Adjustment costs and fluctuations in competitions

Abstract 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.