scholarly journals Success in contests

2021 ◽  
Author(s):  
David K. Levine ◽  
Andrea Mattozzi
Keyword(s):  
Political Economy ◽  
Production Function ◽  
Theory Of The Firm ◽  
Contest Success Function ◽  
Existence Of Equilibrium ◽  
Success Function

AbstractModels of two contestants exerting effort to win a prize are very common and widely used in political economy. The contest success function plays as fundamental a role in the theory of contests as does the production function in the theory of the firm, yet beyond the existence of equilibrium few general results are known. This paper seeks to remedy that gap.

scholarly journals Axiomatizing additive multi-effort contests

2021 ◽  
Vol 1 (11) ◽  
Author(s):  
Kjell Hausken
Keyword(s):  
Production Function ◽  
Rent Seeking ◽  
Production Functions ◽  
Contest Success Function ◽  
Additive Production ◽  
Success Function ◽  
Douglas Production Function

AbstractA 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.

scholarly journals Revenue Sharing, Competitive Balance and the Contest Success Function

2011 ◽  
Vol 12 (3) ◽  
pp. 256-273 ◽  
Author(s):  
Marco Runkel
Keyword(s):  
Revenue Sharing ◽  
Competitive Balance ◽  
Contest Success Function ◽  
Success Function

Abstract This paper investigates revenue sharing in an asymmetric two-teams contest model of a sports league with Nash behavior of team owners. The innovation of the analysis is that it focuses on the role of the contest success function (CSF). In case of an inelastic talent supply, revenue sharing turns out to worsen competitive balance regardless of the shape of the CSF. For the case of an elastic talent supply, in contrast, the effect of revenue sharing on competitive balance depends on the specification of the CSF. We fully characterize the class of CSFs for which revenue sharing leaves unaltered competitive balance and identify CSFs ensuring that revenue sharing renders the contest closer.

Pareto and the Wicksell–Cobb–Douglas Functional Form

1998 ◽  
Vol 20 (2) ◽  
pp. 203-210 ◽  
Author(s):  
Christian E. Weber
Keyword(s):  
Political Economy ◽  
Economic Analysis ◽  
Utility Function ◽  
Production Function ◽  
Functional Form ◽  
French Translation ◽  
Joseph Schumpeter

It is understood that Charles Cobb and Paul Douglas (1928) were not the first to use the production function named after them. Joseph Schumpeter (1954, p. 1042), Carl-Axel Olsson (1971), and Henry Spiegel (1991, p. 816) all note that the production function Y = AKαL1-α had been used by Knut Wicksell (1901, 1906) more than twenty years before Cobb and Douglas published their study. While it is quite possible that Wicksell was the first to use the Cobb-Douglas functional form to study production, he was not the first to apply it to economic analysis in general. Vilfredo Pareto had worked out several implications of a specific version of the Cobb-Douglas utility function as early as 1892. Later, he repeated and extended this analysis in the mathematical appendix to the French translation of his Manual of Political Economy (1909).

The Optimal Accuracy Level in Asymmetric Contests

2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Zhewei Wang
Keyword(s):  
Discriminatory Power ◽  
Contest Success Function ◽  
Equilibrium Set ◽  
Accuracy Level ◽  
Success Function ◽  
Optimal Accuracy ◽  
Asymmetric Contests ◽  
The Difference

We interpret the discriminatory power, r, in the Power Contest Success Function (Tullock, 1980) as the contest designer's accuracy level. We look at the cases where two contestants are heterogeneous in ability and construct an equilibrium set for r > 0. We find that if the contestants are sufficiently different in ability, there always exists an optimal accuracy level for the contest designer. Additionally, as the difference in their abilities increases, the optimal accuracy level decreases.

scholarly journals ON THE IMPOSSIBILITY OF DETERRENCE IN SEQUENTIAL COLONEL BLOTTO GAMES

2012 ◽  
Vol 14 (02) ◽  
pp. 1250011 ◽  
Author(s):  
KJELL HAUSKEN
Keyword(s):  
Resource Constraints ◽  
Rent Seeking ◽  
Contest Success Function ◽  
Resource Constrained ◽  
Common Ratio ◽  
Unit Effort ◽  
Success Function ◽  
Colonel Blotto ◽  
The Common ◽  
Colonel Blotto Games

A sequential Colonel Blotto and rent seeking game with fixed and variable resources is analyzed. With fixed resources, which is the assumption in Colonel Blotto games, we show for the common ratio form contest success function that the second mover is never deterred. This stands in contrast to Powell's (Games and Economic Behavior67(2), 611–615) finding where the second mover can be deterred. With variable resources both players exert efforts in both sequential and simultaneous games, whereas fixed resources cause characteristics of all battlefields or rents to impact efforts for each battlefield. With variable resources only characteristics of a given battlefield impact efforts are to win that battlefield because of independence across battlefields. Fixed resources impact efforts and hence differences in unit effort costs are less important. In contrast, variable resources cause differences in unit effort costs to be important. The societal implication is that resource constrained opponents can be expected to engage in warfare, whereas an advantaged player with no resource constraints can prevent warfare.

scholarly journals The effect of within-group inequality in a conflict against a unitary threat

2012 ◽  
Vol 18 (3) ◽  
Author(s):  
Maria Cubel ◽  
Santiago Sanchez-Pages
Keyword(s):  
Cost Function ◽  
Contest Success Function ◽  
Individual Income ◽  
Atkinson Index ◽  
Success Function ◽  
External Threat ◽  
Index Of Inequality ◽  
The Cost ◽  
Individual Effort ◽  
Group Inequality

AbstractA group of agents must defend their individual income from an external threat by pooling their efforts against it. The winner of this confrontation is determined by a contest success function where members’ efforts display a varying degree of complementarity. Individual effort is costly and its cost follows a convex isoelastic function. We investigate how the success of the group in the conflict and its members’ utilities vary with the degree of within-group inequality. We show that there is a natural relationship between the group’s probability of victory and the Atkinson index of inequality. If members’ efforts are complementary or the cost function convex enough, more egalitarianism within the group increases the likelihood of victory against the external threat. The opposite holds when members’ efforts are substitutes and the cost linear enough.

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