Separable Games
Certain 2‐person oscilloscope‐based continuous games are known to give rise to dynamic behavior resembling that of the Prisoner's Dilemma game and other 2‐choice games. We explain this similarity of behavior in terms of structural equivalence between the 2‐person continuous games and a subset o...
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| Published in | Behavioral Science Vol. 14; no. 2; pp. 121 - 132 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
California
John Wiley & Sons, Ltd
01.03.1969
University of Michigan, Mental Health Research Institute |
| Online Access | Get full text |
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| Abstract | Certain 2‐person oscilloscope‐based continuous games are known to give rise to dynamic behavior resembling that of the Prisoner's Dilemma game and other 2‐choice games. We explain this similarity of behavior in terms of structural equivalence between the 2‐person continuous games and a subset of all possible 2‐person, 2‐choice (2 × 2) games, called the separable games. A game is defined as separable if each player's payoff can be expressed as a sum of partial payoffs, each of which depends only on the strategy choice of one player. All separable games can be described in terms of the same two psychologically relevant parameters. They can be played in staggered, graduated, or continuous form. Non‐separable games, including “Chicken” and many other interesting games, cannot be staggered, and their graduated and continuous versions are subject to a reinterpretation. |
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| AbstractList | Certain 2‐person oscilloscope‐based continuous games are known to give rise to dynamic behavior resembling that of the Prisoner's Dilemma game and other 2‐choice games. We explain this similarity of behavior in terms of structural equivalence between the 2‐person continuous games and a subset of all possible 2‐person, 2‐choice (2 × 2) games, called the separable games. A game is defined as separable if each player's payoff can be expressed as a sum of partial payoffs, each of which depends only on the strategy choice of one player. All separable games can be described in terms of the same two psychologically relevant parameters. They can be played in staggered, graduated, or continuous form. Non‐separable games, including “Chicken” and many other interesting games, cannot be staggered, and their graduated and continuous versions are subject to a reinterpretation. |
| Author | Hamburger, Henry |
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| Cites_doi | 10.1002/bs.3830100408 10.1177/000276426601000303 10.1037/h0024914 10.1177/002200276701100308 10.1016/0022-2496(68)90076-X 10.1177/002200276500900406 10.1002/bs.3830070107 10.1007/BF02481857 10.1007/BF02477841 |
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| Copyright | Copyright © 1969 John Wiley & Sons, Ltd. |
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| DOI | 10.1002/bs.3830140205 |
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| Notes | ark:/67375/WNG-CB16S7L3-6 The author wishes to thank Dr. Melvin Guyer for pointing out most of the relevant empirical literature, Professor Anatol Rapoport for counsel and inspiration, and Professor Seymour Rosenberg and other members of the Workshop on Mathematical Social Psychology (under the aegis of the Mathematical Social Sciences Board of the National Science Foundation) conducted in July, 1967, for helpful discussion. istex:856333D778C3AAB8CB53E989814F6F20B2C9172C ArticleID:BS3830140205 ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 |
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| Publisher | John Wiley & Sons, Ltd University of Michigan, Mental Health Research Institute |
