Monica Patriche

• University of Bucharest

In this paper, first of all, we consider a generalized game in choice form with 2 constraints and its corresponding equilibrium in choice. We assert new conditions under which the equilibrium in choice exists. As a consequence, we establish the existence of the equilibrium for generalized abstract economies. Then, we apply the obtained theorems to...

In this paper, we prove the existence of the equilibrium in choice for games in choice form. Thus, we add to the research recently appeared in the scientific literature. In fact, our results link the most recent research to the older approaches of the games in normal-form and the qualitative games.

In this paper, we state a new fixed point theorem for correspondences defined on Hausdorff locally convex spaces and we use it to prove the existence of the generalized weighted Nash equilibrium and the generalized Pareto equilibrium of a constrained multi-criteria game.

In this paper, we study the existence of solutions for generalized vector quasi-equilibrium problems. Firstly, we prove that in the case of Banach spaces, the assumptions of continuity over correspondences can be weakened. The theoretical analysis is based on fixed-point theorems. Secondly, we establish new equilibrium theorems as applications of t...

In this paper, we establish coincidence-like results in the case when the values of the correspondences are not convex. In order to do this, we define a new type of correspondences, namely properly quasi-convex-like. Further, we apply the obtained theorems to solve equilibrium problems and to establish a minimax inequality. In the last part of the...

In this paper, we consider a generalized strong vector quasi-equilibrium problem and we prove the existence of its solutions by using some suxiliary results. One of the established theorems is proved by using an approximation method.

In this paper, we introduce a generalized game in choice form, which differs slightly from the model defined by Ferrara and Stefanescu (2015) and we obtain the existence of the equilibrium for this model. As applications, we obtain new theorems concernong the existence of solutions for systems of vector equilibrium problems.

This paper has two central aims: first, to provide simple conditions under which the generalized games in choice form and, consequently, the abstract economies, admit equilibrium; second, to study the solvability of several types of systems of vector quasi-equilibrium problems as an application. Our work outlines that there still is much to be gain...

In this paper, we study the existence of the random fixed points for lower semicontinuous condensing random operators defined on Banach spaces. Our results extend corresponding ones present in literature.

In this paper, we study the existence of the random approximations and fixed points for random almost lower semicontinuous operators defined on finite dimensional Banach spaces, which in addition, are condensing or 1-set-contractive. Our results either extend or improve corresponding ones present in literature.

In this paper we prove the existence of equilibrium pairs for the new model of a Bayesian free abstract economy which extends Kim and Lee’s deterministic model of a free abstract economy (2006). Our existence theorems are proved for the case of upper semicontinuous correspondences. We also define a model of a general Bayesian abstract economy and i...

In this paper, we study the existence of the random fixed points under mild continuity assumptions. The main theorems consider the almost lower semicontinuous operators defined on Frechet spaces and also operators having properties weaker than lower semicontinuity. Our results either extend or improve corresponding ones present in literature.

In this paper, we firstly prove the existence of the equilibrium for the generalized abstract economy. We apply these results to show the existence of solutions for systems of vector quasi-equilibrium problems with multivalued trifunctions. Secondly, we consider the generalized strong vector quasi-equilibrium problems and study the existence of the...

In this paper, we introduce an abstract fuzzy economy (generalized fuzzy game) model with a countable space of actions and we study the existence of the fuzzy equilibrium. As applications, two types of results are obtained. The first ones concern the existence of the solutions for systems of generalized quasi-variational inequalities with random fu...

We introduce new types of systems of generalized quasi-variational inequalities and we prove the existence of the solutions by using results of pair equilibrium existence for free abstract economies. We consider the fuzzy models and we also introduce the random free abstract economy and the random equilibrium pair. The existence of the solutions fo...

In this paper, we introduce a Bayesian abstract fuzzy economy model and we prove the Bayesian fuzzy equilibrium existence. As applications, we prove the existence of the solutions for two types of random quasi-variational inequalities with random fuzzy mappings and we also obtain random fixed point theorems.

