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Multicriteria games
Tichá, Michaela ; Dlouhý, Martin (advisor) ; Lachout, Petr (referee) ; Čičková, Zuzana (referee)
Theory of multicriteria games is a special field of game theory, when one or more players have at least two payoff functions and want to maximize simultaneously. The work introduces a number of new findings. It examined the concept of finding equilibria in pure strategies in noncooperative multicriteria game. It is possible to find all the equilibria in pure strategies by full search and solving two linear programs for each point. Furthermore, two linear programs are formulated for verifying that a selected point is the equilibrium of the game or not. In the noncooperative games is also introduced the concept that with knowledge of the equilibrium of bimatrix game determines preferences of the players. Although finding the equilibrium point of the bimatrix game is nonlinear problem, finding the preferences is linear problem. The latest findings in the noncooperative games is a generalization of the concept that solves multicriteria game by assigning weights to each criterion of each player. The work demonstrates that it may not be necessarily linear weights, but it can be more general function that describes the player's preference. The remaining part is devoted to knowledge in cooperative games. There is considered that the players know their preferences and are able to express them by weights. The game with known preferences is defined and solved with the use of bargaining theory. Then it is generalized to a case where players have more payoff functions, from which they can choose. Finally, the multicriteria case of voting game is defined. It is designed completely new concept, which selects the winning coalition in the voting game. This concept is then applied to the real situation after the elections to the Chamber of Deputies in 2013.
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