Repeated Games with Voluntary Information Purchase

We consider discounted repeated games in which players can voluntarily purchase information about the opponents’ actions at past stages. Information about a stage can be bought at a fixed but arbitrary cost. Opponents cannot observe the information purchase by a player. For our main result, we make the usual assumption that the dimension of the set FIR of feasible and individually rational payoff vectors is equal to the number of players. We show that, if there are at least three players and each player has at least four actions, then every payoff vector in the interior of the set FIR can be achieved by a Nash equilibrium of the discounted repeated game if the discount factor is sufficiently close to 1. Therefore, nearly efficient payoffs can be achieved even if the cost of monitoring is high. We show that the same result holds if there are at least four players and at least three actions for each player. Finally, we indicate how the construction can be extended to sequential equilibrium.mathematical economics;

Strategic Disclosure of Random Variables

We consider a game G(n) played by two players. There are n independent random variables Z(1),...,Z(n), each of which is uniformly distributed on [0,1]. Both players know n, the independence and the distribution of these random variables, but only player 1 knows the vector of realizations z := (z(1),...,z(n)) of them. Player 1 begins by choosing an order z(k(1)),...,z(k(n)) of the realizations. Player 2, who does not know the realizations, faces a stopping problem. At period 1, player 2 learns z(k(1)). If player 2 accepts, then player 1 pays z(k(1)) euros to player 2 and play ends. Otherwise, if player 2 rejects, play continues similarly at period 2 with player 1 offering z(k(2)) euros to player 2. Play continues until player 2 accepts an offer. If player 2 has rejected n-1 times, player 2 has to accept the last offer at period n. This model extends Moser''s (1956) problem, which assumes a non-strategic player 1.We examine different types of strategies for the players and determine their guarantee levels. Although we do not find the exact value v(n) of the game G(n) in general, we provide an interval I(n) = [a(n),b(n)] containing v(n) such that the length of I(n) is at most 0.07 and converges to 0 as n tends to infinity. We also point out strategies, with a relatively simple structure, which guarantee that player 1 has to pay at most b(n) and player 2 receives at least a(n). In addition, we completely solve the special case G(2) where there are only two random variables. We mention a number of intriguing open questions and conjectures, which may initiate further research on this subject.mathematical economics;

The spin density matrix of top quark pairs produced in electron-positron annihilation including QCD radiative corrections

We calculate the spin density matrix of top quark pairs for the reaction $e^+e^-\to t\bar{t}X$ to order $\alpha_s$. As an application we show next-to-leading order results for a variety of spin observables for the $t\bar{t}$ system. These include the top quark and antiquark polarizations and $t\bar{t}$ spin-spin correlations as a function of the center-of-mass energy and of the top quark scattering angle for arbitrary longitudinal polarization of the electron/positron beam.Comment: 26 pages, 13 Postscript figures, uses REVTE

Polarization and spin correlations of top quarks at a future e+ e- linear collider

We discuss the polarization and spin correlations of top quarks produced above threshold at a future linear collider, including QCD radiative corrections.Comment: 11 pages (LaTeX), 16 Postscript figure. Contribution to the International Workshop on "Symmetry and Spin", PRAHA-SPIN99, Prague, Czech Republic, September 5 -12, 199

Effects of Higgs sector CP violation in top-quark pair production at the LHC

A striking manifestation of CP violation in the electroweak symmetry breaking sector would be the existence of neutral Higgs boson(s) with undefined CP parity. We analyse signatures of such a boson, with a mass of about 300 GeV or larger, produced in high energy proton-proton collisions at LHC energies in its top-quark antitop-quark decay channel. The large irreducible $t\bar t$ background is taken into account. We propose, both for the dilepton and the lepton + jets decay channels of $t\bar t$, several correlations and asymmetries with which (Higgs sector) CP violation can be traced. We show that for judiciously chosen cuts on the $t\bar t$ invariant mass these CP observables yield, for an LHC integrated luminosity of 100 $\rm{fb}^{-1}$, statistically significant signals for a range of Higgs boson masses and Yukawa couplings.Comment: 36 pages, 25 Postscript figure

Multiplet effects in orbital and spin ordering phenomena: A hybridization-expansion quantum impurity solver study

Orbital and spin ordering phenomena in strongly correlated systems are commonly studied using the local-density approximation + dynamical mean-field theory approach. Typically, however, such simulations are restricted to simplified models (density-density Coulomb interactions, high symmetry couplings and few-band models). In this work we implement an efficient general hybridization-expansion continuous-time quantum Monte Carlo impurity solver (Krylov approach) which allows us to investigate orbital and spin ordering in a more realistic setting, including interactions that are often neglected (e.g., spin-flip and pair-hopping terms), enlarged basis sets (full d versus eg), low-symmetry distortions, and reaching the very low-temperature (experimental) regime. We use this solver to study ordering phenomena in a selection of exemplary low-symmetry transition-metal oxides: LaMnO3 and rare-earth manganites as well as the perovskites CaVO3 and YTiO3. We show that spin-flip and pair hopping terms do not affect the Kugel-Khomskii orbital-order melting transition in rare-earth manganites, or the suppression of orbital fluctuations driven by crystal field and Coulomb repulsion. For the Mott insulator YTiO3 we find a ferromagnetic transition temperature 50 K, in remarkably good agreement with experiments. For LaMnO3 we show that the classical t2g-spin approximation, commonly adopted for studying manganites, yields indeed an occupied eg orbital in very good agreement with that obtained for the full d 5-orbital Hubbard model, while the spin-spin e_g-t_{2g} correlation function calculated from the full d model is 0.74, very close to the value expected for aligned eg and t2g spins; the eg spectral function matrix is also well reproduced. Finally, we show that the t2g screening reduces the eg-eg Coulomb repulsion by about 10%Comment: 9 pages, 5 figure