This dissertation combines four studies which investigate the strategic behavior in games. The first two studies are based on experiments and develop theories of bounded rationality in order to explain the observed behavior. This behavior violates the minimal conditions of game-theoretic rationality, i.e., that equilibrium strategies must be chosen. Instead, real behavior is driven by heuristics like fairness standards and rules of thumb. Game-theoretic rationality is too strong or it is simply inadequate to explain the behavior. The two other studies are concerned with equilibrium selection. For this purpose, game-theoretic rationality is too weak to be able to single out a unique equilibrium as the rational solution of a game. A theory of unbounded rationality is applied to determine the solutions of specific games. The first study (Selten, Mitzkewitz & Uhlich, 1997) is concerned with a finite repetition of a Cournot duopoly. Experienced subjects program strategies for this game and computer tournaments among these programs were performed. The typical structure of these programmed strategies reveals that no expectations are formed and nothing is optimized. Instead, fairness criteria are used to determine cooperative goals which are supported by a policy of fairness and firmness. Measure-for-measure strategies respond to opponent’s movements towards and away from the cooperative goal by similar movements. Strategies tend to be more successful in the tournaments the more typical they are. In the second study (Mitzkewitz & Nagel, 1993) experiments on two versions of ultimatum games with incomplete information are reported and analyzed. As in the study above, subjects must determine complete strategies for the game. Game theory predicts very similar outcomes for both versions of the game, but the experimental results show significant differences. A theory of boundedly rational theory based on expectation fairness is proposed which is well supported by the experimental data. The third study (Mitzkewitz, 2017) analyzes a class of simple signaling games. The Harsanyi-Selten theory of equilibrium selection in games is applied and for each generic game of this class a unique equilibrium is singled out as its rational solution. The results can be used as building stones for the analysis of much more complicated signaling games. The study also contains a brief introduction to the Harsanyi-Selten theory. The last study (Potters, van Winden & Mitzkewitz, 1991) is an application of game theory to political science. A pressure group tries to influence the behavior of the government by threatening or carrying out punishments. A two-period model shows a multiplicity of equilibria. However, most of them seem to be implausible. The Kohlberg-Mertens refinement concept of stable equlibria is used to reduce this multiplicity. The Harsanyi-Selten theory of equilibrium selection for this model is also calculated. It turns out that for a fairly large set of parameter values both solution concepts coincide and show that punishment is executed even if the government makes in advance concessions to the pressure group.