From Custer to Thermopylae: Last stand behavior in multi-stage contests

In a multi-stage contest known as a two-player race, players display two fundamental behaviors: (1) the laggard will make a last stand in order to avoid the cost of losing; and (2) the player who is ahead will defend his lead if it is threatened. Last stand behavior, in particular, contrasts with previous research where the underdog simply gives up. The distinctive results are achieved by introducing losing penalties and discounting into the racing environment. This framework permits the momentum effect, typically ascribed to the winner of early stages, to be more thoroughly examined. I study the likelihood that the underdog will catch up. I find that neck-and-neck races are common when the losing penalty is large relative to the winning prize, while landslide victories occur when the prize is relatively large. Closed-form solutions are given for the case where players have a common winning prize and losing penalty.     

Credible communication and cooperation: Experimental evidence from multi-stage Games

It is well known that communication often serves as a facilitator for cooperation in static games. Yet, communication can serve entirely different purposes in dynamic settings as communication during the game may work as a means for renegotiation, potentially undermining the credibility of cooperative strategies. To explore this issue, this paper experimentally investigates cooperation and non-binding communication in a two-stage game. More specifically, two treatments are considered: one with only pre-play communication and one where subjects can also communicate intra-play between the stages of the game. The results highlight a nontrivial difference concerning the effects of pre-play communication between the two treatments. Sending or receiving pre-play messages has a positive and significant effect on cooperation if there is no possibility of intra-play communication. However, this effect is significantly reduced when when intra-play communication is allowed. The results suggest that the credibility of pre-play messages may depend crucially on future communication opportunities.     

Proxy contests and corporate democracy

A proxy contest is a fight between two management teams to gain proxies from shareholders.The management team which accumulates a majority of votes wins the competition for corpo rate control. This paper attempts to construct a formal model of proxy contests and analyze their implications for the shareholders’ benefit and power of control over the firm.     

Effort and performance in group contests

We study contest performance by focusing on the per capita payoffs of the contestants in an important class of asymmetric two-group contests. The group with the higher valuation has a greater chance of winning the contest whenever the rent-seeking technology is increasing and concave. We note that equilibrium efforts and payoffs per capita are uniquely defined and can be subjected to a comparative statics analysis. We show that payoff per capita for a group increases with its own valuation but decreases with the valuation of the opposing group. Per capita payoff for a group increases with its population.     

Collective contests for commons and club goods

This paper focuses on collective contests for commons and club goods. Our main objective is to examine in this context the effect of group size on its performance. The main results specify conditions for the existence (non-existence) of the group-size paradox, namely, the situation where a larger group is less (more) effective in pursuing its interest because of (despite) the combined effect of the incentives that result in the free-riding problem and the tragedy of the commons. The paper also explains under what circumstances there exists a bias towards excessive or inadequate winning group size. Finally, it examines the effect of restricted excludability of the commons good within the winning group on the relationship between group-size and its winning probability.     

Risk aversion in symmetric and asymmetric contests

We analyze existence, uniqueness and properties of equilibria in incompletely discriminating Tullock contests with logistic contest success functions, when contestants are risk averse. We prove that a Nash equilibrium for such a contest exists, but give an example of a symmetric contest with both symmetric and asymmetric equilibria, showing that risk aversion may lead to multiple equilibria. Symmetric contests have unique symmetric equilibria but additional conditions are necessary for general uniqueness. We also study the effects on incumbents of additional competitors entering the contest under these conditions and examine the effects of risk aversion on rent dissipation in symmetric and asymmetric contests.     

Selective incentives and intragroup heterogeneity in collective contests

A group taking part in a contest has to confront the collective action problem among its members, and devices of selective incentives are possible means of resolution. We argue that heterogeneous prize‐valuations in a competing group normally prevent effective use of such selective incentives. To substantiate this claim, we adopt cost‐sharing as a means of incentivizing the individual group members. We confirm that homogeneous prize valuations within a group result in a cost‐sharing rule inducing the first‐best individual contributions. As long as the cost‐sharing rule is dependent only on the members’ contributions, however, such a first‐best rule does not exist for a group with intragroup heterogeneity. Our main result clarifies how unequal prize valuations affect the cost‐sharing rule and, in particular, the degree of cost‐sharing. If the relative rate of change of the marginal effort costs is decreasing, it is reduced by intragroup heterogeneity. If the rate is increasing, the cost is fully shared, but it cannot induce the first‐best contributions for the group.     

Hierarchical thinking and learning in rank order contests

We analyze a class of coordination games in which the Kth player to submit an entry wins a contest. These games have an infinite number of symmetric equilibria and the set of equilibria does not change with K. We run experiments with 15 participants and with K=3, 7, and 11. Our experiments show that the value of K affects initial submissions and convergence to equilibrium. When K is small relative to the number of participants, our experiments show that repeated play converges to or near zero. When K is large, an equilibrium is often not reached as a result of repeated play. We seek explanations to these patterns in hierarchical thinking and direction learning.      

