Elimination Contests Research Articles

Overconfidence and large executive salaries are linked, with significant implications for HR

PurposeThe purpose of this paper is to argue that large executive compensation can be one of the reasons why so many chief executive officers (CEOs) are overconfident. It also discusses the implications of this finding for boards and human resource directors.Design/methodology/approachThe research investigated how overconfidence – an overestimation of ability – affects how hard people work to win an elimination contest. These kinds of contests exist in the workplace where employees strive for a senior position or CEO role. The study involved a two-stage contest with four players. The first stage consists of two semi-finals. The two semi-final winners move on to compete in the second stage, the final. Overconfident players overestimate the impact of effort on their probability of winning at each stage. Each player is deemed the same, aside from their confidence levels. Finally, the study assumes an overconfident player’s bias is observable by rivals.FindingsOverconfident individuals can have the highest chance of winning elimination contests compared to more rational rivals. When executive pay is high, and overconfidence is not too extreme, they exert more effort than their rational rivals in the semi-finals. High executive pay, or in this case, prize money, is more appealing to overconfident individuals because they think they are more likely to win the bigger prize money in the final. This can be likened to people’s careers. High executive pay incentivises overconfident employees more and they exert more effort early in their careers to achieve this.Originality/valueTo the best of the authors’ knowledge, this is one of the first studies to measure the impact of overconfidence on elimination contests, providing a new explanation for why overconfident employees often reach CEO positions. This has implications for how HR practitioners should manage overconfident and rational employees, including the effort they deliver to a business.

When to use tournament incentives? Evidence from an investment experiment

This paper theoretically and experimentally investigates how different tournament incentives affect managerial decision-making and firm value. Our theoretical model shows that when the economy is in a downturn, linear incentive and elimination contests can ensure that CEO-optimal investment (maximize personal income) is consistent with firm-optimal investment (maximize firm value), while a winner-take-all tournament makes CEO-optimal investment deviate from firm-optimal investment. When the economy is prosperous, a linear incentive and winner-take-all can ensure that CEO-optimal investment is consistent with firm-optimal investment, while elimination contests make CEO-optimal investment deviate from firm-optimal investment. The experimental results broadly support the above predictions. However, elimination contests (winner-take-all) are more efficient than linear incentives when the economy is in a downturn (i.e., prosperous). We conjecture that this result occurs because elimination contests and winner-take-all, which involve interactions between subjects, induce learning effects. In addition, winner-take-all and elimination contests lead to more rational behavior than linear incentives.

Disclosure and Favoritism in Sequential Elimination Contests

We consider a two-stage contest, in which only a subset of contestants enters the finale. We explore the optimal policy for disclosing contestants’ interim status after the preliminary round, i.e., their interim ranking and elimination decision. The optimum depends on the design objective. We fully characterize the conditions under which disclosure or concealment emerges as the optimum. We further allow the organizer to bias the competition based on finalists’ interim rankings, which endogenizes the dynamic structure of the contest. Concealment outperforms in generating total effort, while disclosure prevails when maximizing the expected winner’s total effort. (JEL C72, L22)

Elimination contests with collusive team players

AbstractWe consider a standard two‐stage elimination (Tullock) contest where multiple (team) players can perfectly and publicly collude with each other throughout. We analyze and compare equilibrium outcomes under various seedings where the collusive players meet or are separated in the group stage. We identify the impact of collusion on the contest organizer and non‐collusive players, as well as the organizer's optimal seeding. We find that collusion, while always undermining fairness of the competition, can hurt or benefit the organizer, depending on the discriminatory powers of the two stages. We also discuss issues such as sequential group‐stage competitions, comparison between the elimination contest and the corresponding one‐shot contest, secret collusion, and large discriminatory powers.

