Axiomatizing additive multi-effort contests

Kjell Hausken

doi:10.1007/s43546-021-00155-5

Abstract

A rent seeking model is axiomatized where players exert multiple additive efforts which are substitutable in the contest success function. The axioms assume the sufficiency of exerting one effort, and that adding an amount to one effort and subtracting the same amount from a second equivalent substitutable effort keeps the winning probabilities unchanged. In contrast, the multiplicative Cobb–Douglas production function in the earlier literature requires players to exert all their complementary efforts. The requirement follows from assuming a homogeneity axiom where an equiproportionate change in two players’ matched efforts does not affect the winning probabilities. This article abandons the homogeneity axiom and assumes an alternative axiom where the winning probabilities remain unchanged when a fixed positive amount is added to all players’ efforts. This article also assumes a so-called summation axiom where the winning probabilities remain unchanged when a player substitutes an amount of effort from one effort into another effort. The summation axiom excludes multiplicative production functions, and furnishes a foundation for additive production functions.

Highlights

BackgroundAxiomatization within the contest literature has progressed gradually
Axioms and lemmas are developed for rent seeking where two players exert multiple additive efforts
The implication for theory is that the satisfied axioms assume the sufficiency of exerting one effort under certain conditions, because efforts can substitute for each other

Summary

Background

Axiomatization within the contest literature has progressed gradually. Axioms ensure solid, consistent, theoretical foundations from which other statements are logically derived. An example is competition for elected office applying political strategists, campaigners, media operatives, speech writers, advertisements, ground troops speaking with people, etc. Whereas multiplicative efforts complement each other, additive efforts substitute each other in the contest success function. When multiplying the contest success function with the rent, and subtracting the expenditure of exerting efforts, a new function arises where multiple efforts can be substitutes, complements, or neither substitutes nor complements. 24) state for multiplicative efforts that firms may obtain rents from the government by improved efficiency, or by lobbying or bribery. The article assumes that efforts may differ regarding unit costs, impacts, and contest intensities. Different contest intensities are not commonly analyzed in the literature

Literature

= 1 . Appendix D generalizes summation applying Axioms

Conclusion