A Dynamic Model of Collective Bargaining
We use high-low search algorithms to compute equilibria in a multi-period model of collective bargaining. In this model, a group of workers bargains collectively with a firm which knows the per period incremental value v of each worker. The workers don't know their individual values, but use high-low search to learn them, given the known distribution of values in the group. In the first period the workers make a common wage demand w1 and then the firm chooses a cutoff level y for the workers they will hire (i.e., those with v≥ y). Since y is observable through numbers hired, workers may update their beliefs about their values, based on whether or not they were hired. In later periods workers with common beliefs make common wage demands. The main question addressed in the paper is how the firm can choose the hiring cutoff level to hinder the workers' learning process. We find (Theorem 1) that the firm's equilibrium strategy is to (i) hire some workers at a loss, and also (ii) to forego some profitable hirings. However (Theorem 2) the equilibrium outcome involves only the first kind of strategic loss by the firm. We also find (Theorem 3) that the firm's profit is less than when the worker optimizes against a predictable myopic firm (which chooses y=w1). Thus the firm would wish to commit to the myopic hiring strategy if it were possible.
Interactive High-low Search: The Case of Lost Sales
We consider the problem of supplying perishable goods to disloyal customers. As in traditional stock-control literature, a penalty is incurred whenever there is a stockout. However, in contrast to mainstream models, loss of goodwill is explicitly treated by incorporating the behavioural assumption that a fixed proportion of unsatisfied demand is lost forever after each stockout. The problem consists of finding supply levels which minimize costs of over- and underproduction, given unknown but deterministic demand. We derive optimal adaptive search procedures under varying assumptions of a priori knowledge about demand. Optimal strategies are compared to myopic strategies. Our methodology extends the mathematical theory of ‘high-low search’ for a hidden point to incorporate the ‘Heisenberg principle’: the position of the hidden point (demand) is directly influenced by the actions (supply levels) of the searcher.
An Optimization Approach to Occupant Safety and Fuel Economy in Vehicle Design
1. Abstract A major challenge in automotive design is the creation of safe vehicles with minimal environmental impact. This study presents a modeling framework for evaluating and optimizing body designs for improved occupant safety and fuel efficiency. Vehicle body mass is considered as the main link between safety and sustainability. The modeling framework includes frontal crash energy absorption, restraint system design and fuel economy. Preliminary results indicate a Pareto-optimal curve between safety and sustainability may exist when other factors are not taken into account. A more complete modeling framework that includes more sophisticated sustainability and safety metrics, cost and other market considerations, is suggested in order to support better design and regulatory decisions. 2. Keywords: Automotive body structures, fuel economy, occupant safety, optimal vehicle design, restraint systems