Joint Production Games with Mixed Sharing Rules

We study Nash equilibria of joint production games under a mixed output sharing rule in which part of the output (the mixing parameter) is shared in proportion to inputs and the rest according to exogenously determined shares. This rule includes proportional sharing and equal sharing as special cases. We show that this game has a unique equilibrium and discuss comparative statics. When the game is large, players unanimously prefer the same value of the mixing parameter: the equilibrium value of the elasticity of production. For this value, equilibrium input and output are fully efficient. Our approach exploits the fact that payoffs in the joint production game are a function only of a player's input and the aggregate input and has indepen-dent interest as it readily extends to other "aggregative games".Production externalities, non-cooperative games

WEAK LINKS, GOOD SHOTS AND OTHER PUBLIC GOOD GAMES: BUILDING ON BBV

We suggest an alternative way of analyzing the canonical Bergstrom-Blume-Varian model of non-cooperative voluntary contributions to a public good that avoids the proliferation of dimensions as the number of players is increased. We exploit this approach to analyze models in which the aggregate level of public good is determined as a more general social composition function of individual gifts – specifically, as a generalized CES form – rather than as an unweighted sum as well as the weakest-link and best-shot models suggested by Hirshleifer. In each case, we characterize the set of equilibria, in some cases establishing existence of a unique equilibrium as well as briefly pointing out some interesting comparative static properties. We also study the weakest-link and best-shot limits of the CES composition function and show how the former can be used for equilibrium selection and the latter to show that equilibria of some better-shot games are identical to those of the much simpler best-shot game.non cooperative games, public goods, weakest links, best shots

Dissipation in Rent-seeking Contests with Entry Costs

This paper considers the extent to which expenditure by contestants in imperfectly discriminating rent-seeking contests dissipates all or only part of the rent. In particular, we investigate strategic effects, technological effects and asymmetry under an assumption of diminishing returns to scale. Although asymmetry can reduce dissipation when there are few contestants, we show that this effect disappears in the Nash equilibria of large contests. Similarly, strategic effects are diminished if the cost of entry, which restricts the number of contestants, is fully taken into account. When individual entry costs fall to zero, the reduction in dissipation arising from technological factors is entirely eliminated in the limit. More generally, the dissipation-reducing properties of all three effects operating simultaneously disappear as individual entry fees fall to zero provided the aggregate cost of entry is added to the expenditure of entrants. These conclusions are robust to details of the entry process which can be sequential, in which case the ordering is irrelevant to the limiting results, or simultaneous. Our principal theoretical tool is the share function which expresses the probability of a player winning the contest as a function of aggregate expenditure. However, this methodology has independent interest as it can be applied in many other contexts (not formally analyzed here).Non-cooperative games, rent-seeking, rent dissipation, entry costs

Joint Production Games with Mixed Sharing Rules

We study joint production games under a mixed sharing rule in which part of the ouput (the mixing parameter) is shared in proportion to inputs and the rest according to exogenously determined shares. We show that this game has a unique Nash equilibrium and discuss comparative statics. When the game is large, we show that players unanimously prefer the same value of the mixing parameter: the equilibrium elasticity of production. At this value, the equilibrium allocation is fully efficient. Our approach heavily exploits the fact that payoffs depend only on a player's input and the aggregate input.production externalities, non-cooperative games

Mixed sharing rules

It is wellknown that a group of individuals contributing to a joint production process with diminishing returns will tend, in equilibrium, to put in too little effort if shares of the output are exogenous, and will put in too much effort if their shares are proportional to their inputs. We consider 'mixed' sharing rules, in which some proportion of the output will be shared exogenously, and the rest proportionally. We examine the efficiency properties of such rules, compare them with serial sharing rules, and suggest a sharing game whose noncooperative equilibrium is, in certain circumstances, Pareto efficientsurplus sharing, cost sharing, aggregative games

Generalized Weiszfeld algorithms for Lq optimization

In many computer vision applications, a desired model of some type is computed by minimizing a cost function based on several measurements. Typically, one may compute the model that minimizes the L₂ cost, that is the sum of squares of measurement errors with respect to the model. However, the Lq solution which minimizes the sum of the qth power of errors usually gives more robust results in the presence of outliers for some values of q, for example, q = 1. The Weiszfeld algorithm is a classic algorithm for finding the geometric L1 mean of a set of points in Euclidean space. It is provably optimal and requires neither differentiation, nor line search. The Weiszfeld algorithm has also been generalized to find the L1 mean of a set of points on a Riemannian manifold of non-negative curvature. This paper shows that the Weiszfeld approach may be extended to a wide variety of problems to find an Lq mean for 1 ≤ q <; 2, while maintaining simplicity and provable convergence. We apply this problem to both single-rotation averaging (under which the algorithm provably finds the global Lq optimum) and multiple rotation averaging (for which no such proof exists). Experimental results of Lq optimization for rotations show the improved reliability and robustness compared to L₂ optimization.This research has been funded by National ICT Australia

Multilingual generation of controlled languages

We describe techniques based on natural language generation which allow a user to author a document in controlled language for multiple natural languages. The author is expected to be an expert in the application domain but not in the controlled language or in more than one of the supported natural languages. Because the system can produce multiple expressions of the same input in multiple languages, the author can choose among alternative expressions satisfying the constraints of the controlled language. Because the system offers only legitimate choices of wording, correction is unnecessary. Consequently, acceptance of error reports and corrections by trained authors are non-issues