Human-Algorithm Interaction in the Centipede Game: an Experiment

Participants take part in an online experiment involving repeated strategic interactions in variants of the Centipede game. They are asked to specify strategies and make choices in a series of decision tasks. Some participants interact with other human players, while others interact with an algorithmic opponent. The study observes how decisions and beliefs evolve across multiple rounds, taking place during five subsequent days.

2025-12-15

2025-12-19

Realized efficiency at the matching-group/day level.

Realized efficiency is evaluated as the sum of the payoffs realized by the two players divided by the maximum potential surplus (which is equal to 3200 in all treatments). To make sure efficiency does not depend on the specific implementation of the random matching procedure, in the Human-Human treatments, for each day we will:
- match each first mover with each and every second mover in the group, thus forming n^2 pairs per matching group, where 2n is the total number of players in a matching group.
- compute efficiency in each of these pairs
- take the average at the matching group level as our unit of observation.
We will thus have one observation, per matching group, per day, in each of the treatments.
In the Human-Algorithm and Algorithm-Human treatments, all human players in a single matching group are paired with the same algorithm, so we compute efficiency as the average across all players in a matching group, in a day.

Secondary outcomes include individual choice patterns, belief reports, and derived measures of strategic sophistication (e.g., indicators of nonstrategic versus strategic reasoning). These outcomes characterize how participants’ decision rules and expectations evolve across rounds and how they differ across treatments.

In addition to the primary outcome of efficiency, the study analyzes several behavioral and cognitive variables that help interpret treatment differences. These include:
• participants’ selected strategy in each day of play;
• participants’ beliefs about opponents’ strategies;
• classifications of players into nonstrategic and strategic types based on their strategies and beliefs;
• changes in these patterns over the five-day longitudinal period.

These secondary outcomes are not used to define treatment effect but instead provide insight into the mechanisms underlying observed efficiency differences and allow comparison with predictions from the cognitive-hierarchy framework.

The study employs an online experimental design with repeated interactions in a centipede game. Participants are assigned to treatments that vary only in game structure and opponent type. They provide strategies over multiple rounds, enabling the study of how behavior changes with experience. Outcomes of interest include decision patterns and cooperation levels under different interaction conditions.

Not available

Participants in Experiment 2 are randomly allocated to roles and treatments at the beginning of day 1 by Prolific, the platform we use to recruit participants. They are randomly allocated to matching groups in day 1, through a procedure embedded in the experimental software, developed in oTree.

Individual.

Yes

We plan to have 17 matching groups (clusters) per treatment, for a total of 6 treatments and 102 matching groups.

1360, which results from - 17 matching groups of 20 participants in the Human-Human treatment with standard payoffs - 17 matching groups of 20 participants in the Human-Human treatment with equalized payoffs - 17 matching groups of 10 participants in the Human-Algorithm treatment with standard payoffs (Algorithm in the role of second mover) - 17 matching groups of 10 participants in the Human-Algorithm treatment with equalized payoffs (Algorithm in the role of second mover) - 17 matching groups of 10 participants in the Algorithm-Human treatment with standard payoffs (Algorithm in the role of first mover) - 17 matching groups of 10 participants in the Algorithm-Human treatment with equalized payoffs (Algorithm in the role of first mover)

17 matching groups per treatment

A priori power analysis was conducted in G*Power 3.1 for an F-test, ANOVA: repeated measures (between-subjects factor), testing the between-groups main effect in a 2 (group) × 5 (time) design. Assuming an effect size of f(V) = 0.5, α = .05, two groups, and five repeated measurements, a total sample size of N = 34 yields statistical power of 1 − β ≈ 0.81 to detect the between-groups effect.