Dynamic Effort Allocation in Information Processing

In this experiment we study memory and cognition, and how they respond to rewards.

Human attention and memory are costly tasks. They are also complex: decisions about how closely to pay attention to something, whether to remember it, and how stored memories influence subsequent choice take place over time, are only party under conscious control, and are influenced by a variety of factors. We propose a stylized model of how cognitive effort is allocated to different tasks across time. More effort translates into a more faithful representation of the task (word recall task) and better performance upon recall. Critically, we assume that effort choices in memory acquisition, memory maintenance, and memory recall are complements. In more technical terms, the "production function" of memory is supermodular in effort choices across time.

Our experimental paradigm uses this basic model to do two things: 1) test the hypothesis that effort choices are complements and efforts are chosen rationally, and 2) use the structure of the model to find the source of errors and bound the utility costs of effort.

The intervention is a remunerated laboratory experiment; data collection will take place at the University of Tennessee, Knoxville's Experimental Economics Laboratory. The subjects will be individuals recruited by the lab manager for the purpose of completing this experiment.

Participants will be asked to complete the word recall tasks (as described elsewhere) on site, and paid for their choices.

2025-04-14

2025-11-01

The key variables of interest are the (conditional on the true answer in experiment two and unconditional in experiment one) proportions of correct responses on each question for each trial and for each participant. Using these variables, we will test the hypothesis of supermodularity, and bound the costs of information processing for each participant.

The unconditional probabilities of correct answers will be used to test the main prediction of a model of supermodular dynamic effort allocation. This prediction states that the overall performance should respond less to differences in incentive when the incentive level is revealed later in the information handling process. High reward will lead to less of an increase in performance and low reward will lead to less of a decrease when revealed later.
The conditional probabilities of correct responses with be used to construct matrices (with probabilities of correct responses on the diagonal), which will then be. Given these matrices in various conditions (reward level, timing) and two additional possibilities (rounds without delay, and nonremunerated responses to the same requested again, right after the remunerated response), we will estimate the objects of choice (cognitive error matrices) and bound the utility costs of these objects for the participants, first at the aggregate level, and then at the participant level.

In this experiment people will complete a series of memory-based cognitive tasks with varying reward levels.

In our experimental task, individuals are presented with a verbal recall list of words that they are invited to memorize, and later, recall. More correct answers translate into higher payments. A round consists of presentation of the word list for that round, time to study the list, then a delay period, and then a recall task, where individuals are asked to identify which of the words on a new list (containing both words from the original word list, and new words) they were presented with in the beginning of a round are present. During the delay period, players engage in an incentivized distractor task where they must press the space bar whenever a green square on screen turns blue. Individuals may be informed about the actual payoffs at a random point in the process. Payoffs are high or low with equal prior probability and they can be revealed at different times. Low payoffs mean zero reward for success in the current task while high reward means some non-zero payoff for correct responses.

There are two experiments in this study. The first is the paradigm described above, where there are twenty rounds of this procedure. In this experiment, the reward (high or low) is revealed either before the word list is given, after the word list is given but before the wait, or immediately before recall. Each reward timing is equally likely.

We use the data from experiment one to (jointly) test the assumptions of complementarity and rationality in effort choices.

Experiment two makes several changes to the experimental setup. First, the revelation of reward information is changed.

If rewards are low in experiment two then the following will occur each one quarter of the time: (1) Low reward is revealed before stimulus. (2) Low reward is revealed after stimulus and before delay. (3) Low reward is revealed after the delay and before the response. (4) Low reward is never revealed. Each of these outcomes is equally likely. However, if rewards are high, this fact will never be revealed.

Second, several additional conditions are added. With 50% probability, the distractor task is skipped each task. In addition, with 50% probability, after a response is given, the same recall list is asked for again, this time with no reward. Both of these extra conditions are assigned independently of the reward level and independently of information revelation.

Finally, the experiment two breaks up the memory tasks into two blocks of twenty memory tasks each. One block has a larger "high" reward than the other. Both low rewards still give zero payoff. .

We use the data from the experiment two to determine the error rates in specific phases and to bound the costs of information processing at all three stages - acquisition, storage, and recall.

Randomization performed using the built-in features in Qualtrics.

The randomization unit is a round; in each round the level of the reward, and the timing of the revelation reward are randomized. In experiment 2 the additional conditions and order of blocks are also randomized.

No

Subjects maybe be clustered by session if strong evidence of session effects is found but otherwise observations will not be clustered.

500 participants. 20 memory tasks per person in experiment one and 40 tasks per person in experiment two. Each task results in 10 responses. Aggregate analysis will treat a participant as an observation. Individual analysis will treat a response as an observation.

2000 individuals in experiment one and 300 for experiment two (note that we are using a within-subjects design).

Sample size: 500 individuals. We use a within-subjects design, which significantly reduces the number of participants. We consider testing Corollary 1 (our "experiment 1") as one experiment with a within-subjects design, and the cost-bounding exercise (our experiment two block 1 and and experiment two block 2, the only difference between which is the level of the "high" reward ) as another experiment with a within-subjects design. For each of these two experiments, for a small effect size (Cohen's d_z - not: NOT Cohen's d) of 0.2, Type I error (alpha) of 0.05, a power level of 0.8, and a two-sided ("difference is greater than 0" for experiment 2, or, for testing corollary 1, that the difference in revelation earlier is greater than the difference for revelation later) test, the R package "pwr" yields that 199 participants are necessary, which we round up to 200. Thus, 200 individuals are necessary for each of two experiments. We allow participants to take part in both experiments; given the randomness in the experiment (which implies that not all of the 200 participants will have all of the necessary data), and assuming (conservatively) that about 200 participants (across both experiments together) will not have enough data, we arrive at the necessary number: 200 (for the first experiment) + 200 (for the second experiment) + 100 (to account for missing data issues)=500 participants. Not that the effect size used for this computation is small (Cohen (1998) defines "small" to be 0.2 or less), and thus, this setup can detect quite small differences in behavior.