Three faces of game theoryWorkshop by the Corvinus Institute of Advanced Studies
- 13:00-13:30: Ziv Hellman: Mentors and Recombinators: Multi-Dimensional Social Learning
- 13:30-14:00: David Bartl: On the Non-Emptiness of the Core of a Cooperative Fuzzy Game
- 14:00-14:30: Coffee break
- 14:30-15:50: Dov Samet: Interim agreements
Keynote speaker: Dov Samet (Tel-Aviv University)
Speakers: David Bartl (University in Opava) and Ziv Hellman (Bar-Ilan University)
Dov Samet: Interim agreements
Abstract: Processes of bargaining are studied in which the players reach interim agreements that serve as status quo points for further bargaining. This is modeled in Nash’s setup of bargaining problems, where the solution is a time parameterized path of interim agreements rather than a single point. We characterize path solutions for linear problems that satisfy the axioms of restarting and covariance, and show that if a Pareto efficient agreement is not reached immediately, then it is never reached in finite time. Adding the axioms of individual rationality, relevance, and monotonicity, we characterize the family of continuous Raiffa solutions and show that these solutions converge to a Pareto efficient agreement but never reach it in finite time. Finally, if a deadline is added to the bargaining problem, and the speed of bargaining is proportionally inverse to the deadline, then a Pareto efficient agreement is reached exactly at the deadline.
David Bartl: On the Non-Emptiness of the Core of a Cooperative Fuzzy Game
Abstract: First, we consider a classical cooperative game with transferable utility. Recalling the notion of core with respect to a general coalition structure (Aumann and Dreze, 1974), we generalize the concept of balancedness and the Bondareva-Shapley Theorem accordingly. Next, we introduce the concept of a fuzzy coalition structure on a finite set of players, and we also propose a new model of a cooperative fuzzy game with transferable utility: an existing coalition is assumed to endeavour in a branch of industry, and a deviation of a new coalition from the coalition structure is seen as an opportunity of the coalition. Based on these premisses, we introduce the concept of the core of the cooperative fuzzy TU-game with respect to a general fuzzy coalition structure. Finally, we again define the concept of balancedness and formulate a generalization of the Bondareva-Shapley Theorem.
Ziv Hellman (joint with Srinivas Arigapudi, Omer Edhan and Yuval Heller): Mentors and Recombinators: Multi-Dimensional Social Learning
Authors: Srinivas Arigapudi, Omer Edham, Yuval Heller, Ziv Hellman
Abstract: We study games in which the set of strategies is multi-dimensional, and new agents might learn various strategic dimensions from different mentors. We introduce a new family of dynamics, the recombinator dynamics, which is characterised by a single parameter, the recombination rate r \in [0,1]. The case of r = 0 coincides with the standard replicator dynamics. The opposite case of r = 1 corresponds to a setup in which each new agent learns each new strategic dimension from a different mentor and combines these dimensions into her adopted strategy. We characterise stationary states and stable states under these dynamics, and we show that they predict novel behaviour in various applications.
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