Matching Law

MATCHING LAW

COMPLEX SCHEDULES:

Concurrent Schedule of Reinforcement - two or more responses are simultaneously

available, each has its own simple schedule of reinforcement (e.g. FR, VR, FI, VI).

Multiple Schedule of Reinforcement - two or more responses are successively available,

each has its own simple schedule of reinforcement.

TWO RESPONSE FORM OF THE MATCHING LAW:

The relative rate of behavior one (behavior one divided by the sum of behavior one

plus behavior two) is equal to the relative rate of reinforcement for behavior one (the

rate of reinforcement for behavior one divided by the sum of the reinforcement rates

for both behaviors).

Symbolic Form, where: B's are rates of behaviors, and

R's are rates of reinforcers

B1 / B1 + B2 = R1 / R1 + R2

Example 1: A hungry pigeon in a Skinner Box with two keys to peck and food as the reinforcer.

Concurrent VI 60-sec VI 30-sec

Left key is the VI 60-sec

Right key is the VI 30-sec

Assume: (1) The pigeon gets all scheduled reinforcers

(2) Total keypecks in 10 minutes = 100

Question 1: How many keypecks in the ten minutes will occur on the left key?

Solution: (1) In ten minutes the pigeon will obtain 10 reinforcers on the left,

VI 60-sec schedule.

R1 = 10

(2) In ten minutes the pigeon will obtain 20 reinforcers on the right,

VI 30-sec schedule.

R2 = 20

(3) B1 + B2 is given as 100 keypecks.

Matching Law Page 2

(4) Using B1 / B1 + B2 = R1 / R1 + R2

B1 / 100 = 10 / 10 + 20

(5) Summing and reducing

B1 / 100 = 1 / 3

(6) Multiply both sides of the equality by 100

B1 = 100 / 3

B1 = 33

(7) Answer:

B1 = 33 keypecks on the left key

B2 = 67 keypecks on the right key

Question 2: If the right keypeck schedule changed to VI 120-sec so the complex

schedule was now Concurrent VI 60-sec VI 120-sec, and everything

else remained the same, how may keypecks will now occur on the

left key?

Solution: (1) R1 = 10

(2) R2 = 5 (One every 2 minutes)

(3) B1 / 100 = 10 / 10 + 5

(4) B1 = (.67) (100)

(5) Answer B1 = 67 (left keypecks)

B2 = 33 (right keypecks)

NOTE: The reinforcement schedule for keypecks on the left key was VI 60-sec in

both questions. If the absolute rate of reinforcement determined the rate of behavior,

as most oversimplified accounts of reinforcement processes suggest, then the rate of

keypecking on the left key would be the same in both situations. Because relative

rate of reinforcement is the determiner of response rate, when the reinforcement

rate on the right key was changed the rate of keypecking on the left key increased,

even though the rate of reinforcement for that behavior