Balance of power and the propensity of conflict

Abstract:

We study the role of an imbalance in fighting strengths when players bargain in the shadow of conflict. Our experimental results suggest: In a simple bargaining game with an exogenous mediation proposal, the likelihood of conflict is independent of the balance of power. If bargaining involves endogenous demand choices, however, the likelihood of conflict is higher if power is more imbalanced. Even though endogenous bargaining outcomes reflect the players’ unequal fighting strengths, strategic uncertainty causes outcomes to be most efficient when power is balanced. In turn, the importance of exogenous mediation proposals depends on the balance of power.

JEL Classification: C78, C91, D72, D74

Keywords: Conflict, balance of power, contest, bargaining, Nash demand game, conflict resolution, asymmetries, experiment

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528.pdf

Fight Alone or Together? The Need to Belong

Abstract:

Alliances often face both free-riding and hold-up problems, which under- mine the effectiveness of alliances in mobilizing joint fighting effort. Despite of these disadvantages, alliances are still ubiquitous in all types of contests. This paper asks if there are non-monetary incentives to form alliances, e.g., intimidating/discouraging the single player(s) who is/are left alone. For this purpose, I compare symmetric (2 vs. 2) and asymmetric (2 vs. 1) contests to their equivalent 4-player and 3-player individual contests, respectively. We find that alliance players in symmetric (2 vs. 2) contests behave the same as those in equivalent 4-player individual contests. However, in asymmetric (2 vs. 1) contests, stand-alone players were strongly discouraged to exert effort (especially the females), compared to the 3-player individual contests. Alliance players may have anticipated this effect and also reduced their effort, if alliances share the prize according to the merit rule. Behavioural factors such as the need to belong can help reconcile the "paradox of alliance formation".

Keywords: Alliance Formation, Contest and Conflict, Experiment.

JEL Codes: D72; D74; C91

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421.pdf

Alliances in the Shadow of Con‡flict

Abstract:

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.

Keywords: Conflict; Contest; Alliance; Endogenous internal conflict; Hold-up problem; Non-aggression pact; Experiment

JEL Codes: D72; D74

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420.pdf

Endogenous group formation in experimental contests

Abstract:

We study endogenous group formation in tournaments employing experimental three-player contests. We find that players in endogenously formed alliances cope better with the moral hazard problem in groups than players who are forced into an alliance. Also, players who are committed to expending effort above average choose to stand alone. If these players are forced to play in an alliance, they invest even more, whereas their co-players choose lower effort. Anticipation of this exploitation may explain their preference to stand alone.

Keywords: Endogenous group formation, contest, conflict, alliance, experiment, moral hazard problem, free-riding, in-group favoritism

JEL codes: D72, D74

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419.pdf

Evolutionary determinants of war

Abstract:

This paper considers evolutionarily stable decisions about whether to initiate violent conflict rather than accepting a peaceful sharing outcome. Focusing on small sets of players such as countries in a geographically confined area, we use Schaffer’s (1988) concept of evolutionary stability. We find that players ‘evolutionarily stable preferences widen the range of peaceful resource allocations that are rejected in favor of violent conflict, compared to the Nash equilibrium outcomes. Relative advantages in fighting strength are reflected in the equilibrium set of peaceful resource allocations.

Keywords: Conflict; Contest; Endogenous fighting; Balance of power; Evolutionary stability

JEL Codes: D72; D74

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418.pdf

Information sharing in contests

Abstract:

We study the incentives to share private information ahead of contests, such as markets with promotional competition, procurement contests, or R&D. We consider the cases where firms have (i) independent values and (ii) common values of winning the contest. In both cases, when decisions to share information are made independently, sharing information is strictly dominated. With independent values, an industry-wide agreement to share information can arise in equilibrium. Expected effort is lower with than without information sharing. With common values, an industry-wide agreement to share information never arises in equilibrium. Expected effort is higher with than without information sharing.

Keywords: information sharing; contest; all-pay auction
JEL Classification: D82; D43; D44; L13; D74

September 2010

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334.pdf

Information acquisition in conflicts

Abstract:

This paper considers incentives for information acquisition ahead of conflicts. First, we characterize the (unique) equilibrium of the all-pay auction between two players with one-sided asymmetric information where one player has private information about his valuation. Then, we use ou rresults to study information acquisition prior to an all-pay auction. If the decision to acquire information is observable, but not the informatio nreceived, one-sided asymmetric information can occur endogenously in equilibrium. Moreover, the cutoff values of the cost of information that determine equilibrium information acquisition are higher  than in the first best.  Thus, information  acquisition is excessive. Incontrast, with open or covert information acquisition,  the equilibrium cut-off values are as in the  first best.

