Sad-Loser contests

We consider asymmetric winner-reimbursed contests. It turns out that such contests (Sad-Loser) have multiple internal pure-strategy equilibria (where at least two players are active). We describe all equilibria and discuss their properties. In particular, we find (1) that an active player is indifferent among all her non-negative choices and her expected payoff is zero in any internal equilibrium, (2) that a higher-value (stronger) player always spends less than a lower-value (weaker) player and therefore always has a lower chance to win a Sad-Loser contest in any internal equilibrium, and (3) a sufficient condition for a net total spending to be higher in a Sad-Loser contest than in the corresponding asymmetric contest.     

When does universal peace prevail? Secession and group formation in conflict

This paper analyzes secession and group formation in the general model of contests due to Esteban and Ray (1999). This model encompasses as special cases rent seeking contests and policy conflicts, where agents lobby over the choice of a policy in a one-dimensional policy space. We show that in both models the grand coalition is the efficient coalition structure and agents are always better off in the grand coalition than in a contest among singletons. Individual agents (in the rent seeking contest) and extremists (in the policy conflict) only have an incentive to secede when they anticipate that their secession will not be followed by additional secessions. Incentives to secede are lower when agents cooperate inside groups. The grand coalition emerges as the unique subgame perfect equilibrium outcome of a sequential game of coalition formation in rent seeking contests. Received: March 2004, Accepted: October 2004, JEL Classification: D72, D74 We thank Joan Maria Esteban, Kai Konrad, Debraj Ray, Stergios Skaperdas and two anonymous referees for helpful comments on the paper. We also benefitted from comments by seminar participants in Barcelona, Istanbul, Paris and WZB Berlin.     

Time Discounting in Strategic Contests

In many contests, such as political campaigns or R&D expenditures, there is at least some trade‐off between immediate money outlay and potential future benefits. This timing aspect has mostly been ignored by the contest literature. If contestants exhibit a strong present bias, such as that shown by past individual choice experiments, then benefits that are deferred to the future will lead to a significant drop in investment. This paper uses controlled laboratory experiments to explore how the timing of prize payment impacts behavior in a contest with a unique Nash equilibrium strategy. We find no evidence that people significantly discount future prizes in our contests, despite the fact that we do replicate present bias in a separate individual choice experiment.     

Lobbying contests with alternative instruments

This is a model of a contest where, in order to win, each opponent can use two instruments. The probabilities of winning are explored, as well as the expenditures of the interest groups, and the relative rent-dissipation in both cases where the players have the option to use only one instrument (the standard Tullock contest) and where the players have the option to use two instruments in the contest. We show that the use of two instruments strengthens the player with the higher stake, decreases the relative rent dissipation and it decreases total expenditure if the parties are sufficiently asymmetric. Received: February 23, 2001 / Accepted: March 25, 2002 RID="*" ID="*" We are grateful to two anonymous referees and the editor Kai Konrad, for constructive comments.     

MULTIPLE-PRIZE CONTESTS – THE OPTIMAL ALLOCATION OF PRIZES

Abstract.  Multiple-prize contests are important in various fields of economics ranging from rent seeking over labour economics, patent and R&D races to tendering for (governmental) projects. Hence it is crucial to understand the incentive effects of multiple prizes on effort investment. This survey attempts to outline, compare and evaluate the results from the literature. While a first prize always results in a positive incentive to invest effort, second and later prizes lead to ambiguous effects. Depending on the objective function, the characteristics of the individuals and the type of contest a different prize allocation is optimal.     

Efficient Contests

In their seminal contribution, Lazear and Rosen (1981) show that wages based upon rank induce the same efficient effort as incentive‐based reward schemes. They also show that this equivalence result is not robust toward heterogeneity in worker ability, as long as ability is private information because it is not possible to structure contests to simultaneously satisfy self‐selection constraints and first‐best incentives. This paper demonstrates that efficiency can be achieved by a simple modification of the prize scheme in a mixed (heterogenous) contest where contestants learn their type after entry. If contestants know their type before entering the contest, rent extraction becomes an issue. Implications for optimal contest design are also explored. Finally, the relationship between effort maximizing contests and profit maximizing contests are discussed.     

Contests with multiple alternative prizes: Public-good/bad prizes and externalities

We study contests in which there are multiple alternative public-good/bad prizes, and the players compete, by expending irreversible effort, over which prize to have awarded to them. Each prize may be a public good for some players and a public bad for the others, and the players expend their effort simultaneously and independently. We first prove the existence of a pure-strategy Nash equilibrium of the game, then establish when the total effort level expended for each prize is unique across the Nash equilibria, and then summarize and highlight other interesting and important properties of the equilibria. Finally, we discuss the effects of heterogeneity of valuations on the players’ equilibrium effort levels and a possible extension of the model.     

