Since the early 18th Century, expected utility theory became the leading theory in explaining behavior of decision makers under uncertainty. For most of this time it was used as a purely descriptive theory. For example, Ramsey (1931) explicitly assumed that people evaluate a risky prospect by its expected utility. He expressed this idea in the following words: I suggest that we introduce as a l...

A stationary variant of the repeated prisoners’ dilemma in which the game frontier is a parallelogram is analyzed. By using the probabilistic cheap talk concept of [3], the discount factor becomes fungible, and for a critical value of the discount factor a unique Pareto-optimal and Pareto-dominant solution can be found. The relative bargaining power of the players can be quantified in terms of ...

A. Katok has conjectured that a C map g : Mn → Mn, n ≥ 2, which is Hölder conjugated to an Anosov diffeomorphism is also an Anosov diffeomorphism. Using Pesin stable manifold theorem and Liao spectrum theorem, we show that under the hypothesis of such a conjecture, g is an Axiom A diffeomorphism having no cycles. Particularly, if g is Hölder conjugated to a hyperbolic toral automorphism, then g...

In [13] we defined a class of so-called ‘Hyperbolic Analytic Maps’. Given a map in this class one associates a Banach space and a family of transfer operators with analytic weights on the space. These operators are nuclear in the sense of Grothendieck. An elementary proof was given in the case of 1+1 dimensional maps [Fried has extended the proof to higher dimensional systems]. In this case suc...

This paper presents a cut-elimination proof for the logic LG, which is an extension of a proof system for encoding generic judgments, the logic FOλ of Miller and Tiu, with an induction principle. The logic LG, just as FOλ, features extensions of first-order intuitionistic logic with fixed points and a “generic quantifier”, ∇, which is used to reason about the dynamics of bindings in object syst...

We study the spectrum of forcing notions between the iterations of σ-closed followed by ccc forcings and the proper forcings. This includes the hierarchy of α-proper forcings for indecomposable countable ordinals α, the Axiom A forcings and forcings completely embeddable into an iteration of a σ-closed followed by a ccc forcing. For the latter class, we present an equivalent characterization in...

Assuming Jensen’s principle ♦, there is a compact Hausdorff space X which is hereditarily Lindelöf, hereditarily separable, and connected, such that no closed subspace of X is both perfect and totally disconnected. The Proper Forcing Axiom implies that there is no such space. The ♦ example also fails to satisfy the CSWP (the complex version of the Stone-Weierstrass Theorem). This space cannot c...

Suppose that f and f ′ are axiom A flows with attractors A and A′. Then the attractor A×A′ for the product flow gt = ft×f ′ t on the product manifold is no longer hyperbolic (although there is a hyperbolic action of R2). It is easy to see that the attractor cannot explode but we show here that it cannot implode: for any flow (ht) sufficiently close to (gt) any attractor whose basin is not too t...

In this note we prove some results concerning volume-preserving Anosov diffeomorphisms on compact manifolds. The main theorem is that if a C, α > 0, volume-preserving diffeomorphism on a compact manifold has a hyperbolic invariant set with positive volume, then the map is Anosov. This is not necessarily true for C maps. The proof uses a special type of measure density points different from the ...