We introduce a new variant of hedonic coalition formation games in which agents have two levels of preference on their own coalitions: preference on the set of “roles” that makes up the coalition, and preference on their own role within the coalition. We define several stability notions and optimization problems for this model. We prove the hardness of the decision problems related to our optim...

Popular models for decision making under ambiguity assume that people use not one but multiple priors. This paper is a first attempt to experimentally elicit multiple priors. In an ambiguous scenario with two underlying states we measure a subject’s single prior, her other potential priors (multiple priors), her confidence in these priors valuation of an ambiguous asset with the same underlying...

This paper develops algorithms for dynamically consistent updating of ambiguous beliefs in the maxmin expected utility model of decision making under ambiguity. Dynamic consistency is the requirement that ex-ante contingent choices are respected by updated preferences. Such updating, in this context, implies dependence on the feasible set of payoff vectors available in the problem and/or on an ...

We define an opportunity act as a mapping from an exogenously given objective state space to a set of lotteries over prizes, and consider preferences over opportunity acts. We allow the preferences to be possibly uncertainty averse. Our main theorem provides an axiomatization of the maxmin expected utility model. In the theorem we construct subjective states to complete the objective state spac...

In 1991, Edelsbrunner and Tan gave an O(n) algorithm for finding the MinMax Length triangulation of a set of points in the plane. In this paper we resolve one of the open problems stated in that paper, by showing that finding a MaxMin Length triangulation is an NPcomplete problem. The proof implies that (unless P=NP), there is no polynomial-time approximation algorithm that can approximate the ...

We solve the following problem proposed by H. Straubing. Given a two letter alphabet A, what is the maximal number of states f(n) of the minimal automaton of a subset of An, the set of all words of length n. We give an explicit formula to compute f(n) and we show that 1 = lim n→∞ nf(n)/2n ≤ limn→∞ nf(n)/2 n = 2. The purpose of this note is to solve the following question, raised by H. Straubing...

Given a planar straight line graph we seek a covering triangulation whose minimumangle is as large as possible A covering triangulation is a Steiner triangulation with the following restriction No Steiner vertices may be added on an input edge We give an explicit upper bound on the largest possible minimum angle in any covering triangulation of a given input This upper bound depends only on loc...

1 We study the properties associated to various de…nitions of ambiguity ([8], [9], [18] and [23]) in the context of Maximin Expected Utility (MEU). We show that each de…nition of unambiguous events produces certain restrictions on the set of priors, and completely characterize each de…nition in terms of the properties it imposes on the MEU functional. We apply our results to two open problems. ...

This paper introduces the concept of firm belief, which is proposed as a new epistemic model for a wide class of preferences. In particular, firm beliefs are shown to have the following desirable properties: (i) they are derived from preferences according to a plausible rule of epistemic inference; (ii) they satisfy standard logical properties; and (iii) tractable representations of firm belief...

Control charts are the most important tools of statistical process control used to discriminate between assignable and common causes of variation and to improve the quality of a process. To design a control chart, three parameters including sample size, sampling interval, and control limits should be determined. The objectives are hourly expected cost, in-control average run length, power of th...