Bidding in hierarchies

This paper reconsiders the comparison between hierarchical contests and single-stage contests. A condition is given that characterizes whether and when the aggregate equilibrium payoff of contestants is higher in the single-stage contest, and when the single-stage contest is more likely to award the prize to the contestant who values it most highly. The outcome depends on inter- and intra-group heterogeneity, and is not driven by free-rider incentives. -- Diese Arbeit untersucht das Bietverhalten in einstufigen Turnieren und in sogenannten hierarchischen Turnieren, in denen zunächst Gruppen um einen Preis konkurrieren und anschließend die Mitglieder der siegreichen Gruppe um den Preis konkurrieren. Im Gegensatz zu existierenden Ergebnissen, wonach der Gesamtturnieraufwand in einstufigen Turnieren höher ist als in hierarchischen Turnieren, ergibt sich bei heterogenen Bietern eine Bedingung, die beschreibt, ob und wann die aggregierten gleichgewichtigen Aufwendungen der Turnierteilnehmer im nicht-hierarchischen Wettkampf größer sind und wann ein nicht-hierarchischer Wettkampf den zu gewinnenden Preis mit höherer Wahrscheinlichkeit an einen Wettkämpfer vergibt, der den Preis besonders hoch schätzt. Für das Zustandekommen der Ergebnisse ist nicht das Trittbrettfahrerverhalten von Gruppenmitgliedern, sondern die Heterogenität innerhalb der Gruppen im Verhältnis zur Heterogenität innerhalb der Gruppen von besonderer Bedeutung.Contest,hierarchies,rent dissipation

Inter-Group Conflict and Intra-Group Punishment in an Experimental Contest Game

We study how conflict in a contest game is influenced by rival parties being groups and by group members being able to punish each other. Our main motivation stems from the analysis of socio-political conflict. The relevant theoretical prediction in our setting is that conflict expenditures are independent of group size and independent of whether punishment is available or not. We find, first, that our results contradict the independence of group-size prediction: conflict expenditures of groups are substantially larger than those of individuals, and both are substantially above equilibrium. Towards the end of the experiment material losses in groups are 257% of the predicted level. There is, however, substantial heterogeneity in the investment behaviour of individual group members. Second, allowing group members to punish each other after individual contributions to the contest effort are revealed leads to even larger conflict expenditures. Now material losses are 869% of the equilibrium level and there is much less heterogeneity in individual group members? investments. These results contrast strongly with those from public goods experiments where punishment enhances efficiency and leads to higher material payoffs.Laboratory experiments, Rent-seeking, Conflict, Group competitiveness

Brothers in Arms - An Experiment on the Alliance Puzzle

Our experimental analysis of alliances in conflicts leads to three main findings. First, even in the absence of repeated interaction, direct contact or communication, free-riding among alliance members is far less pronounced than what would be expected from non-cooperative theory. Second, this possible solidarity among ‘brothers in arms’ when fighting against an outside enemy may rapidly deteriorate or disappear as soon as the outside enemy disappears. Third, when fighting an outside enemy, ‘brothers in arms’ may already anticipate future internal conflict about dividing the spoils of winning; however, this subsequent internal conflict does not discourage alliance members from expending much effort in the contest against the external enemy.alliance, conflict, contest, free-riding, hold-up problem, solidarity

Brothers in arms: An experiment on the alliance puzzle

Our experimental analysis of alliances in conflicts leads to three main findings. First, even in the absence of repeated interaction, direct contact or communication, free-riding among alliance members is far less pronounced than what would be expected from non-cooperative theory. Second, this possible solidarity among brothers in arms when fighting against an outside enemy may rapidly deteriorate or disappear as soon as the outside enemy disappears. Third, when fighting an outside enemy, brothers in arms may already anticipate future internal conflict about dividing the spoils of winning; however, this subsequent internal conflict does not discourage alliance members from expending much effort in the contest against the external enemy. -- Unsere experimentelle Studie zu Allianzen in Konflikten führt zu drei Hauptergebnissen. Selbst ohne wiederholte Interaktion, direkten Kontakt oder Kommunikation zwischen den Teilnehmern ist das Trittbrettfahren der Mitglieder der Allianz viel weniger stark ausgeprägt, als es die nicht-kooperative Theorie erwarten lassen würde. Diese Solidarität zwischen den Kampfgefährten, die im Wettbewerb mit einem Außenstehenden zu beobachten ist, nimmt jedoch rapide ab, sobald der Gegner verschwunden ist. Im Kampf mit dem externen Gegner können die Kampfgefährten bereits damit rechnen, dass es zu einem internen Konflikt über die Aufteilung der Kriegsbeute kommen wird; dieser folgende interne Verteilungskonflikt hält die Mitglieder der Allianz jedoch nicht davon ab, einen hohen Einsatz im Kampf mit dem externen Gegner zu leisten.Alliance,conflict,contest,free-riding,hold-up problem,solidarity

