Enhancing cooperation in non-linear systems in game theory / Tey Siew Kian - Tey, Siew Kian (2017)
Game theory is a branch of mathematics involving the study of cooperation and conflicts in the society. Given the importance of cooperation in the fight for common goods, the emergence of cooperation amongst selfish individuals is a fundamental and important issue in the economics and behavioural sciences. The aim of this thesis is to further our understanding of the roles of various factors such as incentives and network on the enhancement of cooperation in different economic models involving non-linear systems. In particular, two models, one involving social dilemma with N-players and the other involving economic behaviours with two players are studied. These two models are used to develop a third model which retains the main features of the second model, but modified to include N-players with an evolutionary trait as in the first model. This is to give some insights on the effects of the various features in the first model on the frequency of cooperation and magnitude of incentives, i.e. technological leapfrogging in the second model. Punishing strategy, which can be regarded as a form of direct or indirect reciprocity, is another important mechanism in promoting cooperation. In a recent model of N-player Snowdrift game with evolutionary trait incorporating a costly punishing strategy, the role of punishment and the effects of a structured population connected through a square lattice in promoting cooperation are investigated. One of the main challenges in the studies of evolutionary games is bridging the gap between theoretical and empirical research. Different problems have been studied in the hope of applying the findings to implement game theory to a practical scenario where the market is dominated by only a few players. Therefore, the role of punishment is studied in a Cournot duopoly. In the industry, the role of the punisher in Snowdrift game can be taken up by the patent system as the latter punishes the free-riders by giving intellectual property rights to the innovators (cooperators), thereby causing technological lagging in the free-riders (defectors). Therefore, punishment in this case is given in the form of incentive-denial. The effect of patenting on cooperation and defection is thus studied in a long-term research and development (R&D) Cournot duopoly differential game, as well as to determine the sustainability of R&D incentives in an environment where technological innovation is almost a public good. Finally, the R&D Cournot duopoly differential game model is simplified to an extent which allows the study of the model in an evolutionary well-mixed N-player setting to identify precisely the factors directly affecting the firms’ investment rate and technological leapfrogging. With the introduction of an evolutionary feature to the simplified R&D Cournot duopoly model, the latter allows the study of the effect of an N-player evolutionary game on the various factors in the original R&D Cournot duopoly model. The R&D Cournot duopoly model is modified with the view that it can be readily generalized to incorporate other interesting and practical features such as real-life networking effects not present in the original Cournot duopoly game.