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.
A Discrete Search Game
We consider the following search game: the first player, to be called the hider, chooses y, an integer from the set of integers 1 to N. The second player, to be called the searcher, guesses an integer from 1 to N and is told whether his guess is or is not too low; he continues to guess until he identifies y. The payoff to the hider is the number of guesses by the searcher.We present the optimal (mixed) strategies for both players and the value of this game.
Barbarians, Gentlemen and Players : A Sociological Study of the Development of Rugby Football
Part I: Folk Antecedents and Transitional Forms of Football in the Public Schools 1. The folk antecedents of modern rugby and their decline 2. Football in the early 19th century public schools Part II: The Modernisation of Rugby Football 3. The preconditions for modernization: embourgeoisement and public school reform 4. The incipient modernization of rugby football 5. The 'civilising process' and the formation of the RFU. 6. The democratization of rugby football. 7. Professionalisation and the amateur response. 8. The split. 9. The class structure and the professionalisation of British sport. Part III: The Development of Rugby Football as a Modern Sport 10. The professionalisation of rugby league. 11. Rugby union as a modern sport: bureaucracy, gate-taking clubs and the swansong of amateurism. Conclusion: Sociological Reflections on the Crisis in Modern Sport