17,123 research outputs found
von Neumann-Morgenstern and Savage Theorems for Causal Decision Making
Causal thinking and decision making under uncertainty are fundamental aspects
of intelligent reasoning. Decision making under uncertainty has been well
studied when information is considered at the associative (probabilistic)
level. The classical Theorems of von Neumann-Morgenstern and Savage provide a
formal criterion for rational choice using purely associative information.
Causal inference often yields uncertainty about the exact causal structure, so
we consider what kinds of decisions are possible in those conditions. In this
work, we consider decision problems in which available actions and consequences
are causally connected. After recalling a previous causal decision making
result, which relies on a known causal model, we consider the case in which the
causal mechanism that controls some environment is unknown to a rational
decision maker. In this setting we state and prove a causal version of Savage's
Theorem, which we then use to develop a notion of causal games with its
respective causal Nash equilibrium. These results highlight the importance of
causal models in decision making and the variety of potential applications.Comment: Submitted to Journal of Causal Inferenc
Bayesian games with a continuum of states
We show that every Bayesian game with purely atomic
types has a measurable Bayesian equilibrium when the common knowl-
edge relation is smooth. Conversely, for any common knowledge rela-
tion that is not smooth, there exists a type space that yields this common
knowledge relation and payoffs such that the resulting Bayesian game
will not have any Bayesian equilibrium. We show that our smoothness
condition also rules out two paradoxes involving Bayesian games with
a continuum of types: the impossibility of having a common prior on
components when a common prior over the entire state space exists, and
the possibility of interim betting/trade even when no such trade can be
supported
ex ante
A Continuation Method for Nash Equilibria in Structured Games
Structured game representations have recently attracted interest as models
for multi-agent artificial intelligence scenarios, with rational behavior most
commonly characterized by Nash equilibria. This paper presents efficient, exact
algorithms for computing Nash equilibria in structured game representations,
including both graphical games and multi-agent influence diagrams (MAIDs). The
algorithms are derived from a continuation method for normal-form and
extensive-form games due to Govindan and Wilson; they follow a trajectory
through a space of perturbed games and their equilibria, exploiting game
structure through fast computation of the Jacobian of the payoff function. They
are theoretically guaranteed to find at least one equilibrium of the game, and
may find more. Our approach provides the first efficient algorithm for
computing exact equilibria in graphical games with arbitrary topology, and the
first algorithm to exploit fine-grained structural properties of MAIDs.
Experimental results are presented demonstrating the effectiveness of the
algorithms and comparing them to predecessors. The running time of the
graphical game algorithm is similar to, and often better than, the running time
of previous approximate algorithms. The algorithm for MAIDs can effectively
solve games that are much larger than those solvable by previous methods
- …