Compositional game theory

We introduce open games as a compositional foundation of economic game theory. A compositional approach potentially allows methods of game theory and theoretical computer science to be applied to large-scale economic models for which standard economic tools are not practical. An open game represents a game played relative to an arbitrary environment and to this end we introduce the concept of coutility, which is the utility generated by an open game and returned to its environment. Open games are the morphisms of a symmetric monoidal category and can therefore be composed by categorical composition into sequential move games and by monoidal products into simultaneous move games. Open games can be represented by string diagrams which provide an intuitive but formal visualisation of the information flows. We show that a variety of games can be faithfully represented as open games in the sense of having the same Nash equilibria and off-equilibrium best responses.Comment: This version submitted to LiCS 201

Composing games into complex institutions

Game theory is used by all behavioral sciences, but its development has long centered around tools for relatively simple games and toy systems, such as the economic interpretation of equilibrium outcomes. Our contribution, compositional game theory, permits another approach of equally general appeal: the high-level design of large games for expressing complex architectures and representing real-world institutions faithfully. Compositional game theory, grounded in the mathematics underlying programming languages, and introduced here as a general computational framework, increases the parsimony of game representations with abstraction and modularity, accelerates search and design, and helps theorists across disciplines express real-world institutional complexity in well-defined ways. Relative to existing approaches in game theory, compositional game theory is especially promising for solving game systems with long-range dependencies, for comparing large numbers of structurally related games, and for nesting games into the larger logical or strategic flows typical of real world policy or institutional systems.Comment: ~4000 words, 6 figure

TEAM COMPOSITION, LEADERSHIP AND INFORMATION-PROCESSING BEHAVIOR A simulation game study of the locus-of-control personality trait

In this study, we relate the individual locus-of-control personality trait of team members to the team’s information gathering and processing behavior. We adopt a team information-processing approach arguing that a team’s information-processing capacity is a function of its composition with respect to the members’ locus of control and the leadership structure of the group. We develop models that go beyond analyzing simple main effects of differences in team locus-of-control composition. We hypothesize that (a) the impact of the team locus-of-control mean depends on the within-group locus-of-control diversity, and (b) the effect of both the team locus-of-control mean and its standard deviation is contingent upon the leadership structure of the group. The hypotheses were tested on 44 teams participating in an elaborate international management simulation over six time periods. As predicted, we find that teams with a high average internal locus-of-control score collect more information and make more informed decisions when the within-team locus-of-control spread is low, and when the team operates without a leader. The opposite is the case for teams with a high average external locus-of-control score. In addition, locus-of-control diversity induces team information search only in the case when the team has no leader. We also show that team financial performance is comparably affected by our focal independent team variables. On a general level, our results offer strong support for recent pleas to study theoretically relevant individual traits, use proper aggregation models and include structural moderator variables in team composition research.Economics ;

Modal logics are coalgebraic

Applications of modal logics are abundant in computer science, and a large number of structurally different modal logics have been successfully employed in a diverse spectrum of application contexts. Coalgebraic semantics, on the other hand, provides a uniform and encompassing view on the large variety of specific logics used in particular domains. The coalgebraic approach is generic and compositional: tools and techniques simultaneously apply to a large class of application areas and can moreover be combined in a modular way. In particular, this facilitates a pick-and-choose approach to domain specific formalisms, applicable across the entire scope of application areas, leading to generic software tools that are easier to design, to implement, and to maintain. This paper substantiates the authors' firm belief that the systematic exploitation of the coalgebraic nature of modal logic will not only have impact on the field of modal logic itself but also lead to significant progress in a number of areas within computer science, such as knowledge representation and concurrency/mobility