Generalized contest success functions

The key element of models of contest is the contest success function (CSF) which specifies the winning probabilities of agents. The existing axiomatizations of CSFs assume that contestants can make only one type of investment. This paper generalizes these axiomatizations to the case where each agent can have multiple types of investments. This allows us to provide a unified framework to extend and interpret the results of Skaperdas (Econ Theory 7:283–290, 1996) and Clark and Riis (Econ Theory 11:201–204, 1998), and rationalize some seemingly ad hoc CSFs used by applied researchers. This paper has benefitted from the comments of Aicke Hinrichs, Rene Levinsky, and two anonymous referees. We are especially thankful to one of the referees for detailed comments which have helped improve every aspect of this paper.     

Group contest success functions

This paper extends the axiomatic characterization of contest success functions of Skaperdas (Econ Theory 7:283–290, 1996) and Clark and Riis (Econ Theory 11:201–204, 1998) to contests between groups. Comments by Dan Kovenock significantly improved the paper and are gratefully acknowledged. I would also like to thank Pavlo Blavatskyy, Aron Kiss, Kai Konrad, Florian Morath, Dana Sisak, participants of the SFB/TR 15 meeting in Gummersbach 2004, the 2004 meeting of the Verein für Socialpolitik in Dresden, and two anonymous referees. Any errors are mine. Financial support from the Deutsche Forschungsgemeinschaft through SFB/TR 15 is gratefully acknowledged.     

Foundations for contest success functions

In the literature, the outcome of contests is either interpreted as win probabilities or as shares of the prize. With this in mind, we examine two approaches to contest success functions (CSFs). In the first, we analyze the implications of contestants’ incomplete information concerning the ‘type’ of the contest administrator. While in the case of two contestants this approach can rationalize prominent CSFs, we show that it runs into difficulties when there are more agents. Our second approach interprets CSFs as sharing rules and establishes a connection to bargaining and claims problems which is independent of the number of contestants. Both approaches provide foundations for popular CSFs and guidelines for the definition of new ones.

“The strategic approach also seeks to combine axiomatic cooperative solutions and non-cooperative solutions. Roger Myerson recently named this task the ‘Nash program’.”(Rubinstein 1985, p. 1151)

     

Difference-form contest success functions and effort levels in contests

We examine players' equilibrium effort levels in a contest with difference-form contest success functions in which two players compete with each other to win a prize. We show the following. At the pure-strategy Nash equilibrium of a simultaneous-move game, and in the subgame-perfect equilibrium of a sequential-move game, only one of the players expends effort or neither player expends effort. If one player's composite strength is far greater than the other player's, only the player with greater composite strength expends effort whether they move simultaneously or sequentially. If the players' valuations for the prize and their marginal probabilities of winning at (0, 0) are sufficiently small, neither player expends effort whether they move simultaneously or sequentially.     

Uncertain contest success function

In this article, contestants play with a certain probability in Contest A and with the complementary probability in Contest B. This situation is called contest uncertainty. In both contests, effort is additively distorted by a contest noise parameter which affects the sensitivity of the contest success function (CSF). In Contest A (B), this parameter is linearly added to (subtracted from) effort. We analyze the interaction of contest uncertainty and contest noise on contestant behavior and profit. For symmetric contestants, contest noise has an ambiguous effect on effort and profit. We show that more contest uncertainty can imply greater effort. Furthermore, an introduction of an infinitesimal degree of contest uncertainty can have a large impact on effort and profit. Based on the analysis, this article presents the contest organizer's incentive to manipulate the degree of uncertainty in the contest. For profit or effort maximization, the contest organizer should always eliminate any uncertainty. If contestants are asymmetric, more contest noise increases effort as well as competitive balance if both Contests A and B have the same probability of occurrence.     

