Dynamic Models of Reputation and Competition in Job-Market Matching

A fundamental decision faced by a firm hiring employees --- and a familiar one to anyone who has dealt with the academic job market, for example --- is deciding what caliber of candidates to pursue. Should the firm try to increase its reputation by making offers to higher-quality candidates, despite the risk that the candidates might reject the offers and leave the firm empty-handed? Or is it better to play it safe and go for weaker candidates who are more likely to accept the offer? The question acquires an added level of complexity once we take into account the effect one hiring cycle has on the next: hiring better employees in the current cycle increases the firm's reputation, which in turn increases its attractiveness for higher-quality candidates in the next hiring cycle. These considerations introduce an interesting temporal dynamic aspect to the rich line of research on matching models for job markets, in which long-range planning and evolving reputational effects enter into the strategic decisions made by competing firms. The full set of ingredients in such recruiting decisions is complex, and this has made it difficult to model the fundamental strategic tension at the core of the problem. Here we develop a model based on two competing firms to try capturing as cleanly as possible the elements that we believe constitute this strategic tension: the trade-off between short-term recruiting success and long-range reputation-building; the inefficiency that results from underemployment of people who are not ranked highest; and the influence of earlier accidental outcomes on long-term reputations. Our model exhibits all these phenomena in a stylized setting, governed by a parameter $q$ that captures the difference in strength between the top candidate in each hiring cycle and the next best. Building on an economic model of competition between parties of unequal strength, we show that when $q$ is relatively low, the efficiency of the job market is improved by long-range reputational effects, but when $q$ is relatively high, taking future reputations into account can sometimes reduce the efficiency. While this trade-off arises naturally in the model, the multi-period nature of the strategic reasoning it induces adds new sources of complexity, and our analysis reveals interesting connections between competition with evolving reputations and the the dynamics of urn processes.