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In Chapter 9, we explore extensions to the basic model, focusing on Draws, Large Contests, and Entry. Previous chapters assumed contests had one winner, with all others classified as losers. However, alternative outcomes like draws are possible. Draws occur when contestants have equal points or the outcome is inconclusive, as in certain soccer matches, chess games, or wars without a clear winner. They can also happen when prizes are shared or not awarded, like some Nobel Prizes or R&D contests. The chapter examines these extensions, along with equilibrium existence. We display an estimation of a CSF with draws with data from European soccer leagues which is close to one maximizing aggregate effort. In the section on Large Contests, we study scenarios where each contestant feels insignificant in a mass of contestants, such as in official exams, and address the contest as an individual decision problem. Lastly, we discuss complications when contestants can choose among alternative contests. Here, equilibrium existence is not always guaranteed but can occur in specific instances.
Contest theory is an important part of game theory used to analyse different types of contests and conflicts. Traditional microeconomic models focus on situations where property rights are well defined, and agents voluntarily trade rights over goods or produce rights for new goods. However, much less focus has been given to other situations where agents do not trade property rights, but rather fight over them. Contests: Theory and Applications presents a state-of-the art discussion of the economics of contests from the perspective of both core theory and applications. It provides a new approach to standard topics in labour, education, welfare and development and introduces areas like voting, industrial organisation, mechanism design, sport, and military conflict. Using elementary mathematics, this book provides a versatile framework for navigating this growing area of study and serves as an essential resource for its wide variety of applications in economics and political science.
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