Interconnected Games

Abstract

Several real-world problems are characterized by the fact that the same agents are simultaneously involved in several distinct areas of interest. For instance, the Member States of the European Community are simultaneously involved in negotiations about coordinating their economic, foreign and environmental policies. Another example relates to the fact that firms in an oligopolistic setting often simultaneously operate at several distinct markets. The fact that the same agents are simultaneously involved in several areas of interest may put constraints on their strategies in the individual fields but it may also enrich the total of stategies open to them in the sense that there exists greater retaliatory potential. A basic feature of most economic approaches, including game theory, is to model the several areas of interest in isolation. This may seriously limit the applicability and analytic and predictive power of the resulting models, as the consequences of the linkages for the strategy spaces cannot adequately be taken into account. This justifies an interconnected modelling approach. We have learned that this concept has already been discussed in the litterature, but only in the context of very special real world situations and in a not formalized way. This observation inspired the authors of (A) to formalize the notion of interconnected games for two special cases, viz. where each isolated game is a game in strategic form and where each isolated game is a repeated game (with discounting). In this abstract we refer to these types of interconnected games as direct sum games and tensor games, respectively. Properly speaking, only trade-off completely interconnected games were considered in (A).