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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 so-called 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 so-called 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, Aizerman-Malishevski 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 (TSE-R - Toulouse School of Economics - UT1 - Université Toulouse 1 Capitole - Université Fédérale Toulouse Midi-Pyrénées - 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 end-of-period 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 semi-martingales or Markov processes. We introduce a rich class of principal-agent models that encompasses dynamic agency models with memory. From the mathematical point of view, we develop a methodology to deal with the possible non-Markovianity and non-semimartingality of the control problem, which can no longer be directly solved by means of the usual Hamilton-Jacobi-Bellman equation. Our main contribution is to show that, for one-dimensional models, this setting always allows for optimal linear contracts in end-of-period 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: | Principal-Agent,Models,Continuous-time control problems |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-03783062&r=cta |