Mathematik | Informatik
Adrian Hossner, 2008 | Hilterfingen, BE
The present thesis addresses the politically and socially relevant question of how to best counteract erratic behaviour—as is evident in the case of Donald J. Trump. To this end, game theory is used, especially the Prisoner’s Dilemma game. It is implemented in an iterated, continuous and parametrised version where two random strategies play against each other, a rigid and two adaptive strategies. The results are presented in form of absolute-, relative- and overall-gain plots, which are discussed in depth. The summarising recommendation is to avoid escalation and to gently push erratically behaving opponents into the direction of acting rationally.
Introduction
The 47th President of the USA, Donald J. Trump, has put the world upside down. For instance, his tariff policies seem very chaotic, so the question arises—for Swiss politicians for example—how to encounter such erratic behaviour. This question can be tackled from a game-theoretical perspective, thereby considering erratic behaviour as a random strategy in the so-called Prisoner’s Dilemma (PD) game. Consequently, the aim of this thesis is to determine a well-performing strategy against randomly acting players and thus to lay a basis for more elaborate implementations.
Methods
In the PD, two players either cooperate or defect as a so-called investment. While mutual cooperation is more rewarded than mutual defection, the best outcome for each player is to defect if the opponent cooperates. In the simulation, the iterated continuous PD (ICPD) was implemented, meaning that continuous investment values rather than discrete cooperation or defection options were allowed and the encounter was executed 20 times consecutively. In addition, 100 repetitions per game were conducted to avoid accidental peaks in the data. On this basis, two random strategies (discrete and continuous) were used that played against each other, a non-adaptive, rigid strategy and two adaptive strategies (discrete and continuous). The investment calculation depended on a strategy-specific parameter ranging from 0 to 10 inclusively. For instance, the discrete random strategy’s parameter was proportional to the probability of cooperation (from always cooperating to always defecting), whereas the discrete adaptive strategy adapted to the opponent’s last investment according to its parameter (from not adapting via “tit for tat» to “double tit for tat»). The entire simulation was self-written and programmed in Python.
Results
The generated data was plotted in form of surfaces where the x- and y-axis indicate the parameter values of the corresponding strategy and the z-axis display the points gained. For each ICPD, five surfaces were generated: two for absolute-gain (gained points of each player), two for relative-gain (point differences) and one for overall-gain (point summation). In the thesis, peculiarities of the resulting (2 * 5 * 5 =) 50 surfaces were discussed and further explored regarding shallow randomness, dispersion and risk, threshold values for discrete adaptions, dynamics of continuous adaptation and gains against random strategies.
Discussion
The most interesting findings refer to the encounter of the discrete random and the discrete adaptive strategy. First, since small adaptations carry the risk of being completely exploited, one must strike back with sufficient force. Second, exaggerated adaption is not worthwhile as the “double tit for tat” behaviour does not perform better in terms of gaining points than “tit of tat”. Third, since the outcome of the game cannot be determined by the adaptive strategy (except for the already mentioned aspects), one must convince the randomly acting player to maximise their absolute gain. Fourth, with the value of the random strategy’s parameter, its relative gain increases proportionally while its overall gain decreases proportionally. From the perspective of the adaptive strategy, this again implies to persuade the random player to focus on their absolute gain—whereby the overall gain is maximised as well.
Conclusions
As a matter of course, the game-theoretical simulation comes with notable limitations regarding the applicability to the real world. However, one might claim that it creates a valuable basis for more elaborate work which should include parameter adaptations or even strategy adaptations in form of mixed strategies. On the base of the present simulation, one would nonetheless recommend avoiding escalation and gently pushing erratically behaving opponents into the direction of acting rationally—which might be relevant to Swiss politics when encountering problematic characters like Trump…
Würdigung durch den Experten
Berno Büchel
Die Welt steckt voller Interessenskonflikte; viele davon lassen sich mit Hilfe der Spieltheorie modellhaft abbilden. Gerade das Gefangenendilemma ist ein Paradebeispiel für die Divergenz von individuellen und kollektiven Interessen. In seiner Arbeit lässt Adrian Hossner unterschiedliche Strategien in einem wiederholten Gefangenendilemma gegeneinander antreten. Dieses Turnier der Strategien hat er eigenständig entwickelt, in Python programmiert, systematisch ausgewertet und anschaulich visualisiert. Auf dieser Grundlage diskutiert seine Arbeit den Umgang mit erratischem Verhalten.
Prädikat:
Bronze
Gymnasium Thun mit FMS
Lehrer: Dr. Geoffrey Ostrin