CCOR Workshop on Three Faces of Decision

Professor Giancarlo Bigi (Department of Computer Science, University of Pisa, Italy) will be a guest of the Corvinus Center for Operation Research (CCOR) the next week. As part of his visit, a workshop will be organized.

Venue: Corvinus University, Building C, Room: C.714
Date: May 24 Wednesday, 10.30-14.30  

Keynote speaker: Giancarlo Bigi (Department of Computer Science, University of Pisa)

Speakers: Petrus H. Potgieter (Department of Decision Sciences, University of South Africa )                 
Miklós Pintér (CCOR/ODI, Corvinus University)

 10.30-11.00: Petrus H. Potgieter: Problems in choice by way of Kleene and Kőnig 
 11.00-11.30: Miklós Pintér: Computing a Common Prior
 11.30-12.30: Lunch break
 12.30-13.30: Giancarlo Bigi: Equilibrium selection and hierarchical optimization
 13.30-14.30: Discussion



Giancarlo Bigi: Equilibrium selection and hierarchical optimization

The selection of an equilibrium is a central issue in the management of multi-agent systems that can be partially controlled. Once the system has been modelled, the selection between the multiple equilibria can be performed through a two-level hierarchical optimization problem. The lower-level describes the equilibria while the upper-level explicitly addresses the selection criterion through a suitable objective function. Hierarchical programs of this kind are simpler than more general bilevel structures as the lower-level problems are non-parametric with respect to the upper level variables.

Game-theoretic models provide suitable mathematical formulations for many multi-agent systems and hence for the lower-level of the selection program. Hence, the first part of the talk reviews the basics of noncooperative games, variational formulations of Nash equilibria and algorithms for their computation. The second part focuses on hierarchical programs whose lower-level is a variational problem. In order to tackle them, suitable approximated versions of the lower-level are introduced. On the one hand, the approximation does not perturb the original [exact] program too much and allows for some additional flexibility in the choice. On the other hand, it allows relying on suitable exact penalty schemes by recovering those regularity conditions that the original problem does not satisfy. This penalization approach is described in details and the convergence properties of the resulting algorithms are analysed. Some preliminary numerical results are reported as well. Finally, some possible further developments of this approach are addressed.

Petrus H. Potgieter: Problems in choice by way of Kleene and Kőnig

The Kőnig infinity lemma and the Kleene tree are closely tied to the existence of Brouwer fixed-points and the potential impossibility of finding them. We discuss the connection as well the application of randomly generated trees to the problem. Broader issues of computability in choice (including solvability of linear difference systems) are also discussed.

Miklós Pintér: Computing a Common Prior

Morris (1994) and later Feinberg (2000) showed that a finite type space (information structure) attains a common prior if and only if there is no agreeable bet in it. We also consider finite type spaces and observe that deciding about the existence of a common prior is equivalent with considering the intersection of affine spaces each is spanned by the types of a player. This observation implies that we can apply the Fredholm alternative (Fredholm, 1903), and conclude that the computational complexity of computing a common prior or an agreeable bet is strongly polynomial.