Berlin 2015 – scientific programme
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BP: Fachverband Biologische Physik
BP 32: Evolutionary Game Theory II (joint SOE/BP/DY)
BP 32.6: Talk
Tuesday, March 17, 2015, 15:15–15:30, MA 001
A Two-Player Game with Linear State-Dependent Payoff Function — •Tim Herrmann1, Mark Kirstein2, and Katharina Fischer3 — 1TU Dresden — 2TU Dresden, Chair of Managerial Economics — 3TU Dresden, Institut für mathematische Stochastik
In classic game theory all elements of a game (set of players, set of strategies, payoff function) are static. In contrary, real-world strategic interactions are often characterized by changes of at least one of the three elements of a game over time. In our model a game with state-dependent payoff functions is analysed. The payoff function of the (n+1)-st round depends linearly on the payoff of the n-th round. Thereby the structure of the game can change, e.g. from prisoner’s dilemma structure to a structure, where individual rationality coincides with collective rationality. Therefore, the concepts of short-term and long-term rationality are defined. It is shown for our game with a state-dependent payoff function, that the following criteria of long-term rationality are equivalent (besides a few special cases): Pareto optimality, collective rationality and the Nash equilibrium in recursive dominant strategies. For symmetric payoff functions these three criteria of (individual and collective) long-term rationality are additionally equivalent to the collective short-term rationality. The concept of ESS is refined to absolute ESS (ESSA) and relative ESS (ESSR). It is shown that ESSA-tuples are equivalent to the above mentioned criteria for symmetric payoff functions and long-term rationality.