The main purpose of this paper is to introduce an abstract fuzzy economy model with differential asymmetric information and a measure space of agents. It generalizes a previous model proposed by the author in 2009. The applications concern the fuzzy equilibrium existence and the existence of the solutions for two types of random quasi-variational i...

In this paper, we introduce an abstract fuzzy economy model with a measure space of agents which generalizes Patriche's model (2009), we obtain a theorem of fuzzy equilibrium existence and we prove the existence of the solutions for two types of random quasi-variational inequalities with random fuzzy mappings. As a consequence, we obtain random fix...

We introduce the notion of w-upper semicontinuous set valued maps and give a new fixed-point theorem. We also introduce the notion of set valued maps with e-USS-property. These results can be applied to obtain some new equilibrium theorems for abstract economies.

We introduce several classes of set-valued maps with generalized convexity. We obtain minimax theorems for set-valued maps which satisfy the introduced properties and are not continuous, by using a fixed point theorem for weakly naturally quasi-concave set-valued maps defined on a simplex in a topological vector space.

We define the model of an abstract economy with private information and a countable set of actions. We generalize the H. Yu and Z. Zhang's model (2007), considering that each agent is characterised by a preference correspondence instead of having an utility function. We establish two different equilibrium existence results.

In this paper we use the minimax inequalities obtained by S. Park (2011) to prove the existence of weighted Nash equilibria and Pareto Nash equilibria of a multiobjective game defined on abstract convex spaces.

In this paper, we introduce several types of correspondences: weakly naturally quasiconvex, *-weakly naturally quasiconvex, weakly biconvex and correspondences with *--weakly convex graph and we prove some fixed point theorems for these kinds of correspondences. As a consequence, using a version of W. K. Kim's quasi-point theorem, we obtain the exi...

The main purpose of this paper is to introduce the notion of weakly upper semicontinuous set-valued maps and to establish a new fixed-point theorem. The set-valued maps with an approximating upper semicontinuous selection property are also defined. Next, we use our fixed-point result to obtain equilibrium existence in abstract economies with two co...

We study the fixed point property of set-valued maps and the existence of equilibria in the framework of $\mathbb{B}$ -convexity, recently defined by W. Briec and Ch. Horvath. We introduce some classes of the set-valued maps with generalized convexity and prove continuous selection and fixed point properties for them. Finally, we obtain results c...

We extend the study of the iterated elimination of strictly dominated strategies (IESDS) from Nash strategic games to a class of qualitative games. Also in this case, the IESDS process leads us to a kind of 'rationalizable' result. We define several types of dominance relation and game reduction and establish conditions under which a unique and non...

We introduce the notions of w-lower semicontinuous and almost w-lower semicontinuous correspondence with respect to a given set and prove a new fixed-point theorem. We also introduce the notion of correspondence with e-LSCS-property. As applications we obtain some new equilibrium theorems for abstract economies and for generalized multiobjective ga...

We introduce the notions of weakly *-concave and weakly naturally quasi-concave correspondence and prove fixed point theorems and continuous selection theorems for these kind of correspondences. As applications in the game theory, by using a tehnique based on a continuous selection, we establish new existence results for the equilibrium of the abst...

We study the conditions under which the iterated elimination of strictly dominated strategies is order independent and we identify a class of discontinuous games for which order does not matter. In this way, we answer the open problem raised by M. Dufwenberg and M. Stegeman (2002) and generalize their main results. We also establish new theorems co...

We obtain new equilibrium theorems for fuzzy abstract economies with correspondences being w-upper semicontinuous or having e-USS-property.

We consider fractional linear programming production games for the single-objective and multiobjective cases. We use the method of Chakraborty and Gupta (2002) in order to transform the fractional linear programming problems into linear programming problems. A cooperative game is attached and we prove the non-emptiness of the core by using the dual...

