1.1 Background
To gain enhanced legitimacy, theories need axiomatic foundations. Building on such foundations, further statements and relationships can be derived. Rent seeking plays a substantial role in practice, by individuals and groups. Rent seeking can be competition, lobbying, influence campaigns, strategic maneuvers, and advertisements. Examples of rent seeking are competition between groups for budgets, privileges, election opportunities, economic benefits, rights of various kinds, licenses, and Research & Development budgets. Examples of groups are interest groups, collective business units seeking profit, cooperative working groups seeking some kind of end product, political groups, and ideological groups. The literature has clarified the differences between additive and multiplicative efforts, and has axiomatized such efforts. Group contest success functions, however, have not been axiomatized, which is the purpose of this article.
1.2 Contribution
This article’s research question is to determine which axioms apply for group contest success functions, assuming both additive and multiplicative production functions. The research methodology is to review axioms for group contest success functions for general production functions accounting for addition, exponentiation, and multiplication, as expressed by the additive production function and the Cobb-Douglas production function. This article’s contribution is to clarify which existing axioms apply and how they apply. The research is urgent since any theory needs clarification of its axiomatic foundations to justify its continued existence. For contest success functions recent research discussed below has clarified the different implications of additive as opposed to multiplicative production functions. These implications become even more important to clarify for contests between groups rather than individuals since groups consist of members exerting efforts which can be aggregated additively or multiplicatively.
A contest between groups is just as a contest between individuals except that each group is composed of multiple members. A group’s production function sums up the production of all the members within the group. Each group member exerts one effort. That differs from analyses in the literature where each individual exerts multiple additive efforts, which are thus added in the production function. A contest between groups where each group member in each group exerts one effort is thus partly related to a contest between individuals where each individual exerts multiple efforts. The relationship is not straightforward, as illustrated in this article.
A common example in the rent seeking literature, e.g. by Krueger (1974), is that a firm may seek rents through improved efficiency or lobbying. These rent seeking efforts are additive if rent seeking is operational if one of these efforts is present, regardless of whether the other effort is present or not. In contrast, the rent seeking efforts are multiplicative, e.g. as in the Cobb-Douglas production function, if rent seeking is operational if both efforts are present.
When focusing exclusively on the contest success function,1 additive efforts can be interpreted as substitutable, so that employing more of one effort decreases the need for the other effort, while multiplicative efforts can be interpreted as complementary, so that employing more of one effort increases the need for the other effort.2
One example of additive efforts is competition for privileges which are such that many different kinds of efforts are possible to obtain the privileges. The rent seeker may apply its various strengths, which all add up to the total rent seeking effort, and obtain the privileges in multifarious ways. One example of multiplicative efforts is competition for R&D budgets where multiple efforts have to be jointly present, e.g. focus on scientific value, implementation, and impact. See Hausken (2020a, 2020b) for further examples of additive and multiplicative efforts, and Arbatskaya and Mialon (2010) for examples of multiplicative efforts.