On the theoretical and empirical status of the matching law and matching theory

Psychological Bulletin

Volumn 139, Issue 5, 2013, Pages 1000-1028

  McDowell, J J ^a  

^a EMORY UNIVERSITY   (United States)

Author keywords

Adaptive behavior; Choice; Matching law

Indexed keywords

ADAPTIVE BEHAVIOR; ARTICLE; DECISION MAKING; HUMAN; PSYCHOLOGICAL MODEL; PSYCHOLOGICAL THEORY; SOCIAL BEHAVIOR;

ADAPTATION, PSYCHOLOGICAL; CHOICE BEHAVIOR; HUMANS; MODELS, PSYCHOLOGICAL; PSYCHOLOGICAL THEORY; SOCIAL BEHAVIOR;

EID: 84883774833     PISSN: 00332909     EISSN: None     Source Type: Journal    
DOI: 10.1037/a0029924     Document Type: Article

References (139)

1. Baum, W. M. (1966). Choice in the rat as a function of probability and amount of reward (Unpublished doctoral dissertation). Harvard University, Cambridge, MA.
2. Baum, W. M. (1974). On two types of deviation from the matching law: Bias and undermatching. Journal of the Experimental Analysis of Behavior, 22, 231-242
3. Baum, W. M. (1979). Matching, undermatching, and overmatching in studies of choice. Journal of the Experimental Analysis of Behavior, 32, 269-281
4. Baum, W. M. (1981). Optimization and the matching law as accounts of instrumental behavior. Journal of the Experimental Analysis of Behavior, 36, 387-403
5. Baum, W. M. (1983). Matching, statistics, and common sense. Journal of the Experimental Analysis of Behavior, 39, 499-501
6. Baum, W. M., & Rachlin, H. C. (1969). Choice as time allocation. Journal of the Experimental Analysis of Behavior, 12, 861-874
7. Beardsley, S. D., & McDowell, J. J. (1992). Application of Herrnstein's hyperbola to time allocation of naturalistic human behavior maintained by naturalistic social reinforcement. Journal of the Experimental Analysis of Behavior, 57, 177-185
8. Borrero, C. S. W., Vollmer, T. R., Borrero, J. C., Bourret, J. C., Sloman, K. N., Samaha, A. L., & Dallery, J. (2010). Concurrent reinforcement schedules for problem behavior and appropriate behavior: Experimental applications of the matching law. Journal of the Experimental Analysis of Behavior, 93, 455-469
9. Borrero, J. C., Crisolo, S. S., Tu, Q., Rieland, W. A., Ross, N. A., Francisco, M. T., & Yamamoto, K. Y. (2007). An application of the matching law to social dynamics. Journal of Applied Behavior Analysis, 40, 589-601
10. Borrero, J. C., & Vollmer, T. R. (2002). An application of the matching law to severe problem behavior. Journal of Applied Behavior Analysis, 35, 13-27
11. Bradshaw, C. M., Szabadi, E., & Bevan, P. (1976). Behavior of humans in variable-interval schedules of reinforcement. Journal of the Experimental Analysis of Behavior, 26, 135-141
12. Bradshaw, C. M., Szabadi, E., & Bevan, P. (1977). Effect of punishment on human variable-interval performance. Journal of the Experimental Analysis of Behavior, 27, 275-279
13. Bradshaw, C. M., Szabadi, E., & Bevan, P. (1978). Effect of variableinterval punishment on the behavior of humans in variable-interval schedules of monetary reinforcement. Journal of the Experimental Analysis of Behavior, 29, 161-166
14. Bradshaw, C. M., Szabadi, E., Bevan, P., & Ruddle, H. V. (1979). The effect of signaled reinforcement availability on concurrent performances in humans. Journal of the Experimental Analysis of Behavior, 32, 65-74
15. Brownstein, A. J. (1971). Concurrent schedules of response independent reinforcement: Duration of a reinforcing stimulus. Journal of the Experimental Analysis of Behavior, 15, 211-214
16. Buskist, W. F., & Miller, H. L. (1981). Concurrent operant performance in humans: Matching when food is the reinforcer. Psychological Record, 31, 95-100.
