This note gives a simple proof of the existence and monotonicity of optimal debt contracts in simple models of borrowing and lending with ex−post asymmetric information, risk−averse agents and heterogeneous beliefs. Our argument is based on the concept of nondecreasing rearrangement and on a supermodular version of Hardy−Littlewood inequality. Citation: Renou, Ludovic and Guillaume Carlier, (20...

1.1. Plancherel measures. Given a finite group G, by the corresponding Plancherel measure we mean the probability measure on the set G∧ of irreducible representations of G which assigns to a representation π ∈ G∧ the weight (dim π)/|G|. For the symmetric group S(n), the set S(n)∧ is the set of partitions λ of the number n, which we shall identify with Young diagrams with n squares throughout th...

We consider scenarios in which long sequences of data are analyzed and subsequences must be traced that are monotone and maximum, according to some measure. A classical example is the online Longest Increasing Subsequence Problem for numeric and alphanumeric data. We extend the problem in two ways: (a) we allow data from any partially ordered set, and (b) we maximize subsequences using much mor...

We study the uctuations, in the large deviations regime, of the longest increasing subsequence of a random i.i.d. sample on the unit square. In particular, our results yield the precise upper and lower exponential tails for the length of the longest increasing subsequence of a random permutation. i=1 denote a sequence of i.i.d. random variables with marginal law on the unit square Q = 0; 1] 2. ...

"Regret aversion" is proposed to explain a tendency to avoid future choices that have induced past regret. However, regret might also motivate us to repeat previous regret-related choices to make up for their previous selection, a behavior resembling "chasing" in the context of gambling. In the current experiment, we acquired fMRI brain data while participants placed monetary bets on repeated g...

Theorists operating from within a narrative identity framework have suggested that self-reflective reasoning plays a central role in the development of the self. Typically, however, narrative identity researchers have investigated this relationship using correlational rather than experimental methods. In the present study, leveraging on a classic research paradigm from within the social identit...

It frequently has been observed that people discount future rewards relative to present rewards. However, the literature on intertemporal choices involving emotional upsets and losses is fraught with inconsistencies, with some studies finding similar discounting of gains and losses, and others reporting that participants elect to undergo negative experiences sooner rather than later. To help re...

Ignoring information when making a decision is at the heart of the take-the-best (TTB) strategy, according to which decision makers only consider information about the most valid cue (TTB-relevant) and ignore less valid cues (TTB-irrelevant). Results of four experiments, however, show that participants do not ignore information when cues are easily available (Experiments 1a, 1b, and 3) or when ...

Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in O(n log n) time and space. Our goal in this paper is to reduce the space consumption while keeping the time complexity small. For √ n ≤ s ≤ n, we present algorithms that use O(s log n) bits and O( 1 s · n · log n) time for computing the length of a longe...

The deterministic space complexity of approximating the length of the longest increasing subsequence of a stream of N integers is known to be Θ̃( √ N). However, the randomized complexity is wide open. We show that the technique used in earlier work to establish the Ω( √ N) deterministic lower bound fails strongly under randomization: specifically, we show that the communication problems on which...