Axiomatizing additive multi-effort contests

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.

Success in contests

Models 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.

Focality and Asymmetry in Multi-battle Contests

This article examines the influence of focality in Colonel Blotto games with a lottery contest success function, where the equilibrium is unique and in pure strategies. We hypothesize that the salience of battlefields affects strategic behaviour (the salient target hypothesis) and present a controlled test of this hypothesis against Nash predictions, checking the robustness of equilibrium play. When the sources of salience come from asymmetries in battlefield values or labels (as in Schelling, 1960), subjects over-allocate the resource to the salient battlefields relative to the Nash prediction. However, the effect is stronger with salient values. In the absence of salience, we find support for the Nash prediction.

Group Contest Success Function: The Heterogeneous Individuals Case

This paper extends the axiomatic characterization of the group contest success function in [Münster, J. [2009] Group contest success functions, Econ. Theory 41(2), 345–357] to groups with heterogeneous individuals (e.g., individuals with different skills or different cognitive capacities). The obtained function allows for differences in terms of effort effectiveness between the group individuals and differences in terms of returns to scale at the aggregate level.

A new stress–strength model for systems subject to stochastic shocks

A new general approach for obtaining system survival probability under the Poisson shock process is suggested. It takes into account the explicitly defined distribution of shock magnitude (stress) and system strength deterioration caused by the previous shocks. The approach can be used for any form of stress distribution, strength deterioration function and stress–strength interplay model. Specifically, we use the contest success function to model the stress–strength interplay and a cumulative stress ratio form function to represent strength deterioration. Numerical examples illustrating the obtained results are presented.

Nonparasitic warlords and geographic distance

The explicit consideration of geography in the conflict theory literature is still relatively rare. In this article, two warlords are modeled as being located at opposing ends of a hypothetical line. The model includes variables denoting distance and difficulty of terrain. Each warlord allocates resources to the extraction of natural resources, to the production of goods and services (hence, nonparasitic), and to conflict with the opposing warlord. Two forms of a contest success function, a primary tool in the literature, are used to show that the warlord closer to the point of conflict will invest less into the hiring of warriors and more into the production of goods and services, yet will win a larger proportion of total goods and services produced within the economy. [JEL codes: D74, O17]