17. Capaldi, D. M., & Patterson, G. R. (1987). An approach to the problem of recruitment and retention rates for longitudinal research. Behavioral Assessment, 9, 169-177
18. Carr, E. G., & McDowell, J. J. (1980). Social control of self-injurious behavior of organic etiology. Behavior Therapy, 11, 402-409
19. Catania, A. C. (1963a). Concurrent performances: A baseline for the study of reinforcement magnitude. Journal of the Experimental Analysis of Behavior, 6, 299-300
20. Catania, A. C. (1963b). Concurrent performances: Reinforcement interaction and response independence. Journal of the Experimental Analysis of Behavior, 6, 253-263
21. Chung, S.-H., & Herrnstein, R. J. (1967). Choice and delay of reinforcement. Journal of the Experimental Analysis of Behavior, 10, 67-74.
22. Cliffe, M. J., & Parry, S. J. (1980). Matching to reinforcer value: Human concurrent variable-interval performance. Quarterly Journal of Experimental Psychology, 32, 557-570
23. Conger, R., & Killeen, P. R. (1974). Use of concurrent operants in small group research: A demonstration. Pacific Sociological Review, 17, 399- 416.
24. Cording, J. R., McLean, A. P., & Grace, R. C. (2011). Testing the linearity and independence assumptions of the generalized matching law for reinforcer magnitude: A residual meta-analysis. Behavioural Processes, 87, 64-70
25. Dallery, J., McDowell, J. J., & Lancaster, J. S. (2000). Falsification of matching theory's account of single-alternative responding: Herrnstein's k varies with sucrose concentration. Journal of the Experimental Analysis of Behavior, 73, 23-43
26. Dallery, J., McDowell, J. J., & Soto, P. L. (2004). The measurement and functional properties of reinforcer value in single-alternative responding: A test of linear system theory. Psychological Record, 54, 45-65. Retrieved from http://opensiuc.lib.siu.edu/tpr/vol54/iss1/4
27. Dallery, J., & Soto, P. L. (2004). Herrnstein's hyperbolic matching equation and behavioral pharmacology: Review and critique. Behavioural Pharmacology, 15, 443-459
28. Dallery, J., Soto, P. L., & McDowell, J. J. (2005). A test of the formal and modern theories of matching. Journal of the Experimental Analysis of Behavior, 84, 129-145
29. Davison, M. (1993). On the dynamics of behavior allocation between simultaneously and successively available reinforcer sources. Behavioural Processes, 29, 49-63
30. Davison, M. C., & Hunter, I. (1976). Performance on variable-interval schedules arranged singly and concurrently. Journal of the Experimental Analysis of Behavior, 25, 335-345
31. Davison, M., & McCarthy, D. (1988). The matching law: A research review. Hillsdale, NJ: Erlbaum.
32. Daw, N. D., & Touretzky, D. S. (2001). Operant behavior suggests attentional gating of dopamine system inputs. Neurocomputing, 38-40, 1161-1167
33. Dawson, M. R. W., Dupuis, B., Spetch, M. L., & Kelly, D. M. (2009). Simple artificial neural networks that match probability and exploit and explore when confronting a multiarmed bandit. IEEE Transactions on Neural Networks, 20, 1368-1371
34. de Villiers, P. A. (1974). The law of effect and avoidance: A quantitative relationship between response rate and shock-frequency reduction. Journal of the Experimental Analysis of Behavior, 21, 223-235
35. de Villiers, P. A. (1977). Choice in concurrent schedules and a quantitative formulation of the law of effect. In W. K. Honig & J. E. R. Staddon (Eds.), Handbook of operant behavior (pp. 233-287). Englewood Cliffs, NJ: Prentice-Hall.
