
on Contract Theory and Applications 
By:  Danilov, Vladimir; Karzanov, Alexander 
Abstract:  We consider a hypergraph (I, C), with possible multiple (hyper)edges and loops, in which the vertices i ∈ I are interpreted as agents, and the edges c ∈ C as contracts that can be concluded between agents. The preferences of each agent i concerning the contracts where i takes part are given by use of a choice function fi possessing the socalled path independent property. In this general setup we introduce the notion of stable network of contracts. The paper contains two main results. The first one is that a general problem on stable systems of contracts for (I, C, f) is reduced to a set of special ones in which preferences of agents are described by use of socalled weak orders, or utility functions. However, for a special case of this sort, the stability may not exist. Trying to overcome this trouble when dealing with such special cases, we introduce a weaker notion of metastability for systems of contracts. Our second result is that a metastable system always exists. 
Keywords:  Plott choice functions, AizermanMalishevski theorem, stable marriage, roommate problem, Scarf lemma 
JEL:  C71 C78 D74 
Date:  2022–11–29 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:115482&r=cta 
By:  Eduardo Abi Jaber (X  École polytechnique); Stéphane Villeneuve (TSER  Toulouse School of Economics  UT1  Université Toulouse 1 Capitole  Université Fédérale Toulouse MidiPyrénées  EHESS  École des hautes études en sciences sociales  CNRS  Centre National de la Recherche Scientifique  INRAE  Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) 
Abstract:  Can a principal still offer optimal dynamic contracts that are linear in endofperiod outcomes when the agent controls a process that exhibits memory? We provide a positive answer by considering a general Gaussian setting where the output dynamics are not necessarily semimartingales or Markov processes. We introduce a rich class of principalagent models that encompasses dynamic agency models with memory. From the mathematical point of view, we develop a methodology to deal with the possible nonMarkovianity and nonsemimartingality of the control problem, which can no longer be directly solved by means of the usual HamiltonJacobiBellman equation. Our main contribution is to show that, for onedimensional models, this setting always allows for optimal linear contracts in endofperiod observable outcomes with a deterministic optimal level of effort. In higher dimension, we show that linear contracts are still optimal when the effort cost function is radial and we quantify the gap between linear contracts and optimal contracts for more general quadratic costs of efforts. 
Keywords:  PrincipalAgent,Models,Continuoustime control problems 
Date:  2022 
URL:  http://d.repec.org/n?u=RePEc:hal:journl:hal03783062&r=cta 