3,483 research outputs found
Boolean Hedonic Games
We study hedonic games with dichotomous preferences. Hedonic games are
cooperative games in which players desire to form coalitions, but only care
about the makeup of the coalitions of which they are members; they are
indifferent about the makeup of other coalitions. The assumption of dichotomous
preferences means that, additionally, each player's preference relation
partitions the set of coalitions of which that player is a member into just two
equivalence classes: satisfactory and unsatisfactory. A player is indifferent
between satisfactory coalitions, and is indifferent between unsatisfactory
coalitions, but strictly prefers any satisfactory coalition over any
unsatisfactory coalition. We develop a succinct representation for such games,
in which each player's preference relation is represented by a propositional
formula. We show how solution concepts for hedonic games with dichotomous
preferences are characterised by propositional formulas.Comment: This paper was orally presented at the Eleventh Conference on Logic
and the Foundations of Game and Decision Theory (LOFT 2014) in Bergen,
Norway, July 27-30, 201
Possibilistic Boolean games: strategic reasoning under incomplete information
Boolean games offer a compact alternative to normal-form games, by encoding the goal of each agent as a propositional formula. In this paper, we show how this framework can be naturally extended to model situations in which agents are uncertain about other agents' goals. We first use uncertainty measures from possibility theory to semantically define (solution concepts to) Boolean games with incomplete information. Then we present a syntactic characterization of these semantics, which can readily be implemented, and we characterize the computational complexity
Game Networks
We introduce Game networks (G nets), a novel representation for multi-agent
decision problems. Compared to other game-theoretic representations, such as
strategic or extensive forms, G nets are more structured and more compact; more
fundamentally, G nets constitute a computationally advantageous framework for
strategic inference, as both probability and utility independencies are
captured in the structure of the network and can be exploited in order to
simplify the inference process. An important aspect of multi-agent reasoning is
the identification of some or all of the strategic equilibria in a game; we
present original convergence methods for strategic equilibrium which can take
advantage of strategic separabilities in the G net structure in order to
simplify the computations. Specifically, we describe a method which identifies
a unique equilibrium as a function of the game payoffs, and one which
identifies all equilibria.Comment: Appears in Proceedings of the Sixteenth Conference on Uncertainty in
Artificial Intelligence (UAI2000
A Complete Solver for Constraint Games
Game Theory studies situations in which multiple agents having conflicting
objectives have to reach a collective decision. The question of a compact
representation language for agents utility function is of crucial importance
since the classical representation of a -players game is given by a
-dimensional matrix of exponential size for each player. In this paper we
use the framework of Constraint Games in which CSP are used to represent
utilities. Constraint Programming --including global constraints-- allows to
easily give a compact and elegant model to many useful games. Constraint Games
come in two flavors: Constraint Satisfaction Games and Constraint Optimization
Games, the first one using satisfaction to define boolean utilities. In
addition to multimatrix games, it is also possible to model more complex games
where hard constraints forbid certain situations. In this paper we study
complete search techniques and show that our solver using the compact
representation of Constraint Games is faster than the classical game solver
Gambit by one to two orders of magnitude.Comment: 17 page
Compact preference representation and Boolean games
International audienceGame theory is a widely used formal model for studying strategical in- teractions between agents. Boolean games[23, 22] yield a compact rep- resentation of 2-player zero-sum static games with binary preferences: an agent's strategy consists of a truth assignment of the propositional variables she controls, and a player's preferences are expressed by a plain propositional formula. These restrictions (2-player, zero-sum, binary preferences) strongly limit the expressivity of the framework. We first generalize the framework to n-player games which are not necessarily zero-sum. We give simple char- acterizations of Nash equilibria and dominated strategies, and investigate the computational complexity of the associated problems. Then, we relax the last restriction by coupling Boolean games with a representation, namely,CP-nets
Rational Verification in Iterated Electric Boolean Games
Electric boolean games are compact representations of games where the players
have qualitative objectives described by LTL formulae and have limited
resources. We study the complexity of several decision problems related to the
analysis of rationality in electric boolean games with LTL objectives. In
particular, we report that the problem of deciding whether a profile is a Nash
equilibrium in an iterated electric boolean game is no harder than in iterated
boolean games without resource bounds. We show that it is a PSPACE-complete
problem. As a corollary, we obtain that both rational elimination and rational
construction of Nash equilibria by a supervising authority are PSPACE-complete
problems.Comment: In Proceedings SR 2016, arXiv:1607.0269
Pure Nash Equilibria in Concurrent Deterministic Games
We study pure-strategy Nash equilibria in multi-player concurrent
deterministic games, for a variety of preference relations. We provide a novel
construction, called the suspect game, which transforms a multi-player
concurrent game into a two-player turn-based game which turns Nash equilibria
into winning strategies (for some objective that depends on the preference
relations of the players in the original game). We use that transformation to
design algorithms for computing Nash equilibria in finite games, which in most
cases have optimal worst-case complexity, for large classes of preference
relations. This includes the purely qualitative framework, where each player
has a single omega-regular objective that she wants to satisfy, but also the
larger class of semi-quantitative objectives, where each player has several
omega-regular objectives equipped with a preorder (for instance, a player may
want to satisfy all her objectives, or to maximise the number of objectives
that she achieves.)Comment: 72 page
- …