Tullock Contest Research Articles

Tullock contest alliances with proportional prize-sharing agreements: private collective action mechanisms?

Tullock contest alliances with proportional prize-sharing agreements: private collective action mechanisms?

공공재적 상(prizes)을 갖는 Tullock 집단 경합 모형에 대한 소고

The rent-seeking contest theory of Tullock has been deriving a lot of studies on competitions between individuals and/or groups in various settings. Among them, we reviews several works that examine Tullock group contests with group-specific public-good prizes in order to enhance our understanding about the effect of the degree of substitution or complementarity between members in a group on their effort incentives for their group’s winning. We also reviews studies on the optimal degree of substitution (complementarity) that maximizes the objective function of a contest organizer and group members’ payoffs, respectively, and endogenous formation of groups in Tullock contest setting as well. This paper may provide helpful knowledge and information that can be referred to design solutions for alleviating wasteful resources spent on rent-seeking behavior in our society.

Tullock contest with reference‐dependent preferences

AbstractWe study the Tullock contest model with loss aversion and endogenously formed reference points. In a contest with n possibly heterogeneous players and convex effort costs, we establish sufficient conditions for a unique Nash equilibrium in pure strategies. Subsequently, we analyze the impact of loss aversion on players' spending behavior, probability of winning, and rent dissipation.

Appropriability, institutions, and welfare in a Tullock contest

Appropriability, institutions, and welfare in a Tullock contest

Mechanism Design in Sport Matches: Competitive Balance, Intermediate Targets, and Effort Elicitation in a Three-Stage Contest Game

In sport, various examples of intermediate match targets exist that advantage the target-achieving party’s match outcome. We examine said targets within paired, multi-stage Tullock contest games, one a nested contest with intermediate target and one without. In equilibrium, the aggregate match-effort maximizing League sets a substantial subsequent match advantage to the target-achieving party. The nested Tullock contest with intermediate target elicits higher aggregate match effort than any one-shot Tullock contest. The effect of intermediate targets is fully consistent with that of an aggregate effort eliciting mechanism employed by leagues. Extant empirical literature finds clear demand for such a mechanism.

Affirmative action in large population tullock contests

Affirmative action in large population tullock contests

Will the European Green Deal enhance Europe’s security towards Russia? A political economy perspective

The European Green Deal is a set of policy initiatives set by the European Commission with the aim of making the European Union climate neutral in 2050. The Deal is credited with many virtues by its proponents, and in particular that it would reduce geopolitical disputes with Europe’s main supplier of energy, Russia. The nascent literature on energy transition is primarily focused on its economic costs and benefits, and on its contribution to energy security; but it has so far left unaddressed the question of the transition’s military consequences. To address that question, our paper adopts a political economy perspective by looking at how a sizeable drop in the energy revenue, which would result from the successful implementation of the Deal, is likely to affect the intraelite competition underway in Russia. We model that competition by means of a Tullock contest in which the energy revenue may be allocated by the sole winner to the provision of private goods or of club goods. We show that the Deal would favour the currently ruling elite group’s efforts at winning the contest. Given that this elite would thus control energy revenue and would spend it on military investments intended at maintaining it in power, the Deal could have adverse security consequences for Europe. The paper concludes by underlining the importance for the Deal’s success to factor in its unintended geopolitical consequences.

Overbidding and heterogeneous behavior in contest experiments:A meta-comment on cross-cultural differences

We revisit the analyses by Sheremeta (2013) and Chowdhury and Moffatt (2017), who pool experimental data from 30 Tullock contests to explain the phenomenon of overbidding. The authors find that the overbidding rate is positively related to the number of contestants and has an inverted U-shaped relationship with the relative endowment. We reuse their data and extend the analysis in the direction of cross-cultural differences, focusing on ethno-linguistic-religious fractionalization as a country-level measure. The results suggest an increased explanatory power of the model, with fractionalization negatively relating to overbidding. In addition, the extended model shows that in the one-shot game the overbidding rate is significantly higher than in the case of repeated interactions. We discuss possible interpretations of our findings.

Offsetting Distortion Effects of Head Starts on Incentives in Tullock Contests

Abstract In this study, we examine a contest scenario where each player possesses a distinct head start that skews their chances of winning, thereby creating incentive distortions from the efficient level and adversely affecting the contest designer. While affirmative action policies offer a straightforward solution to counteract these distortions, their implementation may not always be viable in real-life applications. We characterize the unique class of non-discriminatory contest success functions (CSF) that enables to achieve an efficient level of effort when there are two players. Additionally, we demonstrate that achieving a symmetric equilibrium is unattainable without affirmative action when the contest involves more than two players.

The yardstick approach in a Tullock contest

AbstractA contest's organizational structure or mechanism is often determined by the organizer's goal. While most contest organizers are interested in maximizing the effort expended by the contestants, some are interested in maximizing social welfare. We examine the corresponding contest mechanisms using a Tullock contest (standard and winner‐pay) combined with the yardstick approach, which in some cases can achieve both goals simultaneously. Two cases are considered. The first is the yardstick approach that takes the form of a payoff scheme in a standard Tullock contest where the contestants (winners or losers) are reimbursed according to the average effort of the other contestants. In the second, the yardstick approach is introduced into a winner‐pay contest, in which the winner pays the average cost of the other contestants' efforts.

