Games without Rules

We introduce the notion of an outcome space, in which strategic interactions are embedded. This allows us to investigate the idea that one strategic interaction might be an expanded version of another interaction. We then characterize the Nash equilibria arising in such extensions and demonstrate a folk-type theorem stating that any individually rational element of the outcome space is a Nash equilibrium.     

Choices Under Ambiguity With Familiar And Unfamiliar Outcomes

This paper considers a decision-making process under ambiguity in which the decision-maker is supposed to split outcomes between familiar and unfamiliar ones. She is assumed to behave differently with respect to unfamiliar gains, unfamiliar losses and customary (familiar) outcomes. In particular, she is supposed to be pessimistic on gains, optimistic on losses and ambiguity neutral on the familiar outcomes. A generalization of the usual Choquet Integral is formalized when the decision maker holds capacities and probabilities. A characterization of the decision-maker’s behavior is provided for a specific subset of capacities, in which it is shown that the decision-maker underestimates the unfamiliar outcomes while is linear in probabilities on customary ones.     

Compound designs for dose‐finding in the presence of nondesignable covariates

Compound optimal designs are considered where one component of the design criterion is a traditional optimality criterion such as the D‐optimality criterion, and the other component accounts for higher efficacy with low toxicity. With reference to the dose‐finding problem, we suggest the technique to choose weights for the two components that makes the optimization problem simpler than the traditional penalized design. We allow general bivariate responses for efficacy and toxicity. We then extend the procedure in the presence of nondesignable covariates such as age, sex, or other health conditions. A new breast cancer treatment is considered to illustrate the procedures. Copyright © 2013 John Wiley & Sons, Ltd.     

Lp (1 < p ⩽ 2) solutions of one-dimensional BSDEs whose generator is weakly monotonic in y and non-Lipschitz in z

ABSTRACT

In this paper, we start with establishing the existence of a minimal (maximal) L^p (1 < p ? 2) solution to a one-dimensional backward stochastic differential equation (BSDE), where the generator g satisfies a p-order weak monotonicity condition together with a general growth condition in y and a linear growth condition in z. Then, we propose and prove a comparison theorem of L^p (1 < p ? 2) solutions to one-dimensional BSDEs with q-order (1 ? q < p) weak monotonicity and uniform continuity generators. As a consequence, an existence and uniqueness result of L^p (1 < p ? 2) solutions is also given for BSDEs whose generator g is q-order (1 ? q < p) weakly monotonic with a general growth in y and uniformly continuous in z.     

A Decomposition of Copulas and Its Use

ABSTRACT

In this article, we create a decomposition that represents and describes the depen-dence structure between two variables. Since copulas provide a deep understanding of the dependence structure by eliminating the effects of the marginals, they play a key role in this study. We define a discretized copula density matrix and decompose it into a set of permutation matrices by using the Birkhoff–von Neumann theorem. This decomposition provides a way to effectively apply the concepts of copulas to solve problems in multivariate statistical data analysis.     

Optimum Designs for Parameter Estimation in Linear Mixture Models with Synergistic Effects

In this article, we derive optimum designs for parameter estimation in a mixture experiment when the response function is linear in the mixing components with some synergistic effects. The D- and A-optimality criteria have been used for the purpose. The Equivalence Theorem has been used to check for the optimality of the proposed designs.     

The Discounted Berry-Esséen Analogue for Autoregressive Processes

In this article, the discounted Berry-Esséen analogs and non uniform estimates for autoregressive processes are obtained.     

Constants on a Uniform Berry-Esseen Bound on Some Borel Sets in ℝ k via Stein's Method

For each n, k ∈ ?, let Y _i  = (Y _i1, Y _i2,…, Y _ik ), 1 ≤ i ≤ n be independent random vectors in ? ^k with finite third moments and Y _ij are independent for all j = 1, 2,…, k. In this article, we use the Stein's technique to find constants in uniform bounds for multidimensional Berry-Esseen inequality on a closed sphere, a half plane and a rectangular set.     

From Conditional Independence to Conditionally Negative Association: Some Preliminary Results

Conditional moment estimates on the cumulative sum of conditionally independent random variables are derived, conditional prophet inequalities for conditionally independent random variables are established, a comparison theorem on conditional moment inequalities between conditionally independent and conditionally negatively associated random variables is established. As applications of these results, a conditional Rosenthal type inequality and two conditional Kolmogorov exponential inequalities for conditionally negatively associated random variables are obtained.