36. de Villiers, P. A., & Herrnstein, R. J. (1976). Toward a law of response strength. Psychological Bulletin, 83, 1131-1153
37. de Villiers, P. A., & Millenson, J. R. (1972). Concurrent performances: A baseline for the study of conditioned anxiety. Journal of the Experimental Analysis of Behavior, 18, 287-294
38. Dishion, T. J., Andrews, D. W., & Crosby, L. (1995). Antisocial boys and their friends in early adolescence: Relationship characteristics, quality, and interactional process. Child Development, 66, 139 -151
39. Dishion, T. J., French, D. C., & Patterson, G. R. (1995). The development and ecology of antisocial behavior. In D. Cicchetti & D. J. Cohen (Eds.), Developmental psychopathology: Vol. 2. Risk, disorder, and adaptation (pp. 421-471). New York, NY: Wiley.
40. Dishion, T. J., Spracklen, K. M., Andrews, D. W., & Patterson, G. R. (1996). Deviancy training in male adolescent friendships. Behavior Therapy, 27, 373-390
41. Elliffe, D., Davison, M., & Landon, J. (2008). Relative reinforcer rates and magnitudes do not control concurrent choice independently. Journal of the Experimental Analysis of Behavior, 90, 169-185
42. Fantino, E., Squires, N., Delbruck, N., & Peterson, C. (1972). Choice behavior and the accessibility of the reinforcer. Journal of the Experimental Analysis of Behavior, 18, 35-43
43. Fernandez, E., & McDowell, J. J. (1995). Response-reinforcement relationships in chronic pain syndrome: Applicability of Herrnstein's Law. Behaviour Research and Therapy, 33, 855-863
44. Frank, Robert, H. (1997). Microeconomics and behavior (3rd ed.). New York, NY: McGraw-Hill.
45. Gray, L. N., & von Broembsen, M. H. (1976). On the generalizability of the law of effect: Social psychological measurement of group structures and process. Sociometry, 39, 175-183
46. Green, D. P., & Shapiro, I. (1996). Pathologies of rational choice theory: A critique of applications in political science. New Haven, CT: Yale University Press.
47. Hamblin, R. L. (1977). Behavior and reinforcement: A generalization of the matching law. In R. L. Hamblin & J. H. Kunkel (Eds.), Behavioral theory in sociology: Essays in honor of George C. Homans (pp. 469- 502). New Brunswick, NJ: Transaction Books.
48. Hamblin, R. L. (1979). Behavioral choice and social reinforcement: Step function versus matching. Social Forces, 57, 1141-1156.
49. Herrnstein, R. J. (1961). Relative and absolute strength of response as a function of frequency of reinforcement. Journal of the Experimental Analysis of Behavior, 4, 267-272
50. Herrnstein, R. J. (1970). On the law of effect. Journal of the Experimental Analysis of Behavior, 13, 243-266
51. Herrnstein, R. J. (1974). Formal properties of the matching law. Journal of the Experimental Analysis of Behavior, 21, 159-164
52. Herrnstein, R. J. (1979). Derivatives of matching. Psychological Review, 86, 486-495
53. Herrnstein, R. J. (1990). Rational choice theory: Necessary but not sufficient. American Psychologist, 45, 356 -367
54. Herrnstein, R. J. (2000). The matching law: Papers in psychology and economics (H. Rachlin & D. I. Laibson, Eds.). Cambridge, MA: Harvard University Press.
55. Heyman, G. M. (1983). A parametric evaluation of the hedonic and motoric effects of drugs: Pimozide and amphetamine. Journal of the Experimental Analysis of Behavior, 40, 113-122
56. Heyman, G. M., & Monaghan, M. M. (1987). Effects of changes in response requirement and deprivation on the parameters of the matching law equation: New data and review. Journal of Experimental Psychology: Animal Behavior Processes, 13, 384 -394
57. Heyman, G. M., & Monaghan, M. M. (1994). Reinforcer magnitude (sucrose concentration) and the matching law theory of response strength. Journal of the Experimental Analysis of Behavior, 61, 505- 516
58. Hull, C. (1943). Principles of behavior. New York, NY: Appleton-Century-Crofts.
59. Hursh, S. R. (1984). Behavioral economics. Journal of the Experimental Analysis of Behavior, 42, 435-452
60. Killeen, P. (1972). The matching law. Journal of the Experimental Analysis of Behavior, 17, 489-495
61. Kollins, S. H., Lane, S. D., & Shapiro, S. K. (1997). Experimental analysis of childhood psychopathology: A laboratory matching analysis of the behavior of children diagnosed with attention-deficit hyperactivity disorder (ADHD). Psychological Record, 47, 25-44.
