History has repeatedly shown that periods of military disarmament are often followed by periods of rearmament when new geopolitical tensions arise. This paper analyses the causes of these cycles in a theoretical model. Two competitors compete in a repeated contest. They invest and build up a capital stock to increase their probability of winning each contest. Any positive or negative adjustment of the capital stock inherited from the previous contest leads to additional adjustment costs. Reducing the capital stock can be beneficial, as the upkeep costs of preserving the capital stock are reduced. The analysis reveals that the adjustment costs can create rigidity in the relative strength of the two competitors. This model can explain various phenomena observed in the real world, such as the emergence of peace dividends or dynasties in military conflicts, overinvestment by competitors in sports competitions, and rigidities within educational systems.

Two contestants compete against each other twice in a repeated contest. They invest and build up a human capital stock in order to increase their probability to win a prize in each contest. In the second-period contest, any positive or negative adjustment of the human capital stock inherited from the first-period contest leads to additional adjustment costs similar to the q models in investment theory. We concentrate on contestants’ behavior in the second period for given first-period decisions. We show that contestants optimal second-period behavior depends on the degree of heterogeneity with respect to the inherited capital stocks from the first period as well as on the relative size of the second-period prize and the adjustment costs. The analysis shows that adjustment costs create rigidity with respect to the relative strength of contestants. In addition, adjustment costs may encourage overinvestment by contestants.

Contestants enter a risky contest when pursuing a sports career or choose a secure outside option. If contestants enter this contest but their sports career fails, they may have asymmetric career opportunities outside of sport. Greater opportunities reduce the risk of entering this contest. However, contestants' incentives to exert effort decrease. Two types of equilibria exist if the initial pool of contestants is large. Either only types with high opportunities or only types with low opportunities enter the sports contest. If the initial pool of contestants is low, both types of contestants participate in the contest.

In parallel contests, the contest organizer controls the entry of heterogeneous contestants by regulating access to the contests and determining the prize allocation across contests. The organizer can prevent a contestant from entering more than one contest. I show that the organizer allows entry to multiple contests and uniquely sets identical prizes across contests to maximize aggregate effort in all contests. Independent of the entry regulation, I find no sorting effects. Thus, a contest with a relatively high prize does not necessarily attract contestants with higher abilities. Furthermore, I discover interesting spillover effects of prizes between contests in the case of restricted entry regulations. For instance, the individual (aggregate) effort increases (decreases) in a contest if the prize in another contest increases. The endogeneity of contestants’ participation drives many of these results.

This paper examines the dynamic competition between platform firms in two-sided markets with network externalities. In our model, two platforms compete with each other via a contest to dominate a certain market. If one platform wins the contest, it can serve the market for a certain duration as a monopolistic platform. Our paper shows that platform firms can compensate for cost disadvantages with network effects. A head start (e.g., technological advantage) does not guarantee future success for platform firms. Network effects and cost efficiency are decisive for future success. Interestingly, higher costs of a platform can induce higher platform profits in our dynamic model. Moreover, we find that a platform’s size and profit are not necessarily positively correlated. Our model also provides new insights with respect to the underlying causes for the emergence of market dominance. The combination of technological carry-over and network effects can explain a long-lasting dominance of a platform that benefits from a head start. The necessary preconditions for this emergence are convex costs, small network effects and high carry-over.

We analyze the effects of future liquidity constraints on contestants' investment in a dynamic contest model. Contestants invest in two consecutive contests to win a prize in each period. The loser of the first-period contest can be liquidity-constrained in the second period due to too little remaining wealth. The winner of the first contest can reinvest the prize in the second contest. We show that future liquidity constraints mainly affect the imbalance of the contest in the future but not today. Moreover, larger contest prizes surprisingly decrease contestants' future investments and amplify the imbalance of future contests.

Bonus taxes have been implemented to prevent managers from taking excessive risks. This paper analyzes the effects of taxing executives' bonuses in a principal--agent model. Our model shows that, contrary to its intention, the introduction of a bonus tax intensifies managers' risk-taking behavior and decreases their effort. The principal responds to a bonus tax by offering the manager a higher fixed salary but a lower incentive-based component (bonus rate).

In parallel contests, the contest organizer is able to steer the entry of heterogeneous contestants by determining the prize distribution between the contests and regulating the access to the contests. Regulations can prevent contestants from entering multiple contests. We show in this article that the organizer faces a trade-off between maximizing the individual efforts and maximizing the aggregate efforts. Moreover, the organizer cannot attract high types by offering a relatively large prize in a contest. We also discover spillover effects between contests in the presence of restrictive entry regulations. The individual (aggregate) effort increases (decreases) in a contest if the prize in a neighboring contest is increased.

Analyzing economic models with possibly many arbitrarily heterogeneous agents is an elusive task already in the static case, and even more so in dynamic settings. We propose a novel, systematic approach to analyze such models building on the notion of aggregate-taking behavior. The usefulness of this approach is demonstrated by analyzing a two-stage contest. Our new set of tools allows us to study how changes in the contest design, particularly variations the prize structure or the intensity of the contest, affect the distribution of the equilibrium success chances and profit inequality, without the need to resort to Computer simulations. JEL Classification: D72; D82; C73; C62; C65

Most articles on sports economics presume the well-known Nash equilibrium concept. In this article, however, we apply evolutionary game theory in a sports-contest model. If clubs follow evolutionarily stable strategies (ESS), then ESS generate greater investments and smaller profits than predicted by Nash’s strategies, independent of whether a club is win-maximizing or profit-maximizing. Overdissipation of the rent is possible for Nash strategies and for ESS.

