Creativity, Unawareness, and Cooperation in Game TheoryPublic Deposited
Game Theory is the branch of applied mathematics that studies the strategic interaction among intelligent agents. So far, standard Game Theory literature has interpreted "intelligent agents" exclusively as "rational agents". This work points out that this interpretation is an important limitation since intelligence consists of more abilities, some of which may play an important role in strategic interactions. In particular, it introduces the concept of creativity (an agent's capacity of finding viable modifications he was previously unaware of to a given game) and emphasizes its relevance in Game Theoretic settings. In order to properly model the introduction of new ideas that some players may be unaware of we can not use a standard formalization where the structure of the game is assumed to be common knowledge among the players. Therefore, the first chapter of this dissertation is devoted to develop a formalization for extensive-form games where players might be unaware of relevant facts of the game. This formalization generalizes the standard one allowing players to have different subjective perceptions of the game at different points. Besides of providing a proper definition of creativity in strategic settings, the second chapter also presents a bluffing creative method that exploits an asymmetric awareness effect to easily modify the outcome of a given game in the desired direction by using creativity. It is shown that this method can be employed to sustain cooperation in the Finitely Repeated Prisoners' Dilemma. The third chapter does not deal with creativity or unawareness but departs from the implicit assumption used by the repeated games literature that the probability of repeating the stage game is completely exogenous. It is shown that when this assumption is not satisfied payoff vectors below the minmax might be possible to sustain whereas others above it might not. Moreover, examples and applications are provided where erroneously making this assumption can lead to completely wrong predictions. Furthermore, a new force able to generate cooperative behavior is identified. This force is the fear or desire that the game stops being repeated and, since it does not rely on punishments, it does not require monitoring to operate.