62. Kollins, S. H., Newland, M. C., & Critchfield, T. S. (1997a). Human sensitivity to reinforcement in operant choice: How much do consequences matter Psychonomic Bulletin & Review, 4, 208-220
63. Kollins, S. H., Newland, M. C., & Critchfield, T. S. (1997b). Human sensitivity to reinforcement in operant choice: How much do consequences matter: Erratum. Psychonomic Bulletin & Review, 4, 431
64. Krull, C., & Pierce, W. D. (1997). Behavior analysis and demographics: Government control of reproductive behavior and fertility in the province of Quebec, Canada. In P. A. Lamal (Ed.), Cultural contingencies: Behavior analytic perspectives on cultural practices (pp. 107-132). Westport, CT: Praeger.
65. Lau, B., & Glimcher, P. W. (2005). Dynamic response-by-response models of matching behavior in rhesus monkeys. Journal of the Experimental Analysis of Behavior, 84, 555-579
66. Lau, B., & Glimcher, P. W. (2008). Value representations in the primate striatum during matching behavior. Neuron, 58, 451-463
67. MacCorquodale, K., & Meehl, P. E. (1948). On a distinction between hypothetical constructs and intervening variables. Psychological Review, 55, 95-107
68. Martens, B. K., & Houk, J. L. (1989). The application of Herrnstein's law of effect to disruptive and on-task behavior of a retarded adolescent girl. Journal of the Experimental Analysis of Behavior, 51, 17-27
69. Matthews, L. R., & Temple, W. (1979). Concurrent schedule assessment of food preferences in cows. Journal of the Experimental Analysis of Behavior, 32, 245-254
70. McDowell, J. J. (1980). An analytic comparison of Herrnstein's equations and a multivariate rate equation. Journal of the Experimental Analysis of Behavior, 33, 397-408
71. McDowell, J. J. (1981). On the validity and utility of Herrnstein's hyperbola in applied behavior analysis. In C. M. Bradshaw, E. Szabadi, & C. F. Lowe (Eds.), Quantification of steady-state operant behaviour (pp. 311-324). Amsterdam, the Netherlands: Elsevier/North-Holland.
72. McDowell, J. J. (1982). The importance of Herrnstein's mathematical statement of the law of effect for behavior therapy. American Psychologist, 37, 771-779
73. McDowell, J. J. (1986). On the falsifiability of matching theory. Journal of the Experimental Analysis of Behavior, 45, 63-74
74. McDowell, J. J. (1988a). Behavior analysis: The third branch of Aristotle's physics. Journal of the Experimental Analysis of Behavior, 50, 297-304
75. McDowell, J. J. (1988b). Matching theory in natural human environments. The Behavior Analyst, 11, 95-109.
76. McDowell, J. J. (1989). Two modern developments in matching theory. The Behavior Analyst, 12, 153-166.
77. McDowell, J. J. (1991). Irreconcilable differences and political reality in these dark ages. The Behavior Analyst, 14, 29-33.
