Diane J. Reyniers

Contract design and the control of quality in a conflictual environment

This paper provides an approach to quality supply by a supplier and quality inspection by a producer, which explicitly recognizes the inherently opposing interests these two parties may have. The supplier and the producer are modeled as players in a nonzero sum game, where the supplier can control the effort invested in the delivery of quality and the producer may or may not inspect incoming materials. We study the effect of contract design (e.g. stipulation of penalties for defective units) on equilibrium behavior and identify conditions on the contract parameters which will result in the implementation of a cooperative solution.

Irrational Exuberance, Entrepreneurial Finance and Public Policy

Unrealistic optimism is a well documented phenomenon. This paper argues that it is important in many economic contexts. Focusing on start-up finance for businesses, optimism may be responsible for or consistent with features such as credit rationing or redlining that are normally taken as symptoms of under-provision of finance requiring intervention to expand lending. Optimism leads to the opposite conclusion, at least if it is legitimate to use fiscal policy to counteract systematic error. The paper reports on an experiment in which, due to optimism, the lower the prizes to entrepreneurial activity the higher the subjects expected income.

Supplier-customer interaction in quality control

We develop a game theoretic model of joint quality control in a single sourcing environment which integrates supplier and customer decisions. In this model, both parties behave strategically and take each others incentives into account when deciding on their respective sampling plans. The specific sampling plans considered are of the “single sample fraction defective with rectifying inspection” type. A method to find the optimal sampling plans for both supplier and customer in two different informational setups is constructed. The resulting models lead to examination of Stackelberg and Nash equilibria. Numerical examples of such equilibria are presented, indicating how optimal strategies depend on the parameters of the problem.

Spatial dispersion as a dynamic coordination problem

Following Schelling (1960), coordination problems have mainly been considered in a context where agents can achieve a common goal (e.g., rendezvous) only by taking common actions. Dynamic versions of this problem have been studied by Crawford and Haller (1990), Ponssard (1994), and Kramarz (1996). This paper considers an alternative dynamic formulation in which the common goal (dispersion) can only be achieved by agents taking distinct actions. The goal of spatial dispersion has been studied in static models of habitat selection, location or congestion games, and network analysis. Our results show how this goal can be achieved gradually, by indistinguishable non-communicating agents, in a dynamic setting.

A high-low search algorithm for a newsboy problem with delayed information feedback

This paper outlines a new approach to the problem of demand uncertainty. It deals with setting optimal supply levels when demand is unknown. The novel feature of this approach is that information is obtained by observing sales. This information is used to determine future supply levels. Thus, supply levels are chosen with a view to current profit and future information. The technical apparatus is based on an extension of the theory of high-low search. We derive an algorithm to determine a sequence of supply quantities which minimizes total costs of over-and undersupply in the most adverse demand conditions. We calculate the value of perfect information, indicating how much a rational risk averse decision maker would be willing to pay to know demand exactly.

Coordinated search for an object hidden on the line

We consider the coordinated search problem faced by two searchers who start together at zero and can move at speed one to find an object symmetrically distributed on the line. In particular we fully analyze the case of the negative exponential distribution given by the density f(x) = e−|x|μ/(2μ), μ > 0. The searchers wish to minimize the expected time to find the object and meet back together (with the object) at zero. We give necessary and sufficient conditions for the existence of an optimal search strategy when the target density is continuous and decreasing. We show that for the negative exponential distribution the optimal time is between 4.728μ and 4.729μ. A strategy with expected time in this interval begins with the searchers going in opposite directions and returning to the origin after searching up to successive distances 0.745μ, 2.11μ, 3.9μ, 6μ, 8.4μ,…. These results extend the theory of coordinated search to unbounded regions. It has previously been studied for objects hidden on a circle (by Thomas) and on an interval (by the author).

A rationale for trade-ins

Abstract We explain trade-ins as a device used by a monopolist to price discriminate between new and repeat buyers. We show how the monopolist creates and subsequently exploits market segmentation. A two-period model is considered. In the first period, the seller sets a price which divides the second-period market into old and new customers. In the second period, he uses trade-ins (discounts for old customers) or introductory offers (discounts for new customers) to price discriminate between buyers. We analyze the optimal segmentation of customers; i.e., we determine the optimal price for each consumer group as a function of the durability of the good, its production cost, and the discount factor. The qualitative decision of whether to give a discount to old or new customers also depends on these parameters. We consider a second model in which discounts are only available to repeat buyers, and compare our results to a base model without price discrimination.

The effect of vertical integration on consumer price in the presence of inventory costs

Abstract This paper investigates the effect on consumer price of a vertical merger between a monopolist manufacturer and his retailer, when inventory costs are taken into consideration. We find that the traditional result (lower prices) remains true only when inventory costs are sufficiently small. The direction of the price change also depends on the market size.

Generalised reciprocity and reputation in the theory of cooperation: a framework

Abstract We study the Iterated Bilateral Reciprocity game in which the need for help arises randomly. Players are heterogeneous with respect to ‘neediness’ i.e. probability of needing help. We find bounds on the amount of heterogeneity which can be tolerated for cooperation (all players help when asked to help) to be sustainable in a collectivity. We introduce the notion of Generalised Reciprocity. Individuals make a costly first move to benefit another under the reasonable expectation that either the other or somebody else will reciprocate. We hope that these tentative attempts at extending Axelrod’s seminal work on cooperation will inspire future efforts in the field of organisational culture and social theory more generally.

Information and rationality asymmetries in a simple high-low search wage model

A simple model of wage bargaining is developed. The firm knows the workers productivity but the worker has only probabilistic information about his value to the firm. The worker acquires information by making wage demands and observing the resulting hiring/firing decisions of the firm. The firm acts strategically and distorts the workers learning process.