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.
An Asymptotic Solution of Dresher's Guessing Game
In his 1961 monograph on Game Theory, Melvin Dresher considered a high-low guessing game on N numbers. The game was solved for N≤11 by Selmer Johnson but solutions for higher values of N have never been reported in the literature. In this paper we derive an asymptotic formula for the value of the game as N→∞ and we present an algorithm that allows us to numerically solve the game for N≤256.
Introduction to Operations Research Techniques
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