78. McDowell, J. J. (2004). A computational model of selection by consequences. Journal of the Experimental Analysis of Behavior, 81, 297- 317
79. McDowell, J. J. (2005). On the classic and modern theories of matching. Journal of the Experimental Analysis of Behavior, 84, 111-127
80. McDowell, J. J., & Ansari, Z. (2005). The quantitative law of effect is a robust emergent property of an evolutionary algorithm for reinforcement learning. In M. S. Capcarrere, A. A. Freitas, P. J. Bentley, C. G. Johnson, & J. Timmis (Eds.), Advances in artificial life: 8th European Conference on Artificial Life (pp. 413-422). Berlin, Germany: Springer-Verlag
81. McDowell, J. J., & Caron, M. L. (2007). Undermatching is an emergent property of selection by consequences. Behavioural Processes, 75, 97- 106
82. McDowell, J. J., & Caron, M. L. (2010a). Bias and undermatching in delinquent boys' verbal behavior as a function of their level of deviance. Journal of the Experimental Analysis of Behavior, 93, 469-481
83. McDowell, J. J., & Caron, M. L. (2010b). Matching in an undisturbed natural human environment. Journal of the Experimental Analysis of Behavior, 93, 413-431
84. McDowell, J. J., Caron, M. L., Kulubekova, S., & Berg, J. P. (2008). A computational theory of selection by consequences applied to concurrent schedules. Journal of the Experimental Analysis of Behavior, 90, 387- 403
85. McDowell, J. J., & Dallery, J. (1999). Falsification of matching theory: Changes in the asymptote of Herrnstein's hyperbola as a function of water deprivation. Journal of the Experimental Analysis of Behavior, 72, 251-268
86. McDowell, J. J., & Popa, A. (2009). Beyond continuous mathematics and traditional scientific analysis: Understanding and mining Wolfram's A New Kind of Science. Behavioural Processes, 81, 343-352
87. McDowell, J. J., & Popa, A. (2010). Toward a mechanics of adaptive behavior: Evolutionary dynamics and matching theory statics. Journal of the Experimental Analysis of Behavior, 94, 241-260
88. McDowell, J. J., Soto, P. L., Dallery, J., & Kulubekova, S. (2006). A computational theory of adaptive behavior based on an evolutionary reinforcement mechanism. In M. Keijzer (Ed.), Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation (pp. 175-182). New York, NY: ACM Press
89. McDowell, J. J., & Wood, H. M. (1984). Confirmation of linear system theory prediction: Changes in Herrnstein's k as a function of changes in reinforcer magnitude. Journal of the Experimental Analysis of Behavior, 41, 183-192
90. McDowell, J. J., & Wood, H. M. (1985). Confirmation of linear system theory prediction: Rate of change of Herrnstein's k as a function of response-force requirement. Journal of the Experimental Analysis of Behavior, 43, 61-73
91. McLean, A. P. (2006). The sampling distribution of k. Behavioural Processes, 72, 300-308
92. McLean, A. P., & White, K. G. (1983). Temporal constraint on choice: Sensitivity and bias in multiple schedules. Journal of the Experimental Analysis of Behavior, 39, 405-426
93. McSweeney, F. K. (1975). Concurrent schedule responding as a function of body weight. Animal Learning & Behavior, 3, 264-270
94. McSweeney, F. K., Melville, C. L., & Whipple, J. E. (1983). Herrnstein's equation for the rates of responding during concurrent schedules. Animal Learning & Behavior, 11, 275-289
95. Moffat, G. H., & Koch, D. L. (1973). Escape performance as a function of delay of reinforcement and inescapable US trials. Psychological Reports, 32, 1255-1261
96. Motulsky, H. J., & Christopoulos, A. (2004). Fitting models to biological data using linear and nonlinear regression. New York, NY: Oxford University Press.
97. Mullainathan, S., & Thaler, R. H. (2000). Behavioral economics (MIT Department of Economics Working Paper No. 00-27). Retrieved from http://papers.ssrn.com/paper.taf?abstract_id_245828
98. Murray, L. K., & Kollins, S. H. (2000). Effects of methylphenidate on sensitivity to reinforcement in children diagnosed with attention deficit hyperactivity disorder: An application of the matching law. Journal of Applied Behavior Analysis, 33, 573-591
99. Myers, D. L., & Myers, L. E. (1977). Undermatching: A reappraisal of performance on concurrent variable-interval schedules of reinforcement. Journal of the Experimental Analysis of Behavior, 27, 203-214
100. Myerson, J., & Hale, S. (1984). Practical implications of the matching law. Journal of Applied Behavior Analysis, 17, 367-380
101. Neuringer, A. J. (1967). Effects of reinforcement magnitude on choice and rate of responding. Journal of the Experimental Analysis of Behavior, 10, 417-424
102. Noll, J. E. (1995). The matching law as a theory of choice in behavior therapy. In W. O'Donohue & L. Krasner (Eds.), Theories of behavior therapy: Exploring behavior change (pp. 129-144). Washington, DC: American Psychological Association
103. Oliver, C., Hall, S., & Nixon, J. (1999). A molecular to molar analysis of communicative and problem behaviors. Research in Developmental Disabilities, 20, 197-213
104. Pear, J. J. (1975). Implications of the matching law for ratio responding. Journal of the Experimental Analysis of Behavior, 23, 139-140
105. Pierce, W. D., & Epling, W. F. (1983). Choice, matching, and human behavior: A review of the literature. The Behavior Analyst, 6, 57-76.
