This applies in particular (i) to mechanisms the range of which contains a degenerate lottery in which a committee is chosen for sure and (ii) to mechanisms that are constructed from extensive game forms with a finite number of strategies. These impossibilities hold on a large set of domains including the domain of additive preferences, and even when probabilistic mechanisms are allowed and voters can report cardinal preferences.     

Optimal deterministic contracting mechanisms for principal-agent problems with moral hazard and adverse selection

For the principal-agent problem with moral hazard and adverse selection we establish that within the collection of all measurable, deterministic contracting mechanisms satisfying the individual rationality and incentive compatibility constraints there exists one that is optimal for a risk averse principal contracting with a risk averse agent. In addition to demonstrating existence, one of the main contributions of the paper is to show that, in general, centralized contracting implemented via a contracting mechanism is equivalent to delegated contracting implemented via a contract menu. Thus, contracting can always be delegated to the agent without gain or loss to the principal. Based on this result, the existence of an optimal contracting mechanism for the principal-agent problem is established by showing that there exists an optimal contract menu for the equivalent delegated contracting problem. Received: 7 October 1994 / Accepted: 14 January 1997