Multi-agent systems comprise entities whose individual decision making behavior may depend on one another’s. Game-theory provides apposite concepts to reason in a mathematically precise fashion about such interactive and interdependent situations. This paper concerns a logical analysis of the game-theoretical notions of Nash equilibrium and its subgame perfect variety as they apply to a particu...

The equilibrium concepts that we now think of as various forms of backwards induction, namely subgame perfect equilibrium (Selten, 1965), perfect equilibrium (Selten, 1975), sequential equilibrium (Kreps and Wilson, 1982), and quasi-perfect equilibrium (van Damme, 1984), are explicitly restricted their analysis to games with perfect recall. In spite of this the concepts are well defined, exactl...

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...

Two-player zero-sum stochastic games with finite state and action spaces, as well as two-player zero-sum absorbing games with compact metric action spaces, are known to have undiscounted values. We study such games under the assumption that one or both players observe the actions of their opponent after some time-dependent delay. We develop criteria for the rate of growth of the delay such that...

In this paper reasonable payoff intervals for players in a game in partition function form (p.f.f. game) are introduced and used to define the notion of compromisable p.f.f. game. For a compromisable p.f.f. game a compromise value is defined for which an axiomatic characterization is provided. Also a generic subclass of games in extensive form of perfect information without chance moves is intr...

We analyze several perfect-information combinatorial games played on planar triangulations. We introduce three broad categories of such games: constructing, transforming, and marking triangulations. In various situations, we develop polynomial-time algorithms to determine who wins a given game under optimal play, and to find a winning strategy. Along the way, we show connections to existing com...

We describe an algorithm, inspired by the biological behavior of ants, to efficiently determine intelligent moves and the genetic algorithm used to learn better strategies in a broad class of games. We present a class of games called Simple War Games that includes both deterministic and nondeterministic, perfect information, two-player, zero sum games. Simple War Games have a branching factor a...

Many important real-world settings contain multiple players interacting over an unknown duration with probabilistic state transitions, and are naturally modeled as stochastic games. Prior research on algorithms for games has focused two-player zero-sum games, perfect information, imperfect-information that is local does not extend between game states. We present algorithm approximating Nash equ...

We consider repeated games with private monitoring that are “close” to repeated games with public/perfect monitoring. A private monitoring information structure is close to a public monitoring information structure when private signals can generate approximately the same distribution of the public signal once they are aggregated into a public signal by some public coordination device. A player’...