106. Pierce, W. D., Epling, W. F., & Greer, S. M. (1981). Human communication and the matching law. In C. M. Bradshaw, E. Szabadi, & C. F. Lowe (Eds.). Quantification of steady-state operant behaviour (pp. 345-352). Amsterdam, the Netherlands: Elsevier/North-Holland.
107. Platt, M. L., & Glimcher, P. W. (1999, July 15). Neural correlates of decision variables in parietal cortex. Nature, 400, 233-238
108. Plaud, J. J. (1992). The prediction and control of behavior revisited: A review of the matching law. Journal of Behavior Therapy and Experimental Psychiatry, 23, 25-31
109. Rachlin, H., Green, L., Kagel, J. H., & Battalio, R. C. (1976). Economic demand theory and psychological studies of choice. In G. H. Bower (Ed.), The psychology of learning and motivation (Vol. 10, pp. 129- 154). New York, NY: Academic Press
110. Rachlin, H., Kagel, J. H., & Battalio, R. C. (1980). Substitutability in time allocation. Psychological Review, 87, 355-374
111. Reed, D. D., Critchfield, T. S., & Martens, B. K. (2006). The generalized matching law in elite sports competition: Football play calling as operant choice. Journal of Applied Behavior Analysis, 39, 281-297
112. Ruddle, H. V., Bradshaw, C. M., & Szabadi, E. (1981). Performance of humans in variable-interval avoidance schedules programmed singly, and concurrently with variable-interval schedules of positive reinforcement. Quarterly Journal of Experimental Psychology: Comparative and Physiological Psychology, 33B, 213-226
113. Ruddle, H. V., Bradshaw, C. M., Szabadi, E., & Foster, T. M. (1982). Performance of humans in concurrent avoidance/positive-reinforcement schedules. Journal of the Experimental Analysis of Behavior, 38, 51-61
114. Seth, A. K. (1999). Evolving behavioural choice: An investigation into Herrnstein's matching law. In D. Floreano, J.-D. Nicoud, & F. Mondana (Eds.), Advances in artificial life: 5th European Conference on Artificial Life (pp. 225-236). Berlin, Germany: Springer-Verlag
115. Seth, A. K. (2001). Modeling group foraging: Individual suboptimality, interference, and a kind of matching. Adaptive Behavior, 9, 67-89
