Lectures by Professors M. Grabish and A. Rusinowska-Grabisch

The lectures will be held at Shabolovka building of HSE.

Seminars 

22.11.2017  from 16.40  (Room 2309)

 “Some remarkable polyhedra in cooperative game theory” (M. Grabisch)

The characteristic function of a TU-game is a set function defined on a finite universe vanishing at the empty set. Set functions appear in many domains of Operations Research and decision theory (capacities, pseudo-Boolean functions, polymatroids, etc.) and induce interesting polyhedra. Remarkable families of set functions form polyhedra, e.g., the polytope of capacities (monotone TU-games), the polytope of $p$-additive capacities, the cone of supermodular games, etc. Also, the core of a set function, defined as the set of additive set functions dominating that set function, is a polyhedron which is of fundamental importance in game theory, decision making and combinatorial optimization. This survey gives an overview of these notions and studies all these polyhedra. We put an emphasis on the (still unsolved) problem of finding the vertices of the core.

“Modeling anonymous influence with anti-conformist agents” (A. Rusinowska-Grabisch)

We study a stochastic model of anonymous influence with conformist and anti-conformist individuals. Each agent with a "yes" or "no" initial opinion on a certain issue can change his opinion due to social influence. We consider anonymous influence, which depends on the number of agents having a certain opinion, but not on their identity. An individual is conformist/anti-conformist if his probability of saying "yes" increases/decreases with the number of "yes"- agents. In order to consider a society in which both conformists and anti-conformists co-exist, we investigate a generalized aggregation mechanism based on ordered weighted averages. Additionally, every agent has a coeffi- cient of conformism which is a real number in [−1, 1], with negative/positive values corresponding to anti-conformists/conformists. The two extreme values −1 and 1 represent a pure anti-conformist and a pure conformist, respectively, and the remaining values – so called "mixed" agents. We consider two kinds of a society: without mixed agents, and with mixed agents who play randomly either as conformists or anti-conformists. For both cases of the model, we deliver a qualitative analysis of convergence, i.e., find all absorbing classes and conditions for their occurrence.

Lectures 

24.11.2017    15.10-16.30   Room 5214

                      16.40-18.00   Room 5306

“Multicriteria decision making with interactive criteria” (M. Grabisch)

We make a general introductrion to multicriteria decision problems in the framework of conjoint measurement and multiattribute utility theory, and explain the central notion of mutual preferential independence and weak independence. We show how capacities (nonadditive measures) arise naturally and permit to model interaction between criteria. Two extensions of capacities are the Choquet integral model and the multilinear model. We explain under which conditions on conjoint measurement these models can live. Finally, we focus on the notion of interaction and its different definitions, and we show how they are related to the previous models.

“Dynamic models of strategic network formation” (A. Rusinowska-Grabisch)

The traditional literature on network formation is basically divided into two branches: one that uses a random network approach (a link is formed by pure chance), and one that models strategic network formation (a link is formed by strategic interaction). In the random networks approach, one usually focuses on dynamic models and examines if emerging networks exhibit some real-world network features. The literature on strategic network formation assumes that agents form links by maximizing their utility functions, and focuses on the analysis of stability and efficiency. Although many models of strategic network formation are developed in static frameworks, there exist a branch of dynamic models of network formation with strategic interactions. More recently, also network formation has been combined with games on networks whose analysis focuses on the impact of the network structure on individual decisions. This recent literature studies the simultaneous determination of actions and links. In the present talk, we provide an overview of important contributions that apply a dynamic approach to strategic network formation.