Valuation of opportunity costs by rats working for rewarding electrical brain stimulation

Abstract

Pursuit of one goal typically precludes simultaneous pursuit of another. Thus, each exclusive activity entails an “opportunity cost:” the forgone benefits from the next-best activity eschewed. The present experiment estimates, in laboratory rats, the function that maps objective opportunity costs into subjective ones. In an operant chamber, rewarding electrical brain stimulation was delivered when the cumulative time a lever had been depressed reached a criterion duration. The value of the activities forgone during this duration is the opportunity cost of the electrical reward. We determined which of four functions best describes how objective opportunity costs, expressed as the required duration of lever depression, are translated into their subjective equivalents. The simplest account is the identity function, which equates subjective and objective opportunity costs. A variant of this function called the “sigmoidal-slope function,” converges on the identity function at longer durations but deviates from it at shorter durations. The sigmoidal-slope function has the form of a hockey stick. The flat “blade” denotes a range over which opportunity costs are subjectively equivalent; these durations are too short to allow substitution of more beneficial activities. The blade extends into an upward-curving portion over which costs become discriminable and finally into the straight “handle,” over which objective and subjective costs match. The two remaining functions are based on hyperbolic and exponential temporal discounting, respectively. The results are best described by the sigmoidal-slope function. That this is so suggests that different principles of intertemporal choice are involved in the evaluation of time spent working for a reward or waiting for its delivery. The subjective opportunity-cost function plays a key role in the evaluation and selection of goals. An accurate description of its form and parameters is essential to successful modeling and prediction of instrumental performance and reward-related decision making.

Forgetful inference in a sophisticated world model

“…We consider a cumulative handling time task (Breton et al, 2009;Solomon et al, 2017) in which rats hold down a lever for an experimenter-defined time period, called the price (P ), in return for rewarding electrical stimulation of the medial forebrain bundle (Olds and Milner, 1954) at a fixed current and a given pulse frequency (f ). In this paradigm, subjects experience many trials, each of which consists of an epoch during which price and frequency are fixed.…”

“…Together frequency, price and duration define the experimentally-set parameters of a given trial. Since duration depends directly on price, being directly proportional to it in many trials, we follow convention Niyogi et al, 2014a;Solomon et al, 2017) and use frequency and price but not duration in our models; see discussion. Frequencies and prices associated with each trial type (for subject 1).…”

“…The data in the present paper are drawn from (Solomon et al, 2017) which describes in detail all aspects of the experiment, including training prior to the full task. Training involved a shaping protocol which eventually introduced lead, test and trail trials, enabling subjects to learn the cyclic triad structure.…”

“…We studied a total of six subjects, each of which had experienced approximately 1500 triads of trials over a period of weeks. To allow adjustment from training to the full task we excluded the first 126 triads from our analysis, corresponding to one complete survey of the test trial frequencies and prices as defined in (Solomon et al, 2017). The number of surveys analysed for subjects 1-6 was 12, 10, 11, 8, 12, and 13 respectively, with each survey being acquired over 2 daily sessions, lasting approximately 6 to 7 hours each.…”

“…The number of surveys analysed for subjects 1-6 was 12, 10, 11, 8, 12, and 13 respectively, with each survey being acquired over 2 daily sessions, lasting approximately 6 to 7 hours each. Subjects 1-6 in this paper correspond to subjects F03, F09, F12, F16, F17 and F18 respectively in (Solomon et al, 2017). Whilst in general the results we describe apply to all six subjects, for simplicity we often display results in full for only subject 1, describing the remaining subjects using summary statistics.…”