This article describes a large number of contestants with high and low levels of talent who individually decide to enter a contest or take their heterogeneous outside options. We derive a critical condition for which only high types, only low types or both types participate in the contest. If a contest organizer is worried about the type participating in the contest, then he/she should provide a contest with low noise to attract high types. However, if a contest organizer's objective is to maximize the individual effort, he/she will not necessarily prefer to have the high types in the contest.

Using a general two-stage imperfectly discriminatory contest with heterogeneous contestants we study how changes in the contest design, particularly variations in stage-wise contest prizes, affect the distribution of the equilibrium success chances, payoffs, and efforts. Examining the outcome distribution with heterogeneous agents analytically is generally a difficult endeavor, but we develop a new set of tools that provide to be powerful in the analysis of heterogeneity in multi-stage contests. Our heterogeneity tools are greatly useful for studying how variations in the prize structure changes equilibrium incentives and profits in the dynamic contest, and generally give more flexibility to the analysis of a dynamic contest with heterogeneous agents. For example, we derive a conceptualization of the “competitive balance” between several agents in a two-stage contest. JEL Classification: D72; D82; C73; C62; C65

This paper analyzes spillover effects in sports leagues that are embedded in a system of promotion and relegation. Based on a contest model of a professional sports league with a top division and a second division, we show that league prizes and club efficiencies have opposing effects; while a stronger second division that offers a higher league prize leads to a more balanced top division, the opposite is true for a stronger second division whose clubs become more cost efficient. Moreover, we demonstrate that a higher second-division prize induces a lower investment level, but higher profits in the top division, while higher club efficiency in the second division leads to both a lower investment level and lower profits in the top division. These results have important policy implications for the organization of sports leagues.

In this article, contestants play with a certain probability in Contest A and with the complementary probability in Contest B. This situation is called contest uncertainty. In both contests, effort is additively distorted by a contest noise parameter which affects the sensitivity of the contest success function (CSF). In Contest A (B), this parameter is linearly added to (subtracted from) effort. We analyze the interaction of contest uncertainty and contest noise on contestant behavior and profit. For symmetric contestants, contest noise has an ambiguous effect on effort and profit. We show that more contest uncertainty can imply greater effort. Furthermore, an introduction of an infinitesimal degree of contest uncertainty can have a large impact on effort and profit. Based on the analysis, this article presents the contest organizer's incentive to manipulate the degree of uncertainty in the contest. For profit or effort maximization, the contest organizer should always eliminate any uncertainty. If contestants are asymmetric, more contest noise increases effort as well as competitive balance if both Contests A and B have the same probability of occurrence.

This paper develops a model of a cooperative enterprise and compares it to a vertically separated market. In our model of a multi‐stage production process, agents can acquire costly knowledge to decrease production costs. Our model shows that the cooperative acquires less non‐generalizable knowledge than the market, but more generalizable knowledge if the large member in the cooperative receives a sufficiently large share of the cooperative's profits. Additionally, we derive that the cooperative generates larger aggregate surplus than the market if the influence of generalizable knowledge on production costs is large. Copyright © 2012 John Wiley & Sons, Ltd.

Several countries have implemented bonus taxes for corporate executives in response to the financial crisis of 2007-2010. Using a principal-agent model, this paper investigates the incentive effects of bonus taxes by analyzing the agent's and principal's behavior. Specifically, we show how bonus taxes affect the agent's incentives to exert effort and the principal's decision regarding the composition of the compensation package (fixed salary and bonus rate). We find that, surprisingly, a bonus tax can increase the bonus rate and decrease the fixed salary. In addition, a bonus tax can induce the principal to pay higher bonuses even though the agent's effort always decreases.

We consider two bidders with asymmetric valuations competing to win an exogenous prize. Capital markets are imperfect, such that the contestants possibly face a liquidity constraint. We show that aggregate investments are lower if at least one bidder has a liquidity constraint, even if the low-valuation bidder possibly increases his/her investments. Furthermore, the effect of the high-valuation bidder’s liquidity constraint on competitive balance is ambiguous. However, if the low-valuation bidder is constrained, greater wealth unambiguously increases competitive balance. Surprisingly, if the low-valuation bidder has a constraint, a tighter constraint can increase his/her profit.

Professional sports leagues have witnessed the appearance of so-called "sugar daddies" - people who invest enormous amounts of money into clubs and become their owners. This paper presents a contest model of a professional sports league that incorporates this phenomenon. We analyze how the appearance of a sugar daddy alters competitive balance and social welfare compared to a league with purely profit-maximizing club owners. We further show that the welfare effect of revenue sharing in a sugar daddy league is ambiguous and depends on the degree of redistribution and on whether the sugar daddy invests in a small or large club.

Several countries have implemented bonus taxes for corporate executives in response to the financial crisis of 2007-2010. Using a principal-agent model, this study analyzes how bonus taxes affect the agent’s effort, compensation package, tax revenue and social welfare. We show that, contrary to its intention, a bonus tax may even increase the pay-performance sensitivity and decrease the fixed salary component. In addition, a bonus tax can induce the principal to pay higher bonuses even though the agent’s effort always decreases. Finally, a bonus tax decreases social welfare unless the social planner puts a sufficiently high weight on tax revenue.