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| References | Rosenberg, S. An experimental test of a stochastic model of intrapersonal conflict in a two-person situation. J. math Psychol., 1968, 5, 281-299. Sawyer, J., & Friedell, M. F. The interaction screen: An operational model for experimentation of interpersonal behavior. Behav. Sci., 1965, 10, 446-460. Swinth, R. L. The establishment of the trust relationship. J. conflict Resolut., 1967, XI, 335-344. Rapoport, A., & Chammah, A. M. The game of chicken. Amer. Behav. Sci., 1966, 10 (3) Part 2, 10-28. Luce, R. D., & Raiffa, H. Games and decisions: Introduction and critical survey. New York: John Wiley, 1957. Pilisuk, M., Potter, P., Rapoport, A., & Winter, J. War hawks and peace doves: Alternate resolutions of experimental conflicts. J. conflict Resolut., 1965, IX, 491-508. Richardson, L. F. Arms and insecurity. Chicago: Quadrangle Books, 1960. Foster, C., & Rapoport, A. Parasitism and symbiosis in an n-person non-constant-sum continuous game. Bull. Math. Biophys., 1956, 18, 219-231. Rapoport, A. & Guyer, M. J. A taxonomy of 2 × 2 games. General Systems, 1966, XI, 203-214. Wilson, K., & Bixenstine, V. E. Forms of social control in two-person two-choice games. Behav. Sci., 1962, 7, 92-102. Rapoport, A. Some game-theoretical aspects of parasitism and symbiosis. Bull. Math. Biophys., 1956, 18, 15-30. Isaacs, R. Differential games. New York: John Wiley, 1965. Pruitt, D. Reward structure and cooperation: The decomposed Prisoner's Dilemma game. J. Personal. soc. Psychol., 1967, 7, 21-27. 1965 1967; 7 1965; IX 1965; 10 1956; 18 1960 1966; XI 1962; 7 1966; 10 1967; XI 1957 1968; 5 Luce (10.1002/bs.3830140205-BIB3) 1957 Rapoport (10.1002/bs.3830140205-BIB6) 1956; 18 Sawyer (10.1002/bs.3830140205-BIB11) 1965; 10 Guyer (10.1002/bs.3830140205-BIB2.1) Rosenberg (10.1002/bs.3830140205-BIB10) 1968; 5 Wilson (10.1002/bs.3830140205-BIB13) 1962; 7 Pruitt (10.1002/bs.3830140205-BIB5) 1967; 7 Pilisuk (10.1002/bs.3830140205-BIB4) 1965 Rapoport (10.1002/bs.3830140205-BIB8) 1966 Isaacs (10.1002/bs.3830140205-BIB2.2) 1965 Rapoport (10.1002/bs.3830140205-BIB7) 1966; 10 Richardson (10.1002/bs.3830140205-BIB9) 1960 Foster (10.1002/bs.3830140205-BIB1) 1956; 18 Swinth (10.1002/bs.3830140205-BIB12) 1967 |
| References_xml | – reference: Luce, R. D., & Raiffa, H. Games and decisions: Introduction and critical survey. New York: John Wiley, 1957. – reference: Pruitt, D. Reward structure and cooperation: The decomposed Prisoner's Dilemma game. J. Personal. soc. Psychol., 1967, 7, 21-27. – reference: Wilson, K., & Bixenstine, V. E. Forms of social control in two-person two-choice games. Behav. Sci., 1962, 7, 92-102. – reference: Rapoport, A. & Guyer, M. J. A taxonomy of 2 × 2 games. General Systems, 1966, XI, 203-214. – reference: Rosenberg, S. An experimental test of a stochastic model of intrapersonal conflict in a two-person situation. J. math Psychol., 1968, 5, 281-299. – reference: Foster, C., & Rapoport, A. Parasitism and symbiosis in an n-person non-constant-sum continuous game. Bull. Math. Biophys., 1956, 18, 219-231. – reference: Isaacs, R. Differential games. New York: John Wiley, 1965. – reference: Swinth, R. L. The establishment of the trust relationship. J. conflict Resolut., 1967, XI, 335-344. – reference: Pilisuk, M., Potter, P., Rapoport, A., & Winter, J. War hawks and peace doves: Alternate resolutions of experimental conflicts. J. conflict Resolut., 1965, IX, 491-508. – reference: Sawyer, J., & Friedell, M. F. The interaction screen: An operational model for experimentation of interpersonal behavior. Behav. Sci., 1965, 10, 446-460. – reference: