This paper aims to significantly impact the way we conceive of, reason about, and construct software for economic game theory. We achieve this by building an new and original model of economic games based upon the computer science idea of compositionality: concretely we i) give a number of operators for building up complex and irregular games from smaller and simpler games; and ii) show how the...

In this section we study games with only two players. We also restrict attention to the case where the interests of the players are completely antagonistic: at the end of the game, one player gains some amount, while the other loses the same amount. These games are called “two person zero sum games”. While in most economics situations the interests of the players are neither in strong conflict ...

The classical, complete-information two-player games assume that the problem data (in particular the payoff matrix) is known exactly by both players. In a now famous result, Nash has shown that any such game has an equilibrium in mixed strategies. This result was later extended to a class of incomplete-information two-player games by Harsanyi, who assumed that the payoff matrix is not known exa...

We introduce a new foundation for game theory based on so-called open games. Unlike existing approaches open games are fully compositional: games are built using algebraic operations from standard components, such as players and outcome functions, with no fundamental distinction being made between the parts and the whole. Open games are intended to be applied at large scales where classical gam...

I ntroduced by John von Neumann and Oskar Morgenstern (1944), energized by the addition of John Nash’s (1950) equilibrium concept, and popularized by the strategic revolution of the 1980s, noncooperative game theory has become a standard tool in economics. In the process, attention has increasingly been focused on game theory’s conceptual foundations. Two questions have taken center stage: Shou...

We examine the state of game theory. Many important questions have been answered, and game theoretic methods are now central to much economic investigation. We suggest areas where further advances are important, and argue that models of learning and of social preferences provide promising routes for improving and widening game theory’s predictive power, while preserving the sucesses of existing...

Decisions made during social interaction are complex due to the inherent uncertainty about their outcomes, which are jointly determined by the actions of the decision maker and others. Game theory, a mathematical analysis of such interdependent decision making, provides a computational framework to extract core components of complex social situations and to analyze decision making in terms of t...