Strategy, Nontransitive Dominance and the Exponential Distribution

The Kruskal-Wallis test is a rank-based one way ANOVA. Its test statistic is shown here to be a quadratic form among the Mann-Whitney or Kendall tau concordance measures between pairs of treatments. But the full set of such concordance measures has more degrees of freedom than the Kruskal-Wallis test uses, and the independent surplus is attributable to circularity, or non-transitive effects. The meaning of circularity is well illustrated by Efron dice. The cases of k = 3, 4 treatments are analysed thoroughly in this paper, which also shows how the full sum of squares among all concordance measures can be decomposed into uncorrelated transitive and non-transitive circularity effects. A multiple comparisons procedure based on patterns of transitive orderings among treatments is implemented. The testing of circularities involves non-standard asymptotic distributions. The asymptotic theory is deferred, but Monte Carlo permutation tests are easy to implement.

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“…Participants have to shoot as accurately as possible in 3 Colonel Blotto Game has been experimentally analyzed by Chowdhury et al (2013). 4 Note that a dynamic sequential version of Colonnel Blotto, called Colonel Blotto Gladiator Game (Kaminsky et al (1984), Rinott et al (2012)), is also different since the players decide the order of the gladiators and if one gladiator wins, he stays on the battlefield. 5 Using a natural experiment, they investigate whether professional tennis players are able to optimally allocate their level of risk across first and second serve.…”

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confidence: 99%

Always doing your best? Effort and performance in dynamic settings

Houy

¹

,

Nicolaï

²

,

Villeval

³

2020

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Achieving an ambitious goal frequently requires succeeding in a sequence of intermediate tasks, some being critical for the final outcome, and others not. However, individuals are not always able to provide a level of effort sufficient to guarantee success in all such intermediate tasks. The ability to manage effort throughout the sequence of tasks is therefore critical when resources are limited. In this paper we propose a criterion that defines the importance of a task and identifies how an individual should optimally allocate a limited stock of exhaustible efforts over tasks. We test this importance criterion in a laboratory experiment that reproduces the main features of a tennis match. We show that our importance criterion is able to predict the individuals' performance and it outperforms the Morris importance criterion that defines the importance of a point in terms of its impact on the probability of achieving the final outcome. We also find no evidence of choking under pressure and stress, as proxied by electrophysiological measures. AbstractAchieving an ambitious goal frequently requires succeeding in a sequence of intermediate tasks, some being critical for the final outcome, and others not. However, individuals are not always able to provide a level of effort sufficient to guarantee success in all such intermediate tasks. The ability to manage effort throughout the sequence of tasks is therefore critical when resources are limited. In this paper we propose a criterion that defines the importance of a task and identifies how an individual should optimally allocate a limited stock of exhaustible efforts over tasks. We test this importance criterion in a laboratory experiment that reproduces the main features of a tennis match. We show that our importance criterion is able to predict the individuals' performance and it outperforms the Morris importance criterion that defines the importance of a point in terms of its impact on the probability of achieving the final outcome. We also find no evidence of choking under pressure and stress, as proxied by electrophysiological measures. JEL Classification: C72, C92, D81.

show abstract

“…Colonel Blotto Game has been experimentally analyzed byChowdhury et al (2013). 4 Note that a dynamic sequential version of Colonnel Blotto, called Colonel Blotto Gladiator Game(Kaminsky et al (1984),Rinott et al (2012)), is also different since the players decide the order of the gladiators and if one gladiator wins, he stays on the battlefield.5 Using a natural experiment, they investigate whether professional tennis players are able to optimally allocate their level of risk across first and second serve. They show that professional players are very good at allocating their risk taking across different serves.…”

mentioning

confidence: 99%

Always Doing Your Best? Effort and Performance in Dynamic Settings

Houy

¹

,

Nicolaï

²

,

Villeval

³

2017

View full text Add to dashboard Cite

Achieving an ambitious goal frequently requires succeeding in a sequence of intermediate tasks, some being critical for the final outcome, and others not. However, individuals are not always able to provide a level of effort sufficient to guarantee success in all such intermediate tasks. The ability to manage effort throughout the sequence of tasks is therefore critical when resources are limited. In this paper we propose a criterion that defines the importance of a task and identifies how an individual should optimally allocate a limited stock of exhaustible efforts over tasks. We test this importance criterion in a laboratory experiment that reproduces the main features of a tennis match. We show that our importance criterion is able to predict the individuals' performance and it outperforms the Morris importance criterion that defines the importance of a point in terms of its impact on the probability of achieving the final outcome. We also find no evidence of choking under pressure and stress, as proxied by electrophysiological measures.

show abstract

Strategy, Nontransitive Dominance and the Exponential Distribution

Cited by 15 publications

References 6 publications

Kruskal–Wallis, Multiple Comparisons and Efron Dice

Kruskal–Wallis, Multiple Comparisons and Efron Dice

Always doing your best? Effort and performance in dynamic settings

Always Doing Your Best? Effort and Performance in Dynamic Settings

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