We define cooperative games on general graphs and generalize Lloyd S. Shapley's celebrated allocation formula for those in terms of stochastic path integral driven by the associated Markov chain each graph. then show that value operator, one player defined integral, coincides with player's component game which is solution to least squares (or Poisson's) equation, light combinatorial Hodge decom...

We introduce a new equilibrium selection mechanism for a class of symmetric coordination games. Taking advantage of the structure of these games, we assert that the equilibrium selected by this mechanism constitutes a “natural solution” in the sense that the associated expected payoff is the highest equilibrium value that can be achieved without any player having to guess how to do so. We illus...

Computer Games are interesting test beds for research in Artificial Intelligence and Machine Learning. Games usually have continuous state spaces, large action spaces and are characterized by complex relationships between components. Without applying abstraction and generalizations, learning in computer games domain becomes infeasible. Through this work, we investigate some designs that facilit...

An algorithm based on backward induction is devised in order to compute the optimal sequence of games to be played in Parrondo games. The algorithm can be used to find the optimal sequence for any finite number of turns or in the steady state, showing that ABABB... is the sequence with the highest steady state average gain. The algorithm can also be generalized to find the optimal adaptive stra...

We show that a symmetric two-player zero-sum game has a pure strategy equilibrium if and only if it is not a generalized rock-paper-scissors matrix. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure equilibrium. Further sufficient conditions for existence are provided. We point out that the class of symmetric two-player zero-sum games coincides with ...