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.
Information and rationality asymmetries in a simple high-low search wage model
A simple model of wage bargaining is developed. The firm knows the worker's 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 worker's learning process.
A Search Model of Optimal Pricing and Production
This paper presents an overview of the application of the mathematical theory of 'high-low' search to firms' pricing and production decisions. We show how this methodology can be used to determine an optimal sequence of price-quantity decisions by a firm through time. We suppose that the firm chooses a sequence of prices and quantities supplied over time not only with a view to earning current profit (given the current information about the demand curve) but also in order to acquire information about the demand curve by observing its inventory stocks as a result of these price and quantity decisions. We compare and contrast the high-low model with the conventional microeconomic model of pricing and production. We show how the firm uses its pricing and production decisions to partition the uncertainty interval it faces and thereby influence the value of the information which it receives.