Optimal two-stage elimination contests for crowdsourcing

As a new business model, crowdsourcing contest is a means of open innovation. To further improve the efficiency of crowdsourcing contests, two-stage elimination contests are often used as a selection mechanism by firms. This paper explores two forms of elimination mechanisms: sub-elimination and sequential-elimination. Using game theory and auction theory approaches, we model the game between a contest seeker and participants and derive the equilibrium results under these two forms, including the equilibrium decisions and corresponding expected payoff for the contest seeker and the effort strategy at each stage and total expected surplus for all participants. Our results show that: (i) Under both forms, it is optimal to have exactly two participants competing with each other in the final stage; (ii) In equilibrium in the sub-elimination contest, all participants exert more effort in each stage when the number of participants remaining is smaller. The equilibrium effort strategy of high-ability participants has the same trend in a sequential-elimination contest, but the low-ability participant’s equilibrium effort level in the final contest is first decreasing and then increasing in the number of remaining participants; (iii) The optimal two-stage elimination form is sequential-elimination for the contest seeker when compared with no-elimination and sub-elimination because under sequential-elimination, all participants in the second stage will exert more effort, leading to higher-quality solutions. Additionally, we find that this form is also preferred by high-ability participants.

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 budgets in sequential elimination contests

AbstractWe study a sequential elimination contest where contestants (e.g., campaigns) spend resources that are provided by strategic players called backers (e.g., donors). In the unique symmetric equilibrium, backers initially provide small budgets, increasing their contributions only if their contestant wins the preliminary round. If backers are only allowed to provide budgets at the start of the game, as opposed to before each round, spending is higher. When unspent resources are refunded to the backer, total spending is higher than when all resources are sunk costs. We also study an extension of the model with asymmetric players.

Sequential Intragroup Elimination Contests

In this paper, we consider a sequence of multi-prize all-pay auctions, where the contestants who exert the lowest efforts in a round are eliminated. We analyze if and how the behavior of contestants is influenced by the possibility that strong rivals are eliminated along the way. The conditions under which behavior is not influenced are rather restrictive. For cases where these conditions are not met, we derive equilibria in a two-period model. We compare our equilibrium predictions to those of a static model and a two-stage contest where the sequential structure is not announced in the first round.

Coping with complexity – Experimental evidence for narrow bracketing in multi-stage contests

This paper investigates whether decision makers bracket their choices narrowly to facilitate complex decision problems. Evidence from a framing variation of rewards in experimental two-stage pairwise elimination contests indicates that decision makers neglect the option value of participation in future stages of the contest if the reward frame facilitates the separate consideration of stages, but not if the reward frame induces forward-looking behavior. Decision makers account for the option value of participation in future stages of the contest independently of the reward frame, however, when complex strategic interactions in future stages of the contest are replaced by simple lotteries that facilitate the determination of the option value. The results present novel evidence for the prevalence and the determinants of choice bracketing as a means to cope with complexity.

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.

Optimal prize structures in elimination contests

We consider multi-stage elimination contests where agents’ efforts at different stages generate some output for the principal. Depending on the output function various prize structures can be optimal. If the output function depends much more on efforts applied at later stages than on those applied at the earlier ones, the optimal prize structure can be non-monotone, that is, at some stages prizes fall and the agents who are more successful may earn less. Necessary and sufficient conditions for the optimality of such structures are provided. We also show that for any increasing prize shape there exists an output function such that this prize shape is optimal. Further, we consider the case of limited liability, where the principal is not allowed to use negative prizes but can choose a contest success function (CSF). There is always an efficient equilibrium under which the principal is able to extract the full surplus from the agents and the corresponding optimal prize structure is always increasing. Moreover, under some plausible assumptions, the optimal CSF is necessary convex, which corresponds to the most frequently used prize schemes in practice.

How tournament incentives affect asset markets: A comparison between winner-take-all tournaments and elimination contests

We investigate the impact of investment managers׳ tournament incentives on investment strategies and market efficiency, distinguishing between winner-take-all tournaments (WTA), where a minority wins, and elimination contests (EC), where a majority wins. Theoretically, we show that investment managers play heterogeneous strategies in WTA and homogeneous strategies in EC, and markets are more prone to mispricing in WTA than in EC. Experimentally, we find that investment managers play more heterogeneous strategies in WTA than in EC, but this does not trigger significant differences in prices. Moreover, prices in WTA and EC do not differ significantly from markets composed of linearly incentivized subjects.

