A number decomposition game (DECO) was investigated in two versions of the game using the same arithmetic operations but differing in their structure of interdependence. The structure of interdependence is defined as the relationship of competition or cooperation between players and the criteria for successful attainment of game goals as defined by pre-established rules. Subjects for the study were 64 second and third grade students at two public elementary schools in Geneva, Switzerland. A two-way analysis of variance was used on grade crossed with game version as measured by percent of interactions, percent of mutual monitoring and control, adequacy of decomposition strategy, and percent of errors. For percent of interaction, all three effects--grade, game version and their interaction--were significant. For monitoring and control, all were non-significant. For decomposition strategy, game was significant and for errors, game version was significant. Quantitative indicators of congruence of playing behavior with game rules, monitoring and control, and decomposition were examined by regression analysis. Quantitative and qualitative measures were used to identify player profiles for both versions of the game. These player profiles did not appear to have a systematic impact on game outcome. (JM)