Bounded Reasoning and Higher-Order Uncertainty

A standard assumption in game theory is that players have an infinite depth of reasoning: they think about what others think and about what others think that othersthink, and so on, ad infinitum. However, in practice, players may have a finite depth of reasoning. For example, a player may reason about what other players think, but not about what others think he thinks. This paper proposes a class of type spaces that generalizes the type space formalism due to Harsanyi (1967) so that it can model players with an arbitrary depth of reasoning. I show that the type space formalism does not impose any restrictions on the belief hierarchies that can be modeled, thus generalizing the classic result of Mertens and Zamir (1985). However, there is no universal type space that contains all type spaces.

Homoclinics for singular strong force Lagrangian systems in $${\mathbb {R}}^N$$

We will be concerned with the existence of homoclinics for Lagrangian systems in $${\mathbb {R}}^N$$ R N ($$N\ge 3 $$ N ≥ 3 ) of the form $$\frac{d}{dt}\left( \nabla \Phi (\dot{u}(t))\right) +\nabla _{u}V(t,u(t))=0$$ d dt ∇ Φ ( u ˙ ( t ) ) + ∇ u V ( t , u ( t ) ) = 0 , where $$t\in {\mathbb {R}}$$ t ∈ R , $$\Phi {:}\,{\mathbb {R}}^N\rightarrow [0,\infty )$$ Φ : R N → [ 0 , ∞ ) is a G-function in the sense of Trudinger, $$V{:}\,{\mathbb {R}}\times \left( {\mathbb {R}}^N{\setminus }\{\xi \} \right) \rightarrow {\mathbb {R}}$$ V : R × R N \ { ξ } → R is a $$C^2$$ C 2 -smooth potential with a single well of infinite depth at a point $$\xi \in {\mathbb {R}}^N{\setminus }\{0\}$$ ξ ∈ R N \ { 0 } and a unique strict global maximum 0 at the origin. Under a strong force type condition around the singular point $$\xi $$ ξ , we prove the existence of a homoclinic solution $$u{:}\,{\mathbb {R}}\rightarrow {\mathbb {R}}^N{\setminus }\{\xi \}$$ u : R → R N \ { ξ } via minimization of an action integral.

Miles Theory Revisited with Constant Vorticity in Water of Infinite Depth

The generation of wind waves at the surface of a pre-existing underlying vertically sheared water flow of constant vorticity is considered. Emphasis is put on the role of the vorticity in water on wind-wave generation. The amplitude growth rate increases with the vorticity except for quite old waves. A limit to the wave energy growth is found in the case of negative vorticity, corresponding to the vanishing of the growth rate.

HYDROGEOPHYSICAL INVESTIGATION USING ELECTRICAL RESISTIVITY METHOD IN TANKE ILORIN, KWARA STATE

Geophysical investigation using electrical sounding technique was carried out in Tanke community Ilorin, in order to characterize or explore ground water potential. The top soil resistivity values vary from 68.1Ωm to 65.1Ωm and thickness varying between 1.7m to 9.9m. The second layer resistivity values varies from 32.9Ωm to 651.1Ωm and the thickness vary from 2.9m to 12.7m.The third layer is the weathered basement with resistivity and thickness values varying between 22.6Ωm to 9562.6Ωm and 7.8m to 51.1m.The fourth layer is the partly weathered and fractured basement with resistivity and thickness values varying between 101Ωm to 2100Ωm and 80.1m to 124m while the fifth layer is apparently fresh basement whose resistivity values vary from 154.9Ωm to 7130Ωm with an infinite depth. The study further reveal VES 3, 4, and 5 as productive fractures within the weathered basement while other VES points are not productive.

Green’s function for the semi-infinite strip in terms of an improper integral

In this paper Green?s function for the semi-infinite strip (which is the two-dimensional Green?s function for a groove of infinite depth and length) is determined in the form of an improper integral, as opposed to the standard summation form. The integral itself, although rather complex, is found in a closed form. By using the derived Green?s function simple formulas are obtained for a single and two-wire line configurations inside the groove.