Early Round Upsets and Championship Blowouts

In equilibrium play of a two-round tournament we find that underdogs exert more effort in the opening round while favorites save more effort for the final. Ability differences between players are therefore compressed in the opening round so upsets are more likely, and amplified in the final so blowouts are more likely. Measures that reduce the need to strategically allocate effort across games make for a more exciting final but a less exciting opening round. Consistent with the model, introduction of a one-day rest period between regional semi-final and final matches in the NCAA men’s basketball tournament was found to increase the favorite’s victory margin in the semi-finals by about five points. Non-sports applications of the model include the allocation of resources across primaries and general elections by candidates and the allocation of resources across a career ladder by managers.contest; tournament; all-pay auction

Prizes and Incentives in Elimination Tournaments

The role of rewards for maintaining performance incentives in multistage, sequential games of survival is studied. The sequential structure is a statistical design-of-experiments for selecting and ranking contestants. It promotes survival of the fittest and saves sampling costs by early elimination of weaker contenders. Analysis begins with the case where competitors' talents are common knowledge and is extended to cases where talents are unknown. It is shown that extra weight must be placed on top ranking prizes to maintain performance incentives of survivors at all stages of the game. The extra weight at the top induces competitors to aspire to higher goals independent of past achievements. In career games workers have many rungs in the hierarchical ladder to aspire to in the early stages of their careers, and this plays an important role in maintaining their enthusiasm for continuing. But the further one has climbed, the fewer the rungs left to attain. If top prizes are not large enough, those who have succeeded in attaining higher ranks rest on their laurels and slack off in their attempts to climb higher. Elevating the top prizes makes the ladder appear longer for higher ranking contestants, and in the limit makes it appear of unbounded length: no matter how far one has climbed, it looks as if there is always the same length to go. Concentrating prize money on the top ranks eliminates the no-tomorrow aspects of competition in the final stages.

Hamilton cycles in sparse robustly expanding digraphs

The notion of robust expansion has played a central role in the solution of several conjectures involving the packing of Hamilton cycles in graphs and directed graphs. These and other results usually rely on the fact that every robustly expanding (di)graph with suitably large minimum degree contains a Hamilton cycle. Previous proofs of this require Szemer\'edi's Regularity Lemma and so this fact can only be applied to dense, sufficiently large robust expanders. We give a proof that does not use the Regularity Lemma and, indeed, we can apply our result to suitable sparse robustly expanding digraphs.Comment: Accepted for publication in The Electronic Journal of Combinatoric

Club guessing and the universal models

We survey the use of club guessing and other pcf constructs in the context of showing that a given partially ordered class of objects does not have a largest, or a universal element

Incentives vs. Selection in Promotion Tournaments: Can a Designer Kill Two Birds with One Stone?

This paper studies the performance of promotion tournaments with heterogeneous participants in two dimensions: incentive provision and selection. Our theoretical analysis reveals a trade-off for the tournament designer between the two goals: While total effort is maximized if less heterogeneous participants compete against each other early in the tournament, letting more heterogeneous participants compete early increases the accuracy in selection. Experimental evidence supports our theoretical findings, indicating that the optimal design of promotion tournaments crucially depends on the objectives of the tournament designer. These findings have important implications for the optimal design of promotion tournaments in organizations.promotion tournaments, heterogeneity, incentive provision, selection

The Stairway to the Top: The Remuneration of Academic Executives

Australian universities have in recent times been undergoing a substantial transformation in the way in which they are managed. They have moved away from the (British-based) traditional collegiate model to one in which professional managers play a centre-stage role. This paper investigates an important element of the managerialism at Australian universities, the market for what we call “academic executives” (AEs). We analyse the remuneration of the top AEs at Australian universities over the past six years and show that institutional size is a dominant driving factor of remuneration, as has been found with compensation of CEOs in the private sector. We also find the pay-size elasticity to be about 0.25 and is the same for both the university and private sectors; and remarkably, this value has also been found in previous studies on executive remuneration for the US and the UK. The remuneration schedule for the university sector is about half as steep as that for the private sector, suggesting that it is a much harder climb to the top of the corporate ladder. We analyse the structure of remuneration among AEs and the Group of Eight universities are found to have a pay parity structure that is closest to that for the private sector.

Using "opposing responses" and relative performance to distinguish empirically among alternative models of promotions

Applying a simultaneous-equations estimation approach that accounts for both worker and firm behavior, I show that six alternative promotion models can be empirically distinguished to a greater extent than previously thought. I show that classic tournaments, market-based tournaments, and performance standards can be sharply distinguished when promotions induce worker effort. I also show that market-based tournaments with effort choices can be sharply distinguished from those with human capital investments. A key insight is that an empirical test can be based on the “opposing responses” property whereby workers and firms adjust their choice variables in opposite directions when the stochastic component of worker performance changes. Finally, I propose a new approach – also requiring simultaneous equations – for empirically distinguishing between classic tournaments and market-based tournaments with human capital investments, showing that the two models differ in their predictions regarding the average wage between job levels.tournaments; promotions; relative performance; internal promotion competitions; wage spreads; tests of tournament theory