116. Skinner, B. F. (1938). The behavior of organisms: An experimental analysis. New York, NY: Appleton-Century-Crofts.
117. Snyder, J., Horsch, E., & Childs, J. (1997). Peer relationships of young children: Affiliative choices and the shaping of aggressive behavior. Journal of Clinical Child Psychology, 26, 145-156
118. Snyder, J. J., & Patterson, G. R. (1995). Individual differences in social aggression: A test of a reinforcement model of socialization in the natural environment. Behavior Therapy, 26, 371-391
119. Snyder, J., Schrepferman, L., & St. Peter, C. (1997). Origins of antisocial behavior: Negative reinforcement and affect dysregulation of behavior as socialization mechanisms in family interaction. Behavior Modification, 21, 187-215
120. Snyder, J., West, L., Stockemer, V., Gibbons, S., & Almquist-Parks, L. (1996). A social learning model of peer choice in the natural environment. Journal of Applied Developmental Psychology, 17, 215-237
121. Soto, P. L., McDowell, J. J., & Dallery, J. (2005). Effects of adding a second reinforcement alternative: Implications for Herrnstein's interpretation of re. Journal of the Experimental Analysis of Behavior, 84, 185-225
122. Staddon, J. E. R. (1968). Spaced responding and choice: A preliminary analysis. Journal of the Experimental Analysis of Behavior, 11, 669- 682
123. Staddon, J. E. R. (1972). Temporal control and the theory of reinforcement schedules. In R. M. Gilbert & J. R. Millenson (Eds.), Reinforcement: Behavioral analyses (pp. 209-262). New York, NY: Academic Press.
124. Stilling, S. T., & Critchfield, T. S. (2010). The matching relation and situation-specific bias modulation on professional football play selection. Journal of the Experimental Analysis of Behavior, 93, 435-454
125. Sugrue, L. P., Corrado, G. S., & Newsome, W. T. (2004, June 18). Matching behavior and the representation of value in the parietal cortex. Science, 304, 1782-1787
126. Sunahara, D. F., & Pierce, W. D. (1982). The matching law and bias in a social exchange involving choice between alternatives. Canadian Journal of Sociology, 7, 145-166
127. Symons, F. J., Hoch, J., Dahl, N. A., & McComas, J. J. (2003). Sequential and matching analyses of self-injurious behavior: A case of overmatching in the natural environment. Journal of Applied Behavior Analysis, 36, 267-270
128. Szabadi, E., Bradshaw, C. M., & Ruddle, H. (1981). Reinforcement processes in affective illness: Towards a quantitative analysis. In C. M. Bradshaw, E. Szabadi, & C. F. Lowe (Eds.), Quantification of steadystate operant behavior (pp. 299-310). Amsterdam, the Netherlands: Elsevier/North-Holland.
129. Takahashi, M., & Iwamoto, T. (1986). Human concurrent performances: The effects of experience, instructions, and schedule-correlated stimuli. Journal of the Experimental Analysis of Behavior, 45, 257-267
130. Taylor, D., Lincoln, A. J., & Foster, S. L. (2010). Impaired behavior regulation under conditions of concurrent variable schedules of reinforcement in children with ADHD. Journal of Attention Disorders, 13, 358-368
131. Thorndike, E. L. (1898). Animal intelligence: An experimental study of the associative processes in animals. Psychological Review Monograph Supplement, 2(4, Whole No. 8).
132. Touretzky, D. S., & Saksida, L. M. (1997). Operant conditioning in Skinnerbots. Adaptive Behavior, 5, 219 -247
133. Vollmer, T. R., & Bourret, J. (2000). An application of the matching law to evaluate the allocation of two- and three-point shots by college basketball players. Journal of Applied Behavior Analysis, 33, 137-150
134. Warren-Boulton, F. R., Silberberg, A., Gray, M., & Ollom, R. (1985). Reanalysis of the equation for simple action. Journal of the Experimental Analysis of Behavior, 43, 265-277
135. Wearden, J. H. (1980). Undermatching on concurrent variable-interval schedules and the power law. Journal of the Experimental Analysis of Behavior, 33, 149-152
136. Wearden, J. H. (1981). Bias and undermatching: Implications for Herrnstein's equation. Behaviour Analysis Letters, 1, 177-185.
137. Wearden, J. H. (1983). Undermatching and overmatching as deviations from the matching law. Journal of the Experimental Analysis of Behavior, 40, 333-340
138. Wearden, J. H., & Burgess, I. S. (1982). Matching since Baum (1979). Journal of the Experimental Analysis of Behavior, 38, 339-348
139. Williams, B. A. (1988). Reinforcement, choice, and response strength. In R. C. Atkinson, R. J. Herrnstein, G. Lindzey, & R. D. Luce (Eds.), Stevens' handbook of experimental psychology: Vol. 1. Learning and cognition (2nd ed., pp. 167-244). New York, NY: Wiley.