 
Keywords: All-pay auctions; Conflicts; Contests; Information acquisition;
Asymmetric information
JEL Classification: D72; D74; D82; D83

March 2010

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314.pdf

Contests with multi-tasking

Abstract:

The standard contest model in which participants compete in a single dimension is well understood and documented. Multi-dimension extensions are possible but are liable to increase the complexity of the contest structure, mitigating one of its main advantages: simplicity. In this paper we propose an extension in which competition ensues in several dimensions and a competitor that wins a certain number of these is awarded a prize. The amount of information needed to run the contest is hence limited to the number of dimensions won by each player. We look at the design of this contest from the point of view of maximizing effort in the contest (per dimension and totally), and show that there will be a tendency to run small contests with few dimensions. The standard Tullock model and its results are encompassed by our framework.

Keywords: contest design, multi-tasking, effort incentives
JEL Classification: D72
May 2006

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125.pdf

Fragmented property rights and R&D competition

Abstract:

Where product innovation requires several complementary patents, fragmented property rights can be a factor that limits firms’ willingness to invest in the development and commercialization of new products. This paper studies multiple simultaneous R&D contests for complementary patents and how they interact with patent portfolios that firms may have acquired already. We also consider how this interaction and the intensity of the contests depends on the type of patent trade regimes and the product market equilibria that result from these regimes. We solve for the contest equilibria and show that the multiple patent product involves an important hold-up problem that considerably reduces the overall contest effort.

Keywords: fragmented property rights, patents, contests, hold-up, R&D, patent pools, licensing
JEL Classification: D44
June 2006

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123.pdf

Multi-battle contests

Abstract:

We study equilibrium in a multistage race in which players compete in a sequence of simultaneous move component contests. Players may win a prize for winning each component contest, as well as a prize for winning the overall race. Each component contest is an all-pay auction with complete information. We characterize the unique equilibrium analytically and demonstrate that it exhibits endogenous uncertainty. Even a large lead by one player does not fully discourage the other player, and each feasible state is reached with positive probability in equilibrium (pervasiveness). Total effort may exceed the value of the prize by a factor that is proportional to the maximum number of stages. Important applications are to war, sports, and R&D contests and the results have empirical counterparts there.

Keywords: all-pay auction, contest, race, conflict, multi-stage, R&D, endogenous uncertainty, preemption, discouragement
JEL Classification: D72, D74
March 2006

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Equilibrium and Efficiency in the Tug-of-War

Abstract:

We characterize the unique Markov perfect equilibrium of a tug-of-war without exogenous noise, in which players have the opportunity to engage in a sequence of battles in an attempt to win the war. Each battle is an all-pay auction in which the player expending the greater resources wins. In equilibrium, contest effort concentrates on at most two adjacent states of the game, the "tipping states", which are determined by the contestants’ relative strengths, their distances to final victory, and the discount factor. In these states battle outcomes are stochastic due to endogenous randomization. Both relative strength and closeness to victory increase the probability of winning the battle at hand. Patience reduces the role of distance in determining outcomes. Applications range from politics, economics and sports, to biology, where the equilibrium behavior finds empirical support: many species have developed mechanisms such as hierarchies or other organizational structures by which the allocation of prizes are governed by possibly repeated conflict. Our results contribute to an explanation why. Compared to a single stage conflict, such structures can reduce the overall resources that are dissipated among the group of players.

Keywords: winner-take-all, all-pay auction, tipping, multi-stage contest, dynamic game, preemption, conflict, dominance
JEL Classification: D72, D74
May 2006

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121.pdf

Contests with Investment

Abstract:

Perfectly discriminating contests (or all pay auction) are widely used as a model of situations where individuals devote resources to win some prize. In reality such contests are often preceded by investments of the contestants into their ability to fight in the contest. This paper studies a two stage game where in the first stage, players can invest to lower their bid cost in a perfectly discriminating contest, which is played in the second stage. Different assumptions on the timing of investment are studied. With simultaneous investments, equilibria in which players play a pure strategy in the investment stage are asymmetric, exhibit incomplete rent dissipation, and expected effort is reduced relative to the game without investment. There also are symmetric mixed strategy equilibria with complete rent dissipation. With sequential investment, the first mover always invests enough to deter the second mover from investing, and enjoys a first mover advantage. I also look at unobservable investments and endogenous timing of investments.

Keywords: contests, all pay auctions, investment
JEL Classification: D44, D72
May 2006

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Rents, dissipation and lost treasures: comment

Abstract:

In an interesting recent paper, Dari-Mattiacci and Parisi (2005) extended Tullock.s (1980) rent-seeking game with an entry decision. The mixed strategies identified by Dari-Mattiacci and Parisi for the case of increasing returns in the contest success function (r > 2) do not constitute an equilibrium of the game they study. However, these strategies are an equilibrium if the strategy space of the game is restricted by a minimum expenditure requirement, and this minimum expenditure requirement is an element of a specific interval.