Endogenous groups and dynamic selection in mechanism design

We create a dynamic theory of endogenous risk sharing groups, with good internal information, and their coexistence with relative performance, individualistic regimes, which are informationally more opaque. Inequality and organizational form are determined simultaneously. Numerical techniques and succinct reformulations of mechanism design problems with suitable choice of promised utilities allow the computation of a stochastic steady state and its transitions. Regions of low inequality and moderate to high wealth (utility promises) produce the relative performance regime, while regions of high inequality and low wealth produce the risk sharing group regime. If there is a cost to prevent coalitions, risk sharing groups emerge at high wealth levels also. Transitions from the relative performance regime to the group regime tend to occur when rewards to observed outputs exacerbate inequality, while transitions from the group regime to the relative performance regime tend to come with a decrease in utility promises. Some regions of inequality and wealth deliver long term persistence of organization form and inequality, while other regions deliver high levels of volatility.     

Anti-dumping measures as a tool of protectionism: A mechanism design approach

In this paper we explore the design of optimal incentive-compatible anti-dumping (AD) measures. When the weight given to the domestic firm's profit in the government's objective function is relatively small, it is shown that no AD duty should be imposed if the foreign firm reports its own costs, but a constant AD duty should be imposed if the domestic firm reports the foreign firm's cost. When this weight is large, in either case of reporting the AD duty is a prohibitive tariff. The optimal AD measures are modified in the presence of a GATT/WTO constraint. JEL Classification: F12, F13
Les mesures anti-dumping en tant qu'outil de protectionnisme: une approche en termes de construction de mécanismes. Ce mémoire examine la construction de mesures optimaales anti-dumping (AD). Quandla valence des profits de la firme domestique est faible dans la fonction objective du gouvernement, on peut montrer qu'aucune mesure AD ne devrait être imposée si l'entreprise étrangère révèle ses propres coûts, mais qu'un droit AD constant devrait être imposé si c'est la firme domestique qui révèle les coûts de l'entreprise étrangère. Quand la valence des profits de la firme domestique est grande, quelle que soit la source de l'information, la mesure AD qui s'impose est un droit de douane prohibitif. Les mesures optimales doivent évidemment être modifiées pour prendre en compte la contrainte engendrée par l'existence des règles du GATT/OMC.     

The cost of inflation: A mechanism design approach

I apply mechanism design to quantify the cost of inflation that can be attributed to monetary frictions alone. In an environment with pairwise meetings, the money demand that is consistent with an optimal, incentive feasible allocation takes the form of a continuous correspondence that can fit the data over the period 1900–2006. For such parameterizations, the cost of moderate inflation is zero. This result is robust to the introduction of match-specific heterogeneity and endogenous participation decisions.     

Contest success functions: an extension

Summary. This note extends the axiomatic characterization of the power success function in fair contests by Skaperdas (1996) to an unfair contest. We show that the results previously obtained are straightforward to generalize; the success function is uniquely characterized by Luces Choice Axiom (implying independence of irrelevant alternatives) and homogeneity of degree zero.Received: July 1, 1996; revised version: October 30, 1996This revised version was published online in February 2005 with corrections to the cover date.     

Contest success functions

Summary Tournaments, conflict, and rent-seeking have been modelled as contests in which participants exert effort to increase their probability of winning a prize. A Contest Success Function (CSF) provides each player's probability of winning as a function of all players' efforts. In this paper the additive CSF employed in most contests is axiomatized, with an independence from irrelevant alternatives property as the key axiom. Two frequently used functional forms are also axiomatized: one in which winning probabilities depend on the ratio of players' efforts and the other in which winning probabilities depend on the difference in efforts.I am grateful to three anonymous referees, Jack Hirshleifer, Guillermo Owen, and especially Duncan Luce for their helpful comments, and to the UC Irvine Academic Senate and the NSF for financial support.     

Total effort, competitive balance and the optimal contest success function

This paper shows that, in the constrained case, the value weighted contest success function (CSF) maximizes not only total effort, but every objective function which is increasing in total effort and competitive balance. In the unconstrained case, a first price all-pay auction with a reserve price is optimal only if the impact of competitive balance on the objective is small. Otherwise, a modified value weighted CSF is optimal.     

