Semifuzzy games

A new type of decomposition of static games is defined in order to describe cases where overt behavior only is cooperative to a degree. The basic idea is to split the original game into a set of subgames defined by sets of decisions made by the players. In each subgame, different coalitions may form (e.g., two chain stores can cooperate in one city and not in another). To motivate the concept we give an example where such schizophrenic behaviour naturally arise between two firms competing on advertising and quantity. The new type of games are then compared to Aubin's fuzzy games and it is demonstrated that the core of these games with or without side-payments is identical to the core of the original games. We finally show how this type of games degenerates to fuzzy games under certain conditions. The concept of semifuzzy games therefore offers us a new way to think about fuzzy games, which allows us to avoid the interpretational difficulties associated with other approaches.