Rent dissipation in large population Tullock contests

Rent dissipation in large population Tullock contests

Anodal tDCS over TPJ reduces bidding in Tullock contest: Implications for social decision-making

Contests, as economic, political, and social interactions, can stimulate high levels of effort, but they can also lead to inefficient expenditure of effort (overbidding), resulting in the wastage of social resources. Prior studies have indicated that the temporoparietal junction (TPJ) is associated with overbidding and speculating on the intentions of others during contests. This study aimed to investigate the neural mechanisms of the TPJ in overbidding and to examine changes in bidding behavior after modulating TPJ activity using transcranial direct current stimulation (tDCS). The experiment randomly allocated participants into three groups, each receiving either anodal stimulation of the LTPJ/RTPJ or sham stimulation. Following the stimulation, the participants engaged in the Tullock rent-seeking game. Our results revealed that participants who received anodal stimulation of the LTPJ and RTPJ significantly reduced their bids compared to the sham group, possibly due to enhanced accuracy in guessing others' strategies or enhanced altruistic preferences. Moreover, our findings suggest that while both the LTPJ and RTPJ are associated with overbidding behavior, anodal tDCS targeting the RTPJ is more effective than stimulation of the LTPJ in decreasing overbidding. The aforementioned revelations offer proof of the neural mechanisms of the TPJ in overbidding and provide fresh substantiation for the neural mechanisms of social behavior.

‘Born this Way’? Prenatal exposure to testosterone may determine behavior in competition and conflict

It is documented that fetal exposure to sexual hormones has long lasting effects on human behavior. The second-to-fourth digit ratio (DR) is a putative marker for prenatal exposure to testosterone (compared to estrogens) while in uterus, with higher relative exposure to testosterone resulting in a lower DR. Although the existing literature documents the correlation of DR with various decisions, and testosterone has been related to competitive behaviors, little research has studied the effect of DR on competition in conflict situations where skills do not matter. We investigate this question in the laboratory. Based on a previously obtained large sample of student subjects, we selectively invite subjects to the laboratory if their right-hand DR is in the top (High type) or bottom (Low type) tercile for their gender. Unbeknownst to the subjects, we perform a controlled match of High and Low types as opponents in a 2-person Tullock contest. We find that Low type (higher exposure to testosterone) males expend significantly higher conflict effort than High type males, that is, they are more aggressive, which reduces their opponents’ earnings. Among females, however, everyone is more aggressive against the High type (who respond less aggressively). These results can partially be explained through high joy of winning and/or spitefulness for Low type males, and high spitefulness for Low type females. This investigation sheds light on the importance of biological aspects in the ex-ante determinants of conflict, and on contest design.

Large Tullock contests

Large Tullock contests

Manipulation of moves in sequential contests

In two-player Tullock contests with endogenous timing of moves, the weak player moves early and the strong player follows. This order of moves is the third-best outcome for a contest organiser as it leads to a contest with lower aggregate effort compared to a contest where the players move in reverse order (first best) or simultaneously (second best). We propose that if the contest organiser—who does not know ex ante which player is the strong and which is the weak one—offers a lower price (effort cost) to the player(s) who choose(s) to exert effort early, she can achieve a greater payoff by affecting the contestants’ sequence of moves. We show that there exists no price that generates the first-best outcome. However, there is a price (or a range of prices) that induces both players to move early and receive it, leading to the second-best outcome. We also discuss the case where both players move early but only one receives the low price, e.g., lobbying or Instagram “giveaway” contests.

Contributing to Peace

Contest theory analyses an anarchic economy where agents use resources for consumption or acquisitive conflict, and explores conditions under which peace or conflict prevail in equilibrium. History suggests that peacekeepers in the shape of kings, dictators or states arise endogenously in such circumstances. I analyse a model where each of the potential contestants first has the option of contributing some resources to a neutral peacekeeper, and then allocates her remaining resources between arms and consumption. If one of the contestants subsequently attacks the other, then the peacekeeper joins its resources with the agent that is attacked. I show that, for less unequal resource distributions, contribution to peacekeeping is positive and leads to peace in equilibrium. These equilibria are pareto-superior to the corresponding equilibria of the pure Tullock contest except in a narrow range. When the distribution is too unequal, no contributions are made and conflict occurs in equilibrium.

Optimal contest design: Tuning the heat

We consider the design of contests when the principal can choose both the prize profile and how the prizes are allocated as a function of a possibly noisy signal about the agents' efforts. We provide sufficient conditions that guarantee optimality of a contest. Optimal contests have a minimally competitive prize profile and an intermediate degree of competitiveness in the contest success function. Whenever observation is not too noisy, the optimum can be achieved by an all-pay contest with a cap. When observation is perfect, the optimum can also be achieved by a nested Tullock contest. We relate our results to a recent literature which has asked similar questions but has typically focused on the design of either the prize profile or the contest success function.

Optimal large population Tullock contests

Abstract We consider Tullock contests where contestants can be divided into a finite set of types according to their strategy cost function. Solving such contests is intractable if the number of players is finite but large and there are nonlinearities and asymmetries present. But by approximating the finite player contest with a large population model that can be solved in closed form, we can approximate equilibrium behavior in the finite player model. We then characterize the optimal bias parameters of the large population contest and interpret them as approximations of optimal bias parameters in finite player contests. We also identify conditions under which those parameters are increasing or decreasing according to the cost parameters. The parameters are biased in favor of high-cost agents if the cost functions are strictly convex and the likelihood of success is sufficiently responsive to strategy.

Equilibria in Two-Player Sequential Tullock Contests

Equilibria in Two-Player Sequential Tullock Contests

Nested Tullock contests with nonmonotone prizes

Nested Tullock contests with nonmonotone prizes