Preferences over Meyer’s Location-Scale Family

This paper extends Meyer’s (1987) location-scale family with general n random seed sources. Firstly, we clarify and generalize existing results to this multivariate setting. Some useful geometrical and topological properties of the location-scale expected utility functions are obtained. Secondly, we introduce and study some general non-expected utility functions defined over the location-scale (LS) family. Special care is made in characterizing the shape of the indifference curves induced by the LS expected utility functions and non-expected utility functions. Finally, efforts are also made to study several well-defined partial orders and dominance relations defined over the LS family. These include the first-, second- order stochastic dominance, the mean -variance rule, and a newly defined location-scale dominance.

Quasiconvex Constrained Multicriteria Continuous Location Problems: Structure of Nondominated Solution Sets

In this paper, we consider constrained multicriteria continuous location problems in two-dimensional spaces. In the literature, the continuous multicriteria location problem in two-dimensional spaces has received special attention in the last years, although only particular instances of convex functions have been considered. Our approach only requires the functions to be strictly quasiconvex and inf-compact. We obtain a geometrical description that provides a unified approach to handle multicriteria location models in two-dimensional spaces which has been implemented in MATHEMATIC

Value without absolute convergence

We address how the value of risky options should be assessed in the case where the sum of the probability-weighted payoffs is not absolutely convergent and thus dependent on the order in which the terms are summed (e.g., as in the Pasadena Paradox). We develop and partially defend a proposal according to which options should be evaluated on the basis of agreement among admissible (e.g., convex and quasi-symmetric) covering sequences of the constituents of value (i.e., probabilities and payoffs).

Using action understanding to understand the left inferior parietal cortex in the human brain

Published in final edited form as: Brain Res. 2014 September 25; 1582: 64–76. doi:10.1016/j.brainres.2014.07.035.Humans have a sophisticated knowledge of the actions that can be performed with objects. In an fMRI study we tried to establish whether this depends on areas that are homologous with the inferior parietal cortex (area PFG) in macaque monkeys. Cells have been described in area PFG that discharge differentially depending upon whether the observer sees an object being brought to the mouth or put in a container. In our study the observers saw videos in which the use of different objects was demonstrated in pantomime; and after viewing the videos, the subject had to pick the object that was appropriate to the pantomime. We found a cluster of activated voxels in parietal areas PFop and PFt and this cluster was greater in the left hemisphere than in the right. We suggest a mechanism that could account for this asymmetry, relate our results to handedness and suggest that they shed light on the human syndrome of apraxia. Finally, we suggest that during the evolution of the hominids, this same pantomime mechanism could have been used to ‘name’ or request objects.We thank Steve Wise for very detailed comments on a draft of this paper. We thank Rogier Mars for help with identifying the areas that were activated in parietal cortex and for comments on a draft of this paper. Finally, we thank Michael Nahhas for help with the imaging figures. This work was supported in part by the NIH grant RO1NS064100 to LMV. (RO1NS064100 - NIH)Accepted manuscrip

A cognitive hierarchy theory of one-shot games: Some preliminary results

Strategic thinking, best-response, and mutual consistency (equilibrium) are three key modelling principles in noncooperative game theory. This paper relaxes mutual consistency to predict how players are likely to behave in in one-shot games before they can learn to equilibrate. We introduce a one-parameter cognitive hierarchy (CH) model to predict behavior in one-shot games, and initial conditions in repeated games. The CH approach assumes that players use k steps of reasoning with frequency f (k). Zero-step players randomize. Players using k (≥ 1) steps best respond given partially rational expectations about what players doing 0 through k - 1 steps actually choose. A simple axiom which expresses the intuition that steps of thinking are increasingly constrained by working memory, implies that f (k) has a Poisson distribution (characterized by a mean number of thinking steps τ ). The CH model converges to dominance-solvable equilibria when τ is large, predicts monotonic entry in binary entry games for τ < 1:25, and predicts effects of group size which are not predicted by Nash equilibrium. Best-fitting values of τ have an interquartile range of (.98,2.40) and a median of 1.65 across 80 experimental samples of matrix games, entry games, mixed-equilibrium games, and dominance-solvable p-beauty contests. The CH model also has economic value because subjects would have raised their earnings substantially if they had best-responded to model forecasts instead of making the choices they did

Center Vortices and the Gribov Horizon

We show how the infinite color-Coulomb energy of color-charged states is related to enhanced density of near-zero modes of the Faddeev-Popov operator, and calculate this density numerically for both pure Yang-Mills and gauge-Higgs systems at zero temperature, and for pure gauge theory in the deconfined phase. We find that the enhancement of the eigenvalue density is tied to the presence of percolating center vortex configurations, and that this property disappears when center vortices are either removed from the lattice configurations, or cease to percolate. We further demonstrate that thin center vortices have a special geometrical status in gauge-field configuration space: Thin vortices are located at conical or wedge singularities on the Gribov horizon. We show that the Gribov region is itself a convex manifold in lattice configuration space. The Coulomb gauge condition also has a special status; it is shown to be an attractive fixed point of a more general gauge condition, interpolating between the Coulomb and Landau gauges.Comment: 19 pages, 17 EPS figures, RevTeX4; v2: added references, corrected caption of fig. 11; v3: new data for higher couplings, clarifications on color-Coulomb potential in deconfined phase, version to appear in JHE

Prospect and Markowitz Stochastic Dominance

Levy and Levy (2002, 2004) develop the Prospect and Markowitz stochastic dominance theory with S-shaped and reverse S-shaped utility functions for investors. In this paper, we extend Levy and Levy's Prospect Stochastic Dominance theory (PSD) and Markowitz Stochastic Dominance theory (MSD) to the first three orders and link the corresponding S-shaped and reverse S-shaped utility functions to the first three orders. We also provide experiments to illustrate each case of the MSD and PSD to the first three orders and demonstrate that the higher order MSD and PSD cannot be replaced by the lower order MSD and PSD. Prospect theory has been regarded as a challenge to the expected utility paradigm. Levy and Levy (2002) prove that the second order PSD and MSD satisfy the expected utility paradigm. In our paper we take Levy and Levy's results one step further by showing that both PSD and MSD of any order are consistent with the expected utility paradigm. Furthermore, we formulate some other properties for the PSD and MSD including the hierarchy that exists in both PSD and MSD relationships; arbitrage opportunities that exist in the first orders of both PSD and MSD; and that for any two prospects under certain conditions, their third order MSD preference will be ???the opposite??? of or ???the same??? as their counterpart third order PSD preference. By extending Levy and Levy's work, we provide investors with more tools for empirical analysis, with which they can identify the first order PSD and MSD prospects and discern arbitrage opportunities that could increase his/her utility as well as wealth and set up a zero dollar portfolio to make huge profit. Our tools also enable investors to identify the third order PSD and MSD prospects and make better choices.Prospect stochastic dominance, Markowitz stochastic dominance, risk seeking, risk averse, S-shaped utility function, reverse S-shaped utility function