Group Contests with Complementarities in Efforts

Usually, groups increase their productivity by the specialization of their group members. In these cases, group output is no longer simply a sum of individual outputs. We analyze contests with group-specific public goods that allow for different degrees of complementarity between group members’ efforts. More specifically, we use a Tullock contest success function and a CES-impact function. We show that in equilibrium the degree of complementarity is irrelevant if groups do not differ in size and group members have an identical valuation of the public good. The equilibrium is discontinuous as the CES function converges to the Cobb-Douglas case. Except for the effects at the discontinuity, higher complementarity tends to favor larger groups. In groups with diverse valuations, higher complementarity also leads to higher similarity in group members’ efforts, which however is not necessarily an advantage for a more diverse group.contests, public goods

Alliances in the Shadow of Conflict

Victorious alliances often fight about the spoils of war. This paper presents an experiment on the determinants of whether alliances break up and fight internally after having defeated a joint enemy. First, if peaceful sharing yields an asymmetric rent distribution, this increases the likelihood of fighting. In turn, anticipation of the higher likelihood of internal fight reduces the alliance’s ability to succeed against the outside enemy. Second, the option to make non-binding declarations on non-aggression in the relationship between alliance members does not make peaceful settlement within the alliance more likely. Third, higher differences in the alliance players’ contributions to alliance effort lead to more internal conflict and more intense fighting

The Attack-and-Defense Group Contests: Best-shot versus Weakest-link

This study analyzes a group contest in which one group (defenders) follows a weakest-link whereas the other group (attackers) follows a best-shot impact function. We fully characterize the Nash and coalition-proof equilibria and show that with symmetric valuation the coalition-proof equilibrium is unique up to the permutation of the identity of the active player in the attacker group. With asymmetric valuation it is always an equilibrium for one of the highest valuation players to be active; it may also be the case that the highest valuation players in the attacker group free-ride completely on a group-member with a lower valuation. However, in any equilibrium, only one player in the attacker group is active, whereas all the players in the defender group are active and exert the same effort. We also characterize the Nash and coalition-proof equilibria for the case in which one group follows either a best-shot or a weakest-link but the other group follows an additive impact function

Optimal prize allocations in group contests

We characterize the optimal prize allocation, namely the allocation that maximizes a group's effectiveness, in a model of contests. The model has the following features: (i) it allows for heterogeneity between and within groups; (ii) it classifies contests as "easy" and "hard" depending on whether the marginal costs are concave or convex. Thus, we show that in an "easy" contest the optimal prize allocation assigns the entire prize to one group member, the most skilled one. Conversely, all group members receive a positive share of the prize when the contest is "hard" and players have unbounded above marginal productivities. If the contest is "hard" and the marginal productivities are bounded above, then only the most skilled group members are certain of receiving a positive share of the prize for any distribution of abilities. Finally, we study the effects of a change in the distribution of abilities within a group. Our analysis shows that if the contest is either "easy" or a particular subset of "hard", then the more the heterogeneity within a group, the higher its probability of winning the prize

Group Contests with Internal Conflict and Power Asymmetry

We investigate simultaneous inter- and intra-group conflict in the shadow of within-group power asymmetry and complementarity in members' group-conflict efforts. A more symmetric group faces a higher degree of internal conflict, and might expend more effort in external conflict when the group-conflict effort technology is highly complementary. Depending on the degree of complementarity, the stronger player's relative contribution to external conflict might be higher in a more asymmetric group and, as a result, it is possible for the weaker player to earn a higher payoff. In the absence of any complementarity, the rent-dissipation is non-monotonic with the within-group power asymmetry

Sabotage in Contests: A Survey

A contest is a situation in which individuals expend irretrievable resources to win valuable prize(s). ‘Sabotage’ is a deliberate and costly act of damaging a rival’s' likelihood of winning the contest. Sabotage can be observed in, e.g., sports, war, promotion tournaments, political or marketing campaigns. In this article, we provide a model and various perspectives on such sabotage activities and review the economics literature analyzing the act of sabotage in contests. We discuss the theories and evidence highlighting the means of sabotage, why sabotage occurs, and the effects of sabotage on individual players and on overall welfare, along with possible mechanisms to reduce sabotage. We note that most sabotage activities are aimed at the ablest player, the possibility of sabotage reduces productive effort exerted by the players, and sabotage may lessen the effectiveness of public policies, such as affirmative action, or information revelation in contests. We discuss various policies that a designer may employ to counteract sabotage activities. We conclude by pointing out some areas of future research