Asymmetric information and multi-stage brain drain

In this paper, multi-stage decision procedures associated with the occurence of the brain drain are considered within an asymmetric information framework. Qualitative properties of multi-stage brain drain processes are characterized. Given additional assumptions, some policy implications are also provided through comparative statics analysis.     

Communication of preferences in contests for contracts

This paper models a contest where several sellers compete for a contract with a single buyer. There are several styles of possible designs with a subset of them preferred by the buyer. We examine what happens when the buyer communicates information about his preferences. If the sellers are unable to change their style, then there is no effect on the welfare of the sellers. If the sellers are able to make adjustments, extra information may either boost or damage the sellers?? profits. While the chance that there will be a proposal of a style preferred by the buyer cannot decrease, the buyer??s surplus may increase or decrease.     

Difference-form contest success functions and effort levels in contests

We examine players' equilibrium effort levels in a contest with difference-form contest success functions in which two players compete with each other to win a prize. We show the following. At the pure-strategy Nash equilibrium of a simultaneous-move game, and in the subgame-perfect equilibrium of a sequential-move game, only one of the players expends effort or neither player expends effort. If one player's composite strength is far greater than the other player's, only the player with greater composite strength expends effort whether they move simultaneously or sequentially. If the players' valuations for the prize and their marginal probabilities of winning at (0, 0) are sufficiently small, neither player expends effort whether they move simultaneously or sequentially.     

The impact of management incentives in intergroup contests

In intergroup contests a manager advises and motivates her group’s members. Her rewards often depend on the subsequent contest expenditure of the members. I test whether such incentives undermine the credibility and effectiveness of a manager’s efforts. In the different experimental treatments the managers either benefit from very high or low expenditure or get a predetermined payment. The results show that different management incentives shape the expenditure of the group members even if managers have an advisory role only. However, group members follow recommendations more closely if management compensation is not linked to contest expenditures.     

Entry into winner-take-all and proportional-prize contests: An experimental study

This experiment compares the performance of two contest designs: a standard winner-take-all tournament with a single fixed prize, and a novel proportional-payment design in which that same prize is divided among contestants by their share of total achievement. We find that proportional prizes elicit more entry and more total achievement than the winner-take-all tournament. The proportional-prize contest performs better by limiting the degree to which heterogeneity among contestants discourages weaker entrants, without altering the performance of stronger entrants. These findings could inform the design of contests for technological and other improvements, which are widely used by governments and philanthropic donors to elicit more effort on targeted economic and technological development activities.     

Selection and incentives in contests: evidence from horse racing

The designer of internal labour market promotion contests must balance the need to select the best candidate with the need to provide incentives for all candidates. We use an extensive data set from horse racing – where there is abundant variation in contest design features – to analyse if there are particular features that help to achieve these two objectives. We find that contests with higher prize money and fewer participants are the most successful at achieving the dual remit of selection and incentives.     

Evolutionary equilibrium in Tullock contests: spite and overdissipation

Tullock's analysis of rent-seeking as a contest is reconsidered from an evolutionary point of view. We show that evolutionarily stable behavior in a Tullock contest exists and differs from behavior in Nash equilibrium. Evolutionarily stable behavior in these contests is robust in a strong sense and may entail overdissipation of the contested rent.     

Entry in contests with incomplete information: Theory and experiments

This paper studies entry decisions in contests with private values. Potential contestants observe their value and the common opportunity cost of entry, and make entry decisions simultaneously. Theory predicts that whether or not contestants are informed of the number of entrants prior to choosing their expenditures has no effect on entry or aggregate expenditures. We test these assertions in our experiments. We find substantial over-entry in both information structures. However, entry is higher when contestants are informed. Since expenditures do not, on average, differ across information structures, aggregate expenditure is also higher when contestants are informed. Contestants earn on average less than the opportunity cost of entry.     

Optimal contest design: volume and timing of rent seeking in contests

This paper undertakes a comparative analysis of rent-seeking contests in terms of the amount and the timing of effort they elicit from the participants. The optimal contest structure—the one that maximizes the discounted sum of efforts—is found to hinge on the degree of impatience of the contest organizers, the more patient of whom prefer longer contests consisting of pairwise matches among the contestants. Heterogeneity of the contestants' quality also turns out to play an important role in the comparison.     

The value of commitment in contests and tournaments when observation is costly

We study the value of commitment in sequential contests when the follower faces small costs to observe the leader's effort. We show that the value of commitment vanishes entirely in this class of games. By contrast, in sequential tournaments—games where, at a cost, the follower can observe the effectiveness of the leader's effort—the value of commitment is preserved completely provided that the observation costs are sufficiently small.     

Unique equilibrium in rent-seeking contests with a continuum of types

It is shown that rent-seeking contests with continuous and independent type distributions possess a unique pure-strategy Nash equilibrium.