790,601 research outputs found
Perfect Prediction in Minkowski Spacetime: Perfectly Transparent Equilibrium for Dynamic Games with Imperfect Information
The assumptions of necessary rationality and necessary knowledge of
strategies, also known as perfect prediction, lead to at most one surviving
outcome, immune to the knowledge that the players have of them. Solutions
concepts implementing this approach have been defined on both dynamic games
with perfect information and no ties, the Perfect Prediction Equilibrium, and
strategic games with no ties, the Perfectly Transparent Equilibrium.
In this paper, we generalize the Perfectly Transparent Equilibrium to games
in extensive form with imperfect information and no ties. Both the Perfect
Prediction Equilibrium and the Perfectly Transparent Equilibrium for strategic
games become special cases of this generalized equilibrium concept. The
generalized equilibrium, if there are no ties in the payoffs, is at most
unique, and is Pareto-optimal.
We also contribute a special-relativistic interpretation of a subclass of the
games in extensive form with imperfect information as a directed acyclic graph
of decisions made by any number of agents, each decision being located at a
specific position in Minkowski spacetime, and the information sets and game
structure being derived from the causal structure. Strategic games correspond
to a setup with only spacelike-separated decisions, and dynamic games to one
with only timelike-separated decisions.
The generalized Perfectly Transparent Equilibrium thus characterizes the
outcome and payoffs reached in a general setup where decisions can be located
in any generic positions in Minkowski spacetime, under necessary rationality
and necessary knowledge of strategies. We also argue that this provides a
directly usable mathematical framework for the design of extension theories of
quantum physics with a weakened free choice assumption.Comment: 25 pages, updated technical repor
Ideology is theft: Thoughts on the legitimacy of a Maori psychology
‘War, in fact, can be seen as a process of achieving equilibrium among unequal technologies’ (McLuhan, 1964)
We are at war. As Western science and its accompanying technology expands the frontiers of knowledge at an ever-increasing rate, ‘indigenous’ perspectives of knowledge are exiled into the borderlands of special interest groups and localized research programmes. Mainstream scientific thought lays claim to objective interpretations of experience at the expense of alternative realities offered by emerging theories of knowledge. Furthermore, as localized worldviews (i.e., those derived from ancestral knowledge bases and pre-industrial or non-scientific premises) challenge existing paradigms, the inevitable interactions threaten to undermine the fidelity of this knowledge. One such arena where this ideological conflict is apparent is the growing field of Maori psychology
Smoothing Method for Approximate Extensive-Form Perfect Equilibrium
Nash equilibrium is a popular solution concept for solving
imperfect-information games in practice. However, it has a major drawback: it
does not preclude suboptimal play in branches of the game tree that are not
reached in equilibrium. Equilibrium refinements can mend this issue, but have
experienced little practical adoption. This is largely due to a lack of
scalable algorithms.
Sparse iterative methods, in particular first-order methods, are known to be
among the most effective algorithms for computing Nash equilibria in
large-scale two-player zero-sum extensive-form games. In this paper, we
provide, to our knowledge, the first extension of these methods to equilibrium
refinements. We develop a smoothing approach for behavioral perturbations of
the convex polytope that encompasses the strategy spaces of players in an
extensive-form game. This enables one to compute an approximate variant of
extensive-form perfect equilibria. Experiments show that our smoothing approach
leads to solutions with dramatically stronger strategies at information sets
that are reached with low probability in approximate Nash equilibria, while
retaining the overall convergence rate associated with fast algorithms for Nash
equilibrium. This has benefits both in approximate equilibrium finding (such
approximation is necessary in practice in large games) where some probabilities
are low while possibly heading toward zero in the limit, and exact equilibrium
computation where the low probabilities are actually zero.Comment: Published at IJCAI 1
Extensive Games with Possibly Unaware Players
Standard game theory assumes that the structure of the game is common
knowledge among players. We relax this assumption by considering extensive
games where agents may be unaware of the complete structure of the game. In
particular, they may not be aware of moves that they and other agents can make.
We show how such games can be represented; the key idea is to describe the game
from the point of view of every agent at every node of the game tree. We
provide a generalization of Nash equilibrium and show that every game with
awareness has a generalized Nash equilibrium. Finally, we extend these results
to games with awareness of unawareness, where a player i may be aware that a
player j can make moves that i is not aware of, and to subjective games, where
payers may have no common knowledge regarding the actual game and their beliefs
are incompatible with a common prior.Comment: 45 pages, 3 figures, a preliminary version was presented at AAMAS0
Instability Proof for Einstein-Yang-Mills Solitons and Black Holes with Arbitrary Gauge Groups
We prove that static, spherically symmetric, asymptotically flat soliton and
black hole solutions of the Einstein-Yang-Mills equations are unstable for
arbitrary gauge groups, at least for the ``generic" case. This conclusion is
derived without explicit knowledge of the possible equilibrium solutions.Comment: 26 pages, LATEX, no figure
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