How Tournament Incentives Affect Asset Markets: A Comparison Between Winner-Take-All Tournaments and Elimination Contests

How Tournament Incentives Affect Asset Markets: A Comparison Between Winner-Take-All Tournaments and Elimination Contests

Optimal prizes in dynamic elimination contests: Theory and experimental evidence

This paper investigates the implications of different prize structures on effort provision in dynamic (two-stage) elimination contests. Theoretical results show that, for risk-neutral participants, a structure with a single prize for the winner of the contest maximizes total effort, while a structure with two appropriately chosen prizes (a runner-up prize and a final prize) ensures incentive maintenance across stages. In contrast, a structure with two prizes may dominate a winner-takes-all contest in both dimensions if participants are risk-averse. Evidence from laboratory experiments is largely consistent with these predictions, suggesting that contest design should account for risk attitudes of participants.

The Role of Information Revelation in Elimination Contests

The Role of Information Revelation in Elimination Contests

CONTESTS WITH STOCHASTIC ABILITIES

We consider the properties of perfectly discriminating contests in which players’ abilities are stochastic, but become common knowledge before efforts are expended. Players whose expected ability is lower than that of their rivals may still earn a positive expected payoff from participating in the contest, which may explain why they participate. We also show that an increase in the dispersion of a player’s own ability generally benefits this player. It may benefit or harm his rival but cannot benefit the rival more than it benefits himself. We also explore the role of stochastic ability for sequential contests with the same opponent (multibattle contests) and with varying opponents (elimination tournaments) and show that it reduces the strong discouragement effects and holdup problems that may otherwise emerge in such games. High own ability dispersion selects such players into the contest and favors them in elimination contests. (JEL D72, D74)

The Role of Information Revelation in Elimination Contests

In this article, we investigate how information revelation rules affect the existence and the efficiency of equilibria in two-round elimination contests. We establish that no symmetric separating equilib rium exists under the full revelation rule and find that the non-existence result is very robust. We then characterise a partially efficient separating equilibrium under the partial revelation rule when players' valuations are uniformly distributed. We finally investigate the no revelation rule and find that it is both most efficient and optimal in maximising the total efforts from the contestants. Within our framework, more information revelation leads to less efficient outcomes. Contests are widely used by various organisations wishing to select the best person or the best team. Sports, for example, are undoubtedly always in the form of contests. Science contests in schools are another example. We can consider a contest as an auction in which players compete for prizes by submitting 'bids'. These 'bids', once submitted, have to be paid regardless of winning or losing. RD (2) in political competition (e.g., for the US presidency), candidates first spend resources to secure their party's nomi nation, and later, if they are nominated, spend more resources to get elected; and (3) science contests among university or high-school students, e.g., the Mathematics Olympiad.'

Strategy in Contests - An Introduction

Competition in which goods or rents are allocated as a function of the various efforts expended by players in trying to win these goods or rents is a very common phenomenon. A subset of examples comes from marketing, litigation, relative reward schemes or promotion tournaments in internal labor markets, beauty contests, influence activities, education filters, R&D contests, electoral competition in political markets, military conflict and sports. I survey here this type of competition which is sometimes called contest or tournament. I focus on the role of its various design aspects, such as prize structure, sequencing, nesting, repetition, elimination contests and many others. Some key insights about the nature and properties of this type of competition emerge from this analysis.

Burning Out in Sequential Elimination Contests

Is it rational for contestants in a sequential elimination contest to expend all their efforts in earlier stages, get burnt out, and have nothing to offer in subsequent stages? This paper identifies three properties of sequential elimination contests which result in burning out: (i) a constraint on aggregate effort across stages or rounds (ii) extreme high-powered incentives in earlier rounds, and (iii) the playing field is even; no contestant is outstanding. I present a model which captures these three features. Burning out is shown to be an equilibrium rational behavior although the ultimate prize is won only if a contestant is successful in all stages including the last stage. I find two burning-out equilibria: a full burning-out equilibrium in which all the contestants burn out and a partial burning-out equilibrium in which some contestants do not burn out. I discuss some applications such as boxing contests, salary caps in the NBA, and incentives in academia.