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These lecture notes attempt a mathematical treatment of game theory akin to mathematical physics. A game instance is defined as a sequence of states of an underlying system. This viewpoint unifies classical mathematical models for 2-person and, in particular, combinatorial and zero-sum games as well as models for investing and betting. n-person games are studied with emphasis on notions of utilities, potentials and equilibria, which allows to subsume cooperative games as special cases. The represenation of a game theoretic system in a Hilbert space furthermore establishes a link to the mathematical model of quantum mechancis and general interaction systems.
Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the so-called replicator equation, that
This paper has been withdrawn by the author due to some errors
We study the implications of endogenous pricing for learning and welfare in the classic herding model . When prices are determined exogenously, it is known that learning occurs if and only if signals are unbounded. By contrast, we show that learning
We consider transferable-utility profit-sharing games that arise from settings in which agents need to jointly choose one of several alternatives, and may use transfers to redistribute the welfare generated by the chosen alternative. One such setting
We add here another layer to the literature on nonatomic anonymous games started with the 1973 paper by Schmeidler. More specifically, we define a new notion of equilibrium which we call $varepsilon$-estimated equilibrium and prove its existence for