Chapter 11 examines the role of institutions. Specifically, it explores how institutions can be undermined by rent-seeking activities that bias decision-making toward suboptimal alternatives and consume valuable resources. Furthermore, this erosion of institutions leads to a decline, or at best stagnation, in the standard of living of the society by diverting a significant portion of productive forces. The chapter presents two models of war in which the armed conflict is produced by resource inequality (the book also acknowledges other types of causes of war like ethnic, religious, etc.) and offers recommendations on how to prevent them. Specifically, a one-sided transfer of resources from wealthy to less developed countries may provide incentives for peace even in the absence of enforceable agreements.

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.

Chapter 6 examines an alternative strategy for increasing the chances of winning in contests, namely sabotage. The chapter provides examples of sabotage in various contexts such as the Luddite movement, the workplace, and political campaigns. It delves into the rational motives for sabotage and studies the determinants of such actions and the individuals or groups that are more likely to be targeted. Contests highly responsive to efforts may create a significant incentive for sabotage, leading to a trade-off between meritocracy and sabotage.

The main CSFs used in the literature are reviewed and their basic properties are explored. Different CSFs yield different games and outcomes, so it is essential to understand the differences between what is embedded in each CSF. In some cases, a little extra effort wins the field, as in racing, while in others, no matter the expense, all contestants receive a positive probability of getting a positive share, as in voting with captive voters. In others, like soccer and some armed conflicts, the probability of winning is proportional to the relative expenses. This chapter also begins an analysis of the existence and properties of a Nash equilibrium in contest games, either with identical contestants or, in the context of a couple of CSFs, with two contestants.

In previous chapters, the CSF is presented as a “black box” that encapsulates the rules and workings of the contest. This chapter explains the mechanisms behind this black box. This could include how efforts may translate, with some uncertainty, into performance, or a planner with given objectives such as designing a contest on television or procuring inputs for a firm. Additionally, the outcome of a conflict may be negotiated or decided by a jury once claims have been presented. Finally, the chapter explores the basic properties that a contest must have, such as the relationship between effort and probability of winning, and how these properties translate into different CSFs. This is known as the axiomatic approach. These different approaches are able to recover some of the main CSFs already presented in the previous chapter.

In Chapter 10, contest models are utilized to illuminate crucial elements of traditional economic problems. These include competition for surplus within divisionalized firms, where inefficient divisions often dominate efficient ones; the significant expenses required to attain a monopoly position, including potentially bribing public officials for the allocation of monopoly rights; and the expenses incurred in obtaining property rights that, once secured (sometimes by violent and costly means), will be efficiently exchanged in the marketplace. In the last two cases, these expenses are so substantial that they might leave no social surplus. Additionally, the cost of political campaigns, in which factions compete for the vote to control a portion or entirety of the public sector through convincing voters of the correct choice, is also examined. Overall, it is shown that contests introduce a substantial and previously unnoticed welfare cost to the traditional issues studied, thereby complementing the existing literature on the subject.

Chapter 5 explores contests among groups, focusing on free-riding issues and the efficacy of group sizes. It also looks at how shares of victory spoils affect contestants’ behavior. Influenced by Mancur Olson’s seminal 1965 work, The Logic of Collective Action, the chapter discusses how stable societies accumulate interest groups. These groups shape government policies, potentially restricting economic growth. The defeat of Germany and Japan in World War II dismantled their key interest groups, unlike in the United Kingdom and the United States, where these groups gained prestige and fueled crony capitalism. The chapter explores how small interest groups can gain significant influence. Olson attributes this to “free riding of effort” in large groups, arguing that smaller groups exert more effort, explaining their success. However, as this chapter discusses, the validity of this assumption depends on several factors, including the nature of the prize – whether it is a private or public good – and the costs associated with exerting effort.

Chapter 8 delves into the complexities introduced by asymmetric information, where some contestants possess more information than others, or neither of the contestants has complete information about the characteristics of the others. The chapter examines contests in which the true common value of the prize may be unknown to certain contestants, such as an incumbent having a better understanding of the value of office than a challenger, or a current resource owner having more information about its true value than potential entrants. It also examines situations where no contestant has complete information about the value assigned for each contestant to the prize, such as companies competing to develop a new product or technology. Each company knows its own valuation of the potential market but does not know the competitor’s valuation. The chapter also analyzes the existence and properties of equilibrium and other related questions, such as the following: How do outcomes in complete and incomplete information scenarios compare? Should a well-informed planner disclose information to maximize total effort in a contest involving both informed and uninformed contestants?

The concept of a contest is introduced, with examples such as political competition, litigation, wars, lobbying, awarding a prize or contract, sports, and patent races. These examples show the wide range of applications of contests, and prepare the reader for the consideration of contests as a field of study in their own right. Additionally, the main game theoretical concepts and the primary tool of this field, the Contest Success Function (CSF), are presented. The CSF, given the expenses/efforts/investments of the contestants, yields the probabilities that the contestants will win the contest or, in the case of a shared prize, the shares of the prize.

Chapter 7 explores contests that occur in stages, as opposed to the one-shot contests analyzed in previous chapters. Examples of one-shot contests include decisive battles in war and final matches in sports. However, some contests are inherently dynamic, such as lengthy wars, electoral competitions, patent races, sports leagues, and advertising campaigns. Dynamic contest theory is still a developing field, and this chapter focuses on analyzing specific examples of dynamic contests, including Endogenous Timing Contests (where contestants choose when to compete), Elimination Contests (where contestants compete and the winner advances to the next stage), Races (where the first contestant to achieve a certain number of victories wins), Contests with Investments (where current efforts impact future outcomes), and Repeated Contests (where contestants compete repeatedly in the same contest).