Optimal contest design: volume and timing of rent seeking in contests

This paper undertakes a comparative analysis of rent-seeking contests in terms of the amount and the timing of effort they elicit from the participants. The optimal contest structure—the one that maximizes the discounted sum of efforts—is found to hinge on the degree of impatience of the contest organizers, the more patient of whom prefer longer contests consisting of pairwise matches among the contestants. Heterogeneity of the contestants' quality also turns out to play an important role in the comparison.     

Persuasion as a contest

We examine how the probability of persuading an audience depends on resources expended by contending parties as well as on other factors. We use a Bayesian approach whereby the audience makes inferences solely based on the evidence produced by the contestants. We find conditions that yield the well-known additive contest success function, including the logit function. We also find conditions that produce a generalized ??difference?? functional form. In all cases, there are three main determinants of audience choice: (i) the truth and other objective parameters of the environment; (ii) the biases of the audience, and (iii) the resources expended by the interested parties.     

Regulation through a revenue contest

This paper proposes a mechanism for the regulation of duopolies a revenue contests among the firms. Under the mechanism, the firm with the lower revenue is to pay a penalty to the firm with the higher revenue proportional to the difference between their revenues. In a homogenous good Cournot duopoly with convex cost and demand functions, the mechanism implements the optimal outcome when the firms have symmetric costs. When one firm is more efficient, the mechanism leads to increased social surplus under a large set of parameters. We also consider extensions that involve cost uncertainty, repeated games and differentiated goods.     

Equilibria in rent-seeking contests with homogeneous success functions

Summary. We characterize pure-strategy Nash equilibria for symmetric rent-seeking contests in which the contest success function is homogeneous of degree zero. The equilibrium strategies have a simple form. We give sufficient conditions for existence of an equilibrium.Received: 11 February 2003, Revised: 27 August 2004, JEL Classification Numbers: D72. Correspondence to: Andrew J. YatesWe thank Douglas Nelson, Jac Heckelman, and two anonymous referees for helpful comments.     

Level-k reasoning in a generalized beauty contest

We study how the predictive power of level-k models changes as we perturb the classical beauty contest setting along two dimensions: the strength of the coordination motive and the information symmetry. We use a variation of the Morris and Shin (2002) model as the unified framework for our study, and find that the predictive power of level-k models varies considerably along these two dimensions. Level-k models are successful in predicting subject behavior in settings with symmetric information and a strong coordination motive. Their predictive power weakens significantly when either private information is introduced or the importance of the coordination motive is decreased.     

Commentary: Nash equilibrium and mechanism design

I argue that the principal theoretical and practical drawbacks of Nash equilibrium as a solution concept are far less troublesome in problems of mechanism design than in most other applications of game theory.     

Rational functions: an alternative approach to asset pricing

This paper shows that asset prices are linear polynomials of various underlying explanatory factors and asset returns being ratios of these polynomials, are rational functions that do not add linearly when averaging. Hence, average returns should be modeled based on stock prices. However, continuous returns may be treated as approximately linear across time and modeled directly. Our new Rational Function (RF) models, empirically outperform the traditional asset pricing models like the Capital Asset Pricing Model (CAPM) and the Fama–French three and five-factor models for both average and continuous returns. Moreover, the RF theory also provides a model to estimate the asset volumes. The average change in asset volumes together with average returns provide the estimates for average change in market values of assets. Thus, the RF model approach can be used to select assets that provide either highest returns for profit maximization or highest change in market values for wealth maximization for given levels of risk.     

Dynamic specification of demand functions: A cointegration approach

The single-equation approach has been commonly used in the studies of energy demand. However, as most of the data used in the energy demand model are unlikely to be stationary, this factor has to be taken into account when estimating the demand behavior. To overcome this problem, the authors have applied the cointegration and error-correction models to model Chinese coal consumption data. In order to contrast their performance with such traditional models as Hendry's general-to-specific approach, a forecast error comparison exercise has been conducted. In terms ofex post forecast errors, the Engle-Granger error correction model outperforms other chosen models. By using the Engle-Granger approach, it is possible to obtain important information about the behavior of coal demand in China.