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.

Reliability Analysis of a Home-scale Microgrid Based on a Threshold System

The reliability of a microgrid power system is an important aspect to analyze so as to ascertain that the system can provide electricity reliably over a specified period of time. This paper analyzes a home-scale model of a microgrid system by using the threshold system model (inadvertently labeled as the weighted k-out-of-n:G system model), which is a system whose success is treated as a threshold switching function. To analyze the reliability of the system, we first proved that its success is a coherent threshold function, and then identified possible (non-unique) values for its weights and threshold. Two methods are employed for this. The first method is called the unity-gap method and the second is called the fair-power method. In the unity-gap method, we utilize certain dominations and symmetries to reduce the number of pertinent inequalities (turned into equations) to be solved. In the fair-power method, the Banzhaf index is calculated to express the weight of each component as its relative power or importance. Finally, a recursive algorithm for computing system reliability is presented. The threshold success function is verified to be shellable, and the non-uniqueness of the set of weights and thresholds is demonstrated to be of no detrimental consequence, as different correct sets of weights and threshold produce equivalent expressions of system reliability.

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.

The Aims of Just Wars and Jus Ex Bello

The chapter discusses the just aims of defensive wars, and, by implication, the duty to end wars, viz., the jus ex bello. It starts with a discussion of the idea of ‘uncompromising wars’ according to which wars may go on until one’s enemy military forces is completely destroyed. We offer a contractarian argument for a rule that categorically prohibits such wars. We then develop two asymmetries between the justice of resort to war and the justice of continuing it. In particular, we show that the conditions of proportionality and of probability of success function differently in constraining resort to war and in constraining its continuation.

Entry Deterrence, Coordinating Advertising and Pricing in Markets with Consumption Externalities

This paper extends the entry deterrence literature by examining coordinating advertising and pricing in markets with consumption externalities using a stochastic success function. Optimal advertising and pricing strategies are analysed when an incumbent firm faces a challenger with a product of equal quality. I show that strategic entry deterrence using advertising is possible and optimal entry deterrence involves strategic pre-commitment to over-investment relative to the non-strategic simultaneous advertising benchmark. I show that when entry deterrence is not possible the incumbent does not possess a first mover advantage and optimal entry accommodation involves strategic investment in advertising with intensified price competition congruent with the non-strategic simultaneous advertising benchmark. The findings suggest that an incumbent’s ability to deter entry through coordinating advertising in a market with products of equal quality is sensitive to the size of the fixed cost of entry that the challenger must incur and the consumption externality parameter.

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.