Influence of Supply Chain Network Topology on the Evolution of Firm Strategies

Abstract

This study investigates the influence of the topological structure of a supply chain network (SCN) on the evolution of cooperative and defective strategies adopted by the individual firms. First, a range of topologies representative of SCNs was generated using a fitness-based network growth model, which enabled cross comparisons by parameterising the network topologies with the power law exponent of their respective degree distributions. Then, the inter-firm links in each SCN were considered as repeated strategic interactions and were modelled by the Prisoner’s Dilemma game to represent the self-interested nature of the individual firms. This model is considered an agent-based model, where the agents are bound to their local neighbourhood by the network topology. A novel strategy update rule was then introduced to mimic the behaviour of firms. In particular, the heterogeneously distributed nature of the firm rationality was considered when they update their strategies at the end of each game round. Additionally, the payoff comparison against the neighbours was modelled to be strategy specific as opposed to accumulated payoff comparison analysis adopted in past work. It was found that the SCN topology, the level of rationality of firms and the relative strategy payoff differences are all essential elements in the evolution of cooperation. In summary, a tipping point was found in terms of the power law exponent of the SCN degree distribution, for achieving the highest number of co- operators. When the connection distribution of an SCN is highly unbalanced (such as in hub and spoke topologies) or well balanced (such as in random topologies), more difficult it is to achieve higher levels of co-operation among the firms. It was concluded that the scale-free topologies provide the best balance of hubs firms and lesser connected firms. Therefore, scale-free topologies are capable of achieving the highest proportion of co- operators in the firm population compared to other network topologies.