Separable Games

• Published in: Behavioral Science Vol. 14; no. 2; pp. 121 - 132
• Main Author: Hamburger, Henry
• Format: Journal Article
• Language: English
• Published: California John Wiley & Sons, Ltd 01.03.1969; University of Michigan, Mental Health Research Institute
• ISSN: 0005-7940; 1099-1743; 1932-300X
• DOI: 10.1002/bs.3830140205

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.