Combinatorical and Algebraic Structures Seminar

Session details

Date: 10.3.2015
Speaker: René Levínský, Max Planck Institute of Economics
Title: On the best response to factor-based strategies and other selected problems from (quantum) game theory
Abstract: In the first part of the talk we offer a new approach to modeling strategies of bounded complexity, the so-called factor-based strategies. In our model, the strategy of a player in the multi-stage game does not directly map the set of histories $H$ to the set of her actions. Instead, the player's perception of $H$ is represented by a factor $\varphi: H \to X,$ where $X$ reflects the ``cognitive complexity'' of the player. Formally, mapping $\varphi$ sends each history to an element of a factor space $X$ that represents its equivalence class. The play of the player can then be conditioned just on the elements of the set $X$. Strategies played by finite automata and strategies with bounded recall are the most prominent examples of factor-based strategies. Finally, we show that for recursive factor $\varphi$ and for every profile of factor-based strategies there is a best reply that is a pure factor-based strategy. In the second (quite informal and interactive) part of the talk, we will discuss the quantum extension of the game theory, namely some links between quantum game theory a mathematical physics.

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