Rapoport, A. Some game-theoretical aspects of parasitism and symbiosis. Bull. Math. Biophys., 1956, 18, 15-30. – reference: Richardson, L. F. Arms and insecurity. Chicago: Quadrangle Books, 1960. – reference: Rapoport, A., & Chammah, A. M. The game of chicken. Amer. Behav. Sci., 1966, 10 (3) Part 2, 10-28. – year: 1957 – year: 1960 – volume: 7 start-page: 92 year: 1962 end-page: 102 article-title: Forms of social control in two‐person two‐choice games publication-title: Behav. Sci. – volume: 7 start-page: 21 year: 1967 end-page: 27 article-title: Reward structure and cooperation: The decomposed Prisoner's Dilemma game publication-title: J. Personal. soc. Psychol. – volume: 10 start-page: 10 issue: 3 year: 1966 end-page: 28 article-title: The game of chicken publication-title: Amer. Behav. Sci. – year: 1965 – volume: 18 start-page: 15 year: 1956 end-page: 30 article-title: Some game‐theoretical aspects of parasitism and symbiosis publication-title: Bull. Math. Biophys. – volume: XI start-page: 335 year: 1967 end-page: 344 article-title: The establishment of the trust relationship publication-title: J. conflict Resolut. – volume: 18 start-page: 219 year: 1956 end-page: 231 article-title: Parasitism and symbiosis in an n‐person non‐constant‐sum continuous game publication-title: Bull. Math. Biophys. – volume: 10 start-page: 446 year: 1965 end-page: 460 article-title: The interaction screen: An operational model for experimentation of interpersonal behavior publication-title: Behav. Sci. – volume: IX start-page: 491 year: 1965 end-page: 508 article-title: War hawks and peace doves: Alternate resolutions of experimental conflicts publication-title: J. conflict Resolut. – volume: 5 start-page: 281 year: 1968 end-page: 299 article-title: An experimental test of a stochastic model of intrapersonal conflict in a two‐person situation publication-title: J. math Psychol. – volume: XI start-page: 203 year: 1966 end-page: 214 article-title: A taxonomy of 2 × 2 games publication-title: General Systems – volume: 10 start-page: 446 year: 1965 ident: 10.1002/bs.3830140205-BIB11 publication-title: Behav. Sci. doi: 10.1002/bs.3830100408 – volume: 10 start-page: 10 year: 1966 ident: 10.1002/bs.3830140205-BIB7 publication-title: Amer. Behav. Sci. doi: 10.1177/000276426601000303 – volume-title: Arms and insecurity year: 1960 ident: 10.1002/bs.3830140205-BIB9 – start-page: 203 year: 1966 ident: 10.1002/bs.3830140205-BIB8 publication-title: General Systems – volume-title: Differential games year: 1965 ident: 10.1002/bs.3830140205-BIB2.2 – volume: 7 start-page: 21 year: 1967 ident: 10.1002/bs.3830140205-BIB5 publication-title: J. Personal. soc. Psychol. doi: 10.1037/h0024914 – volume-title: Games and decisions: Introduction and critical survey year: 1957 ident: 10.1002/bs.3830140205-BIB3 – start-page: 335 year: 1967 ident: 10.1002/bs.3830140205-BIB12 publication-title: J. conflict Resolut. doi: 10.1177/002200276701100308 – volume: 5 start-page: 281 year: 1968 ident: 10.1002/bs.3830140205-BIB10 publication-title: J. math Psychol. doi: 10.1016/0022-2496(68)90076-X – ident: 10.1002/bs.3830140205-BIB2.1 – start-page: 491 year: 1965 ident: 10.1002/bs.3830140205-BIB4 publication-title: J. conflict Resolut. doi: 10.1177/002200276500900406 – volume: 7 start-page: 92 year: 1962 ident: 10.1002/bs.3830140205-BIB13 publication-title: Behav. Sci. doi: 10.1002/bs.3830070107 – volume: 18 start-page: 219 year: 1956 ident: 10.1002/bs.3830140205-BIB1 publication-title: Bull. Math. Biophys. doi: 10.1007/BF02481857 – volume: 18 start-page: 15 year: 1956 ident: 10.1002/bs.3830140205-BIB6 publication-title: Bull. Math. Biophys. doi: 10.1007/BF02477841 |
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