Essays in Applied Contest Theory: Round-Robin Tournaments and Innovation Competition
Authors:   , Lauber Arne 
Published: March 2022

A contest is an interaction in which players provide costly and irretrievable effort to win some prize. Many contests are embedded in larger games with manifold dynamic structures where multiple decisions are made by the same player in sequential stages rather than making only one decision in a single stage. This dissertation focuses on the strategic interactions in two distinct dynamic fields: Round-Robin Tournaments and Innovation Competition. Round-robin tournaments are dynamic contests that are sparsely investigated, despite their frequent use in practice. In a round-robin tournament the players are sequentially matched in pair-wise contests and every player meets every other player in turn. Eventually, the players are ranked and awarded according to the number of matches won. Contest designers, particularly in sports, heavily rely on round-robin tournaments in all kinds and sizes, e.g., for organizing team events like the major European soccer leagues with up to 20 teams, or the group stages of Basketball Olympics and FIFA Soccer World Cups with down to three teams. Innovation competition is often considered as a dynamic game. It describes firms' R&D activity within the scope of markets. In other words, there is interdependence between the firms' incentives to innovate and competition. A dynamic game occurs when firms, subsequent to a R&D-Contest, reap their rewards of a successful innovation in terms of a competitive advantage on the product market. In Chapter 2, Christoph Laica, Marco Sahm and I examine the fairness and intensity of sequential round-robin tournaments with multiple prizes and heterogeneous players. A tournament is called fair if the winning probabilities in each match depend only on the player's characteristics but not on the sequence of matches. We show that a tournament with three players is fair in every match if and only if the second prize is valued half of the first prize (with the third prize normalized to zero). For three symmetric players, the fair tournament also maximizes the players' aggregate expected effort if the randomness in the single matches is sufficiently small. Otherwise, the optimal prize structure may be subject to a trade-off between fairness and intensity. For tournaments with more than three players and an exogenously fixed sequence of matches there exists no fair prize structure. Our analysis suggests that almost all major sports events that deploy round-robin tournaments are inherently unfair. In Chapter 3, Marco Sahm and I experimentally reassess our theoretical results on fairness and intensity of round-robin tournaments with three symmetric players by comparing two alternative match formats: while the all-pay auction is perfectly discriminating (no randomness) and always awards the prize to the player with the highest effort, the lottery contest awards the prize randomly such that the probability of winning is given by the ratio between a player's own effort and the aggregate effort of all players. Irrespective of the randomness, we do not find any significant discrimination with respect to overall winning probabilities. This is in line with the equilibrium predictions for lottery contests, but at odds with those of all-pay auctions. Instead of the predicted discouragement effect in tournaments with all-pay auctions, we observe a dissipation-trap: players end up in an effort-intense, final-like last match which significantly reduces payoffs of the late-mover. While we observe over-dissipation, this may explain why intensity in both tournaments does not differ significantly. In Chapter 4, Marco Sahm and I experimentally explore how the prize structure affects intensity, fairness, and dynamic behavior in three-player round-robin tournaments where single matches are organized as all-pay auctions. We compare tournaments with a second prize equal to either 0%, 50%, or 100% of the first prize. We find that aggregate effort is highest in the 0%-tournament while theory predicts the 50%-treatment (0%-treatment) to be the most (least) intense. The main reason is the absence of the predicted discouragement effect of the late-mover in the 0%-tournament. As predicted by theory, we ascertain a fair ranking induced by the 50%-treatment and find support for the late mover disadvantage (advantage) in the 0%-treatment (100%-treatment). In line with theoretical results, players' dynamic behavior is characterized by momentum effects. In particular, we identify a strategic (reverse) momentum: a player increases (decreases) effort after winning (losing) the first match of the 0%-treatment (100%-treatment). A reverse momentum is also detected in the 50%-treatment. However, mixed-strategy equilibrium play can only partly explain this behavior. Our comprehensive analysis suggests that dynamic behavior is also subject to a reverse psychological momentum. In Chapter 5, I examine the effects of a horizontal merger between two firms on the incentives to innovate and on welfare in oligopolistic markets. I develop a dynamic model with innovation competition that shapes subsequent Cournot competition on the product market. I use a lottery contest that allows for a draw to model the innovation competition as a R&D-Contest with a difficulty to successfully innovate that possibly prevents an innovational breakthrough. In the presence (absence) of this difficulty, a successful innovation is uncertain (certain) and innovation effort is considered as (un-)productive. I show that there is a robust domain where mergers enhance the effciency of R&D activity and, thus, total welfare. When effort is unproductive, a merger can reduce undesired duplicative R&D expenses. When effort is productive, a merger with suffciently large R&D synergies in triopolistic markets provides additional ncentives to innovate and increases the probability of a successful innovation.