We study quantum games with correlated noise through a generalized quantization scheme. We investigate the effects of memory on quantum games, such as Prisoner’s Dilemma, Battle of the Sexes and Chicken, through three prototype quantum-correlated channels. It is shown that the quantum player enjoys an advantage over the classical player for all nine cases considered in this paper for the maxima...

We consider two-player games of perfect information of length some cardinal κ. It is well-known that for κ ≥ ω1 the full axiom of determinacy for these games fails, thus we investigate three weaker forms of it. We obtain the measurability of κ under DCκ-the axiom of dependent choices generalized to κ. We generalize the notions of perfect and meager sets and provide characterizations with some s...

We show that the problem of finding optimal strategies for both players in a simple stochastic game reduces to the generalized linear complementarity problem (GLCP) with a P-matrix, a well-studied problem whose hardness would imply NP = co-NP. This makes the rich GLCP theory and numerous existing algorithms available for simple stochastic games. As a special case, we get a reduction from binary...

We give an axiomatization of the aspiration core on the domain of all TU-games using a relaxed feasibility condition, non-emptiness, individual rationality, and generalized versions of the reduced game property (consistency) and superadditivity. Our axioms also characterize the C-core ([Guesnerie and Oddou, 1979] and [Sun, Trockel, and Yang, 2008]) and the core on appropriate subdomains. The la...

Finite mixture models are an important tool in the statistical analysis of data, for example data clustering. The optimal parameters a model usually computed by maximizing log-likelihood functional via Expectation-Maximization algorithm. We propose alternative approach based on theory Mean Field Games, class differential games with infinite number agents. show that solution finite state space m...

We examine individual behavior in generalized games of matching pennies. Our findings are twofold. First, individuals cooperate in these games; i.e., they systematically select strategies that lead both players to obtain higher expected payoffs than Nash. Second, among the main models in the extant literature (some of which were explicitly designed to induce cooperative behavior) the only one t...

We define an extensive-form analogue of iterated admissibility, called Prudent Rationalizability (PR). In each round of the procedure, for each information set of a player a surviving strategy of hers is required to be rational vis-a-vis a belief system with a full-support belief on the opponents’ previously surviving strategies that reach that information set. Somewhat surprisingly, prudent ra...

We study a class of rational matrix differential equations that generalize the Riccati differential equations. The generalization involves replacing positive definite “weighting” matrices in the usual Riccati equations with either semidefinite or indefinite matrices that arise in linear quadratic control problems and differential games−both stochastic and deterministic. The purpose of this pape...

We show that a recent existence result for the Nash equilibria of generalized games with strategy sets in H-spaces is false. We prove that it becomes true if we assume, in addition, that the feasible set of the game (the set of all feasible multistrategies) is closed.

Distributed monitoring of values is a common task in many distributed systems including sensor networks and online games. In this work we develop a generalized framework for functional monitoring of values and show how it can be applied in the context of online games. We implement a library for general functional monitoring and consider the tradeoff between network usage and accuracy with diffe...