Optimal risk taking in an uneven tournament game with risk averse players

We analyze the optimal choice of risk in a two-stage tournament game between two players that have different concave utility functions. At the first stage, both players simultaneously choose risk. At the second stage, both observe overall risk and simultaneously decide on effort or investment. The results show that those two effects which mainly determine risk taking – an effort effect and a likelihood effect – are strictly interrelated. This finding sharply contrasts with existing results on risk taking in tournament games with symmetric equilibrium efforts where such linkage can never arise. Conditions are derived under which this linkage leads to a reversed likelihood effect so that the favorite (underdog) can increase his winning probability by increasing (decreasing) risk which is impossible in a completely symmetric setting.     

Two-stage elimination contests with optimal head starts

We study two-stage elimination Tullock contests. In the first stage all the players compete against each other; then some advance to the second stage while the others are removed. The finalists compete against each other in the second stage, and one of them wins the prize. To maximize the expected total effort, the designer can give a head start to the winner of the first stage when he competes against the other finalists in the second stage. We show that the optimal head start, independent of the number of finalists, always increases the players’ expected total effort. We also show how the number of players and finalists affect the value of the optimal head start.     

Strategic attractiveness and release decisions for cultural goods

We study how producers of cultural goods can strategically invest in raising the attractiveness of their goods in order to secure the most profitable release dates. In a game‐theoretic setting, where two producers choose their investment expenditure before simultaneously setting the release date of their good, we prove that two equilibria are possible: releases are either simultaneous (at the demand peak) or staggered (one producer delays). In the latter equilibrium, the first‐mover secures its position by investing more in attractiveness. We test this prediction on a dataset of more than 1500 American movies released in 10 countries over 12 years. Results are consistent with the theoretical predictions, indicating that higher budget movies are released closer to seasonal demand peaks.     

Rent seeking and the value of time

This paper focuses on the question of how rivals’ rent-seeking expenditures and investment expenditures are affected by the temporal dimension of those cash flows as well as the timing of the cash flow of monopoly rents. The paper applies methods from statistical reliability theory to derive five propositions establishing the conditions that must be satisfied if the rivals apportion their rent seeking and investment expenditures to maximize their certainty equivalents of the monopoly rent. The propositions explicate the responses of the rivals to changes in economic parameters characterizing the rent-seeking contest such as a change in the duration of the monopoly rent cash flow or a change in the number of rivals.     

Bargaining through Approval

The paper considers two-person bargaining under Approval Voting. It first proves the existence of pure strategy equilibria. Then it shows that this bargaining method ensures that both players obtain at least their mean utility level in equilibrium. Finally it proves that, provided that the players are partially honest, the mechanism triggers sincerity and ensures that no alternative Pareto dominates the outcome of the game.     

Product Differentiation, Strategic Divisionalization, and Persistence of Monopoly

This paper analyzes the strategic incentive of oligopolists to create autonomous rival divisions when products are differentiated. We consider a two-stage game where firms choose the number of autonomous divisions in the first stage and all the divisions engage in Cournot competition in the second. It is shown that product differentiation ensures the existence of an interior subgame perfect Nash equilibrium (SPNE), and the equilibrium number of divisions increases with the degree of substitution among products and the number of firms. Further, if divisions are allowed to divide further, they always will, which leads to total rent dissipation. Thus, parent firms have incentives to unilaterally restrict their divisions from further dividing. In the free-entry equilibrium, it is found that the possibility of setting up autonomous divisions is a natural barrier to entry. Incumbents may persistently earn abnormally high profits. In the cases where product differentiation is difficult, the only pure-strategy free-entry SPNE is the monopoly outcome even if the entry cost is relatively low.     

Optimal contest design under reverse-lottery technology

In this paper, we study effort-maximizing contest design under the “reverse” nested lottery contest model of Fu et al. (2014) — which is the “mirror image” of the conventional nested lottery contest of Clark and Riis (1996). We show that under the reverse-lottery technology, a single-stage winner-take-all grand contest dominates all other feasible designs when the contest is sufficiently noisy. This result is in dramatic contrast to the conventional wisdom on the optimality of multistage elimination contests that is grounded under the conventional nested lottery contest technology in the literature. In the framework of a noisy-performance ranking model, the conventional and reverse models differ only in the noise on players’ performance. Our study therefore reveals the important role that the noise term plays in modeling imperfectly discriminatory contests.     

