On Asymmetric Tournaments

The interventions:
1) In Baseline, the agents are fully symmetric.
2) In Treatment, the agents are asymmetric.

2024-11-07

2025-04-30

1) Principal's choice of the promotion rule, in which they decide how to assign the high prize as a function of the difference of the output of agents (scale: -100 to 100).
2) Beliefs of agents regarding principal's choice of the allocation rule (scale: -100 to 100)
3) Agent's effort provision (effort choice 0 to 100).

The outcomes are directly observable and will not be constructed.

The outcomes are directly observable and will not be constructed.

See below.

Not available

First, participants randomly draw a card that assigns them to their computer / cubicle. This determines whether they are a principal or agent, whether they are in baseline or treatment, and also in which matching group of 9 participants they are (cluster). In each round, a group of 1 principal and 2 agents will be formed randomly by the computer (repeated random re-matching). Finally, the agent's error term is randomly drawn by the computer in each round, too.

We will cluster error terms on matching group level, since there might be correlated error terms within matching group.

No

Matching groups of 9, which means 216/9=24 clusters (matching groups) on which the SE's will be clustered on.

216 participants, 72 agent type 1, 72 agent type 2, 72 principals.

We will collect around 200 observations. Given that we have sessions of the size of 18 participants, this will be 216 participants in total. This yields 24 matching groups à 9 participants; and 72 prinicipals, 72 agents of type 1, and 72 agents of type 2.

There will be 2 treatments. Thus, 216/2=108 participants per treatment arm. Of those, in each treatment: 36 principals, 36 agents type 1, 36 agents type 2.

We will use the following paramaters for the calculation of the minimum detectable effect size ("MDES"): power=0.8; p-value (error probability) = 0.05. We will also conduct the analogous non-parametric tests for the tests described further below, but calculate the MDES for the parametric variant. All numbers reported below obtained from GPower. We will cluster on matching group level, but the power calculations do not take this into account given the lack of method to do so. *************************************************************** Hypothesis 1a: Principals (in treatment) fail to choose the optimal promotion rule by not accounting for the shock of the advantaged player appropriately. Test 1: Two-sided t test against the theoretical optimal value of the allocation rule correction of 16. MDES t: .48. MDES Wilcoxon-rank-sum: .49 Hypothesis 1b: Principals in treatment promote more (often) sub-optimally than principals in baseline. Test 1: Treatment group differences: Subtracting the actual chosen value of the promotion rule from the optimal value (the size of suboptimal delegation), the principals in the treatment group differ from baseline principals - panel regression on treatment dummy. MDES: 0.24 Test 2: Treatment group differences: Frequency (number of deviations from optimal value) of suboptimal delegation the actual chosen value of the promotion rule from the optimal value (the size of suboptimal delegation), the principals in the treatment group differ from baseline principals. Linear panel: MDES: 0.24. In addition, Panel regression: Poisson or Neg-Bin regression. Test 3: Types created according to the average value of deviation across the 20 periods. If someone chooses optimal allocation rule on average classified as rational, otherwise not. Two sample t test, Mann-Whitney-U, MDES: .67. In addition probit regression. *************************************************************** Hypothesis 2a: Agents anticipate that principals promotion rules will be biased. Test 1: Belief of agents. Two-sided t test against the theoretical optimal value of the allocation rule correction of 16. MDES t: .33. MDES Wilcoxon-rank-sum: .34 Hypothesis 2b: Agents in treatment believe the principal promotes more suboptimally than agents in baseline. Test 1: Treatment group differences: Subtracting the actual chosen value (belief) about the principals' promotion rule from the optimal non-biased value 16 (=agents' belief about the size of suboptimal delegation), the agents in the treatment group differ from baseline agents - panel regression on treatment dummy. MDES: 0.17 *************************************************************** Hypothesis 3: In light of distorted incentives, (treated) agents adjust their effort provision downwards accordingly. Test 1: Treatment differences in effort exerted. Panel regression of effort on treatment dummy: MDES: 0.17 t-test (two sample independent): MDES: .48 Test 2: Deviation from the NE effort if the principal would choose the optimal allocation rule. Deviation larger for the treatment group. Treatment differences in effort exerted from optimal effort given principal's optimal decision. Panel regression of effort on treatment dummy: MDES: 0.17 Test 3: Best-response effort given beliefs of agents about the principal's alloaction rule. We do not expect substiantial treatment differences here given that agent's correctly anticipate principal's distortion.