January 2006

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119.pdf

Selection Tournaments, Sabotage, and Participation

Abstract:

This paper studies sabotage in tournaments with at least three contestants, where the contestants know each other well. Every contestant has an incentive to direct sabotage specifically against his most dangerous rival. In equilibrium, contestants who choose a higher productive effort are sabotaged more heavily. This might explain findings from psychology, where victims of mobbing are sometimes found to be overachieving. Further, sabotage equalizes promotion chances. The effect is most pronounced if the production function is linear in sabotage, and the cost function depends only on the sum of all sabotage activities: in an interior equilibrium, who will win is a matter of chance, even when contestants differ a great deal in their abilities. This, in turn, has adverse consequences for who might want to participate in a tournament. Since better contestants anticipate that they will be sabotaged more strongly, it may happen that the most able stay out and the tournament selects one of the less able with probability one. I also study the case where some contestants are easy victims, i.e. easier to sabotage than others.

Keywords: tournament, contest, sabotage, selection
JEL Classification: M51, J41, J29
April 2006

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118.pdf

All Nash Equilibria of the Multi-Unit Vickrey Auction

Abstract:

This paper completely characterizes the set of Nash equilibria of the Vickrey auction for multiple identical units when buyers have non-increasing marginal valuations and there at least three potential buyers. There are two types of equilibria: In the first class of equilibria there are positive bids below the maximum valuation. In this class, above a threshold value all bidders bid truthfully on all units. One of the bidders bids at the threshold for any unit for which his valuation is below the threshold; the other bidders bid zero in this range. In the second class of equilibria there are as many bids at or above the maximum valuation as there are units. The allocation of these bids is arbitrary across bidders. All the remaining bids equal zero. With any positive reserve price equilibrium becomes unique: Bidders bid truthfully on all units for which their valuation exceeds the reserve price.

Keywords: Vickrey auction, Multi-unit auction, ex-post equilibrium, reserve price, uniqueness
JEL Classification: C72, D44
June 2006

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116.pdf

War with Outsiders Makes Peace Inside

Abstract:

In many situations there is a potential for conflict both within and between groups. Examples include wars and civil wars and distributional conflict in multitiered organizations like federal states or big companies. This paper models such situations with a logistic technology of conflict. If individuals decide simultaneously and independently about the amount of internal conflict, external conflict and production, there is typically either only internal conflict, or only external conflict - but not both. If each group decides collectively how much each member has to put into the external conflict before the members individually decide on the amounts put into the internal conflict and production, groups choose sufficiently high external conflict in order to avoid internal conflict. This is a model of the "diversionary use of force". We also study the optimal number of groups.

Keywords: conflict, war, rent-seeking, hierarchy, federalism, diversion
JEL Classification: D72, D74, H11, H74
December 2005

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75.pdf

Lobbying contests with endogenous policy proposals

Abstract:

Lobbyists choose what to lobby for. If they can precommit to certain policy proposals, their choice will have an influence on the behavior of opposing lobbyists. Hence lobbyists have an incentive to moderate their policy proposals in order to reduce the intensity of the lobbying contest. This logic has been explored in a number of recent papers. I reconsider the topic with a perfectly discriminating contest. With endogenous policy proposals, there is a subgame perfect equilibrium where the proposals of the lobbyists coincide and maximize joint welfare; moreover, this equilibrium is the only one that survives repeated elimination of dominated strategies. Hence there is no rent dissipation at all. A politician trying to maximize lobbying expenditures would prefer an imperfectly discriminating contest.

Keywords: Interest groups; Endogenous lobbying targets, Voluntary restraint; Polarization
JEL Classification: D72
May 2005

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Simultaneous inter- and intra-group conflicts

Abstract:

Lecture on the first SFB/TR 15 meeting, Gummersbach, July, 18 - 20, 2004

This paper models the trade-off between production and appropriation in the presence of simultaneous inter- and intra-group conflicts. The model exhibits a ‘group cohesion effect ’: if the contest between the groups becomes more decisive, or contractual incompleteness between groups becomes more serious, the players devote fewer resources to the intra-group conflict. Moreover, there is also a ‘reversed group cohesion effect’: if the intra-group contests become less decisive, or contractual incompleteness within groups becomes less serious, the players devote more resources to the inter-group contest. The model also sheds new light on normative questions. I derive exact conditions for when dividing individuals in more groups leads to more productive and less appropriative activities. Further, I show that there is an optimal size of the organization which is determined by a trade-off between increasing returns to scale in production and increasing costs of appropriative activities.

Keywords: Conflict, rent-seeking, federalism, hierarchy
JEL Classification: D72, D74, H11, H74
May 2004

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