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Whether it be in normal form games, or in fair allocations, or in voter preferences in voting systems, a certain pattern of reasoning is common. From a particular profile, an agent or a group of agents may have an incentive to shift to a new one. This induces a natural graph structure that we call the improvement graph on the strategy space of these systems. We suggest that the monadic fixed-point logic with counting, an extension of monadic first-order logic on graphs with fixed-point and counting quantifiers, is a natural specification language on improvement graphs, and thus for a class of properties that can be interpreted across these domains. The logic has an efficient model checking algorithm (in the size of the improvement graph).
One of the natural objectives of the field of the social networks is to predict agents behaviour. To better understand the spread of various products through a social network arXiv:1105.2434 introduced a threshold model, in which the nodes influenced
In large scale collective decision making, social choice is a normative study of how one ought to design a protocol for reaching consensus. However, in instances where the underlying decision space is too large or complex for ordinal voting, standard
We consider agents in a social network competing to be selected as partners in collaborative, mutually beneficial activities. We study this through a model in which an agent i can initiate a limited number k_i>0 of games and selects the ideal partner
One way of evaluating social choice (voting) rules is through a utilitarian distortion framework. In this model, we assume that agents submit full rankings over the alternatives, and these rankings are generated from underlying, but unknown, quantita
Without monetary payments, the Gibbard-Satterthwaite theorem proves that under mild requirements all truthful social choice mechanisms must be dictatorships. When payments are allowed, the Vickrey-Clarke-Groves (VCG) mechanism implements the value-ma