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

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 Oligopoly, privatization and strategic trade policy: a note

In debates over privatization and global competition mixed Cournot oligopoly models have been used to show that the presence of a state-owned enterprise in the host country is always associated with a distortionary effect that may justify privatization even if the public firm is just as efficient as its private counterparts. This study argues that this result is valid only under Cournot competition and Cournot competition is not a plausible modelling assumption in this context because in this type of market the firms’ simultaneous play strategies lack credibility.Privatization; Mixed oligopoly; Strategic Trade Policy

Market distortions and public enterprise strategies in an international mixed oligopoly

This study investigates the possible sources of distortions in an international mixed oligopoly. We extend the existing linear/quadratic model to a general framework and show that a public enterprise may either serve as a regulatory device or may itself create an additional level of distortion. Which of these is the case depends critically on the timing of firms output decisions. We then extend the basic quantity setting game to incorporate a preplay stage at which firms can choose the timing of action, rather than moving in an exogenously imposed sequence, in order to determine endogenously the equilibrium sequence of moves. We argue that the distortions associated with a public enterprise and the welfare gain of privatization found in earlier studies can be attributed to an arbitrary and unjustified modeling assumption concerning the order of play, rather than to public ownership.Privatization; International Mixed Oligopoly; Strategic Trade Policy

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

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

MODELS WITH TWO OR MORE PUBLIC GOODS

We extend the simple model of voluntary public good provision to allow for two or more public goods, and explore the new possibilities that arise in this setting. We show that, when there are many public goods, voluntary contribution equilibrium typically generates, not only too low a level of public good provision, but also the wrong mix of public goods. We also analyse the neutrality property in the more general setting, and extend a neutrality proposition of Bergstrom, Blume and Varian (1986). The first author would like to thank Professor Peter Bardsley and the Economic Theory Centre, University of Melbourne, for providing a very congenial period as a visitor, during which this paper was completed.Public goods, Neutrality, Constrained Pareto efficiency

A New Approach to Solving Production-Appropriation Games with Many Heterogeneous Players

We set out a model of production and appropriation involving many players, who differ with respect to both resource endowments and productivities. We write down the model in a novel way that permits our analysis to avoid the proliferation of dimensions associated with the best response function approach as the number of heterogeneous players increases. We establish existence of a unique equilibrium in pure strategies, and carry out some comparative static exercises.conflict, noncooperative games, aggregative games

Existence, Uniqueness and Some Comparative Statics for Ratio- and Lindahl Equilibria: New Wine in Old Bottles

We present a rigorous, yet elementary, demonstration of the existence of a unique Lindahl equilibrium under the assumptions that characterize the standard n-player public good model. Indeed, our approach, which exploits the aggregative structure of the public good model, lends itself to a transparent geometric representation. Moreover, it can handle the more general concept of the cost-share or ratio equilibrium. Finally, we indicate how it may be ex-ploited to facilitate comparative static analysis of Lindahl and cost share equilibria.public goods, Lindahl equilibrium, ratio equilibrium