Reimbursement as a tool to reduce sabotaging in rent‐seeking contests

We study standard rent‐seeking contests with reimbursement and sabotaging. This study is conducted for a symmetric model with complete information. We show that changing the contest mechanism by applying a form of reimbursement could be an effective tool against sabotaging, in addition to the fact that it increases contest designer revenue. Simple changes such as sufficient reimbursement to winners/losers might completely stop sabotaging efforts in the contest.     

Deadlines in stochastic contests

We consider a two-player contest model in which breakthroughs arrive according to privately observed Poisson processes. Each player’s process continues as long as she exerts costly effort. The player who collects the most breakthroughs until a predetermined deadline wins a prize.We derive Nash equilibria of the game depending on the deadline. For short deadlines, there is a unique equilibrium in which players use identical cutoff strategies, i.e., they continue until they have a certain number of successes. If the deadline is long enough, the symmetric equilibrium distribution of an all-pay auction is an equilibrium distribution over successes in the contest. Expected efforts may be maximal for a short or intermediate deadline.     

Two-stage contests with effort-dependent values of winning

We study two-stage all-pay contests in which synergy exists between the stages. The value of winning for each contestant is fixed in the first stage while it is effort-dependent in the second one. We assume that a player’s effort in the first stage either increases (positive synergy) or decreases (negative synergy) his value of winning in the second stage. The subgame perfect equilibrium of this contest is analyzed with either positive or negative synergy. We show, in particular, that whether the contestants are symmetric or asymmetric their expected payoffs may be higher under negative synergy than under positive synergy. Consequently, they prefer smaller values of winning (negative synergy) over higher ones (positive synergy).     

Real options game models of R&D competition between asymmetric firms with spillovers

Using real options game models, we consider the characterization of strategic equilibria associated with an asymmetric Research and Development (R&D) race between an incumbent firm and an entrant firm in the development of a new innovative product under market and technological uncertainties. The random arrival time of the discovery of the patent protected innovative product is modeled as a Poisson process. Input spillovers on the R&D effort are modeled by the change in the leader’s hazard rate of success of innovation upon the follower’s entry into the R&D race. Asymmetry between the two competing firms include sunk costs of investment, stochastic revenue flow rates generated from the product, and hazard rates of arrival of success of R&D efforts of the two firms. Under asymmetric duopoly, we obtain the complete characterization of the three types of Markov perfect equilibria (sequential leader–follower, preemption and simultaneous entry) of the firms’ optimal R&D entry decisions with respect to various sets of model parameters. Our model shows that under positive input spillover, preemptive equilibrium does not occur in the R&D race due to the presence of dominant second mover advantage. The two firms choose optimally to enter simultaneously if the sunk cost asymmetry is relatively small; otherwise, sequential equilibrium would occur. When the initial hazard rate is low relative to the level of input spillover, simultaneous entry would occur as an optimal decision, signifying another scenario of dominant second mover advantage. On the other hand, when the initial hazard rate is sufficiently high so that the first mover advantage becomes more significant, simultaneous equilibrium does not occur even under high level of positive input spillover.     

Relative performance as a strategic commitment mechanism

Can managers' personality traits be of use to profit maximizing firm owners? We investigate the case where managers have a variety of attitudes toward relative performance that are indexed by their type. We consider two stage games where profit maximizing owners select managers in the first stage, and these managers, knowing each other's types, compete in a duopoly game in the second stage. The equilibria of various types of competition are derived and comparisons are made to the standard case where managers are profit maximizers. We show that managers' types can be used as a strategic commitment device that can increase firm profits in certain environments. Copyright © 2002 John Wiley & Sons, Ltd.     

Investment and concern for relative position

Economists typically analyze individuals' market behavior in isolation from their nonmarket decisions. While this research strategy has generally been successful, it can lead to systematic errors when agents' nonmarket behavior affects their market choices. In this paper we analyze how individuals' investment behavior changes as a result of nonmarket behavior. Specifically, we analyze a model in which individuals must decide how to allocate their initial endowment between two random investments, where the returns are perfectly correlated across individuals for the first investment but independent across individuals for the second. We consider an environment in which men and women match, with wealthier individuals more successful in matching. We show how individuals' concern about relative wealth can affect their investment decisions, and we provide conditions under which individuals bias their investments either toward or away from the investment with correlated returns. A modification of the model is used to explain why agents' investments might exhibit a home country bias.