11,335 research outputs found
Periodic Strategies: A New Solution Concept and an Algorithm for NonTrivial Strategic Form Games
We introduce a new solution concept, called periodicity, for selecting
optimal strategies in strategic form games. This periodicity solution concept
yields new insight into non-trivial games. In mixed strategy strategic form
games, periodic solutions yield values for the utility function of each player
that are equal to the Nash equilibrium ones. In contrast to the Nash
strategies, here the payoffs of each player are robust against what the
opponent plays. Sometimes, periodicity strategies yield higher utilities, and
sometimes the Nash strategies do, but often the utilities of these two
strategies coincide. We formally define and study periodic strategies in two
player perfect information strategic form games with pure strategies and we
prove that every non-trivial finite game has at least one periodic strategy,
with non-trivial meaning non-degenerate payoffs. In some classes of games where
mixed strategies are used, we identify quantitative features. Particularly
interesting are the implications for collective action games, since there the
collective action strategy can be incorporated in a purely non-cooperative
context. Moreover, we address the periodicity issue when the players have a
continuum set of strategies available.Comment: Revised version, similar to the one published in Advances in Complex
System
Existence results for mean field equations
Let be an annulus. We prove that the mean field equation
-\Delta\psi=\frac{e\sp{-\beta\psi}}{\int\sb{\Omega}e\sp{-\beta\psi}} admits
a solution with zero boundary for . This is a
supercritical case for the Moser-Trudinger inequality.Comment: Filling a gap in the argument and adding 2 referrence
Preemptive Behavior in Sequential-Move Tournaments with Heterogeneous Agents
Rank-order tournaments are usually modeled simultaneously. However, real tournaments are often sequential. We show that agents’ strategic behavior in sequential-move tournaments significantly differ from the one in simultaneous-move tournaments: In a sequential-move tournament with heterogeneous agents, there may be either a first-mover or a second-mover advantage. Under certain conditions the first acting agent chooses a preemptively high effort so that the following agent gives up. The principal is able to prevent preemptive behavior in equilibrium, but he will not implement first-best efforts although the agents are risk neutral.preemption, tournaments
The geometry of Grassmannian manifolds and Bernstein type theorems for higher codimension
We identify a region \Bbb{W}_{\f{1}{3}} in a Grassmann manifold
\grs{n}{m}, not covered by a usual matrix coordinate chart, with the
following important property. For a complete submanifold in \ir{n+m} \,
(n\ge 3, m\ge2) with parallel mean curvature whose image under the Gauss map
is contained in a compact subset K\subset\Bbb{W}_{\f{1}{3}}\subset\grs{n}{m},
we can construct strongly subharmonic functions and derive a priori estimates
for the harmonic Gauss map. While we do not know yet how close our region is to
being optimal in this respect, it is substantially larger than what could be
achieved previously with other methods. Consequently, this enables us to obtain
substantially stronger Bernstein type theorems in higher codimension than
previously known.Comment: 36 page
Existence and non-existence of area-minimizing hypersurfaces in manifolds of non-negative Ricci curvature
We study minimal hypersurfaces in manifolds of non-negative Ricci curvature,
Euclidean volume growth and quadratic curvature decay at infinity. By
comparison with capped spherical cones, we identify a precise borderline for
the Ricci curvature decay. Above this value, no complete area-minimizing
hypersurfaces exist. Below this value, in contrast, we construct examples.Comment: 31 pages. Comments are welcome
The Gauss image of entire graphs of higher codimension and Bernstein type theorems
Under suitable conditions on the range of the Gauss map of a complete
submanifold of Euclidean space with parallel mean curvature, we construct a
strongly subharmonic function and derive a-priori estimates for the harmonic
Gauss map. The required conditions here are more general than in previous work
and they therefore enable us to improve substantially previous results for the
Lawson-Osseman problem concerning the regularity of minimal submanifolds in
higher codimension and to derive Bernstein type results.Comment: 28 page
Minimal graphic functions on manifolds of non-negative Ricci curvature
We study minimal graphic functions on complete Riemannian manifolds \Si
with non-negative Ricci curvature, Euclidean volume growth and quadratic
curvature decay. We derive global bounds for the gradients for minimal graphic
functions of linear growth only on one side. Then we can obtain a Liouville
type theorem with such growth via splitting for tangent cones of \Si at
infinity. When, in contrast, we do not impose any growth restrictions for
minimal graphic functions, we also obtain a Liouville type theorem under a
certain non-radial Ricci curvature decay condition on \Si. In particular, the
borderline for the Ricci curvature decay is sharp by our example in the last
section.Comment: 38 page
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