More strategies, more Nash equilibria

This short paper isolates a non-trivial class of games for which there exists a monotone relation between the size of pure strategy spaces and the number of pure Nash equilibria (Theorem). This class is that of two- player nice games, i.e., games with compact real intervals as strategy spaces and continuous and strictly quasi-concave payoff functions, assumptions met by many economic models. We then show that the sufficient conditions for Theorem to hold are tight.Strategic-form games, strategy spaces, Nash equilibrium, two players

Bilateral Commitment

We consider non-cooperative environments in which two players have the power to commit but cannot sign binding agreements. We show that by committing to a set of actions rather than to a single action, players can implement a wide range of action profiles. We give a complete characterization of implementable profiles and provide a simple method to find them. Profiles implementable by bilateral commitments are shown to be generically inefficient. Surprisingly, allowing for gradualism (i.e., step by step commitment) does not change the set of implementable profiles.Commitment; self-enforcing; generic inefficiency; agreements; Pareto-improvement

Bilateral Commitment

We consider non-cooperative environments in which two players have the power to commit but cannot sign binding agreements. We show that by committing to a set of actions rather than to a single action, players can implement a wide range of action profiles. We give a complete characterization of implementable profiles and provide a simple method to find them. Profiles implementable by bilateral commitments are shown to be generically inefficient. Surprisingly, allowing for gradualism (i.e., step by step commitment) does not change the set of implementable profiles.commitment, self-enforcing, treaties, inefficiency, agreements, Pareto-improvement

Benzyl β-malolactonate polymers: a long story with recent advances

International audiencePoly (-benzyl malolactonate) (PMLABe) is an aliphatic renewable, biocompatible, biodegradable, hydrophobic polyester of the poly(hydroxyalkanoate) (PHA) family. Along with the hydrophilic parent poly(-malic acid) (PMLA), PMLABe and PMLA have been studied as materials for biomedical applications. Herein, advances on the synthesis of benzyl -malolactonate (MLABe) and the related alkyl -malolactonates (MLARs), PMLABe homopolymers and copolymers, are reviewed. Focus is placed on the ring-opening polymerization (ROP) of MLABe and on copolymers of MLABe, with relevant data on the performances of the initiating systems and on the PMLABes molecular characteristics, along with detailed mechanistic insights, being reported

Development and mechanical characterization of porous titanium bone substitutes

The authors wish to thank Dr J.-M. Hiver from Institut Jean Lamour, Ecole des Mines de Nancy for his participation in the computed tomography analysis of the porous samplesCommercially Pure Porous Titanium (CPPTi) can be used for surgical implants to avoid the stress shielding effect due to the mismatch between the mechanical properties of titanium and bone. Most researchers in this area deal with randomly distributed pores or simple architectures in titanium alloys. The control of porosity, pore size and distribution is necessary to obtain implants with mechanical properties close to those of bone and to ensure their osseointegration. The aim of the present work was therefore to develop and characterize such a specific porous structure. First of all, the properties of titanium made by Selective Laser Melting (SLM) were characterized through experimental testing on bulk specimens. An elementary pattern of the porous structure was then designed to mimic the orthotropic properties of the human bone following several mechanical and geometrical criteria. Finite Element Analysis (FEA) was used to optimize the pattern. A porosity of 53% and pore sizes in the range of 860 to 1500 μm were finally adopted. Tensile tests on porous samples were then carried out to validate the properties obtained numerically and identif the failure modes of the samples. Finally, FE elastoplastic analyses were performed on the porous samples in order to propose a failure criterion for the design of porous substitutes

Polyhydroxybutyrate (PHB)-based triblock copolymers: synthesis of hydrophobic PHB/poly(benzyl beta-malolactonate) and amphiphilic PHB/poly(malic acid) analogues by ring-opening polymerization

International audiencePolyhydroxyalkanoates (PHAs) are biocompatible and biodegradable polyesters widely used for biomedical applications. Amphiphilic triblock copolymers with a PHB hydrophobic segment recently demonstrated attractive advantages such as high colloidal stability and low critical micellar concentration (CMC) values for the elaboration of drug delivery systems. Our approach aims at associating PHB with a fully biodegradable hydrophilic block to access new self-assembled systems with unique potential. Well-defined alpha,omega-dihydroxy telechelic PHA-based hydrophobic triblock copolymers with tunable segments length were synthesized by the controlled ring-opening polymerization (ROP) of benzyl beta-malolactonate, using polyhydroxybutyrate (PHB) diol/Nd(OTf)(3) as the catalytic system. Remarkably, the reaction proceeds with the selective oxygen-acyl bond cleavage of the beta-lactone. The corresponding amphiphilic copolymers were then obtained by hydrogenolysis. These copolymers are the only examples of fully biodegradable PHA-PHB-PHA triblock copolymers. The hydrophilic weight fraction of the copolymers was tuned from 7 to 83% upon modulating the monomer loading thus affording the ability to next access different self-assembling architectures

Automata Techniques for Epistemic Protocol Synthesis

International audienceIn this work we aim at applying automata techniques to problems studied in Dynamic Epistemic Logic, such as epistemic planning. To do so, we first remark that repeatedly executing ad infinitum a propositional event model from an initial epistemic model yields a relational structure that can be finitely represented with automata. This correspondence, together with recent results on uniform strategies, allows us to give an alternative decidability proof of the epistemic planning problem for propositional events, with as by-products accurate upper-bounds on its time complexity, and the possibility to synthesize a finite word automaton that describes the set of all solution plans. In fact, using automata techniques enables us to solve a much more general problem, that we introduce and call epistemic protocol synthesis