We introduce, in the first part, the notion of weakly convex pair of correspondences, we give its economic interpretation, we state a fixed point and a selection theorem. Then, by using a tehnique based on a continuous selection, we prove existence theorems of quilibrium for an abstract economy. In the second part, we define the weakly biconvex cor...

We introduce some types of correspondences with e-selection properties: the correspondences with e-USS-property, e-LSCS-property and e-WCGS-property. As applications we obtain some new equilibrium theorems for abstract economies.

We define a model of a general Bayesian abstract economy, which extends the deterministic model of N. C. Yannelis and N. D. Prabhakar (2002) in a Bayesian framework and also introduce the new notion of equilibrium pair. We prove the existence of equilibrium pair and equilibrium for this type of abstract economy.

In this paper we extend Kim and Lee's deterministic model of a free abstract economy (2006) in a Bayesian framework and introduce the concept of Bayesian equilibrium pair. We also prove the existence of equilibrium for a free Bayesian abstract economy with incomplet information and upper semicontinuous correspondences.

We have a Bayesian approach for an equilibrium problem in abstract economies of the Yannelis–Prabhakar type. We consider an economy with a countable or uncountable set of agents, with private information defined by subalgebras as per Yannelis [Yannelis, A Bayesian equilibrium existence theorem, Adv. Math. Econ. 4 (2002), pp. 61–72] and the preferen...

In this paper, we propose the concept of equilibrium pair for an abstract economy and prove several theorems of the existence of equilibrium for abstract economies with different types of correspondences.

We study properties of correspondences and the existence of equilibria in the framework of B-convexity, recently introduced by W. Briec and Ch. Horvath. We study correspondences with weakly B-convex graph and prove that such a correspondence defined on a bimplex has a continuous selection. Finally we obtain results concerning existence of equilibri...

We define the model of an abstract economy with differential (asymmetric) information and a measure space of agents. We generalize N. C. Yannelis's result (2007), considering that each agent is characterised by a random preference correspondence instead of having a random utility function. We establish two different equilibrium existence results.

In this paper, we introduce the concept of free abstract fuzzy econ-omy and, using Wu's existence theorem of maximal elements for lower semicontinuous correspondences [26] and Kim and Lee's existence theo-rems of best proximity pairs [14], we prove the existence of fuzzy equi-librium pairs for free abstract fuzzy economies first with upper semicon-...

We give a new fixed-point theorem for lower semicontinuous correspondences and introduce the notion of Q 0 -majorized correspondences. As applications we obtain some new equilibrium theorems which improve the results of X. Wu in (8), referred to abstract economies with lower semicontinuous correspondences, respectively X. Liu and H.Cai in (4), refe...

We establish new existence results for the equilibrium of the abstract economies. The constraint correspondences have the W. C. G. property. This notion was proposed in 1998 by D. P. Ding and Y. R. He in [Appl. Math. Mech., Engl. Ed. 19, No. 9, 831–836 (1998; Zbl 0921.47046)]. Basically, our proofs are based on a continuous selection theorem for co...

G. Debreu’s model of abstract economy was extended in the last years by several authors. In a paper from 2003, W. Kim proved an existence theorem of equilibrium for a generalized quasi-game with an infinite number of agents. The purpose of this paper is to obtain new existence theorems of equilibrium in a generalized quasi-game.

We establish new existence results for the equilibrium of abstract economies in l.c. (locally convex)-metric spaces. The constraint and preference correspondences are locally-uniformly-weakly lower semicontinuous (w.l.s.c.) or have the local inter-section property. Basically, our proofs are based on J.C. Hou's continuous selection theorem in [12] f...

In this paper, by using an existence theorem of maximal elements for Q'-majorized correspondences and Kim and Lee's existence theorems of best proximity pairs (2006), we prove the existence of fuzzy equilibrium pairs for fuzzy abstract economies with Q'-majorized preference correspondences. Key–Words: Q'-majorized correspondences, upper semicontinu...