Rationality of using phosphorus primary and secondary sources in circular economy: Game-theory-based analysis

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European Union (EU) faces serious disturbances in the supply of phosphorus. To tackle this problem, the Member States have started practicing the principles of circular economy in the management of phosphorus supply chain. A decision to select either primary or secondary sources of phosphorus is one of the major dilemmas in the application of these principles. In this paper, the Bayesian and Nash Equilibrium games are used to analyze the selection of primary or secondary sources of phosphorus in Europe (EU-27), under the condition of supply deficit. The objective of this analysis is to determine the conditions for the use of primary or secondary source. We examined situations of the so called low or high deficit. According to the principles of circular economy, the use of secondary sources is always preferred, and everyday practice shows that it is also rational, under conditions of low deficit. The rationality is justified by the sufficient time an enterprise has got to react. However, in the situation of high deficit, the lack of time makes the use of primary sources a rational decision. In short, rational decision means to opt for using secondary sources when deficit is low and primary sources when the deficit is high. The analysis of phosphorus supply over 15 years, 2002–2017, shows that only the Netherlands made a rational decision with the probability higher than 0.8. The analysis indicates that even if in the next 12 years recycling increases to 50 % of phosphorus supply, it will not improve the rationality of decisions on the use of secondary sources of phosphorus in Ireland, Portugal, Spain, Italy, Poland, Romania, Greece, Malta, and Cyprus. The main finding of this paper is the conclusion that the improvement of recycling technology will not improve the rationality of decisions on the use of secondary sources of phosphorus in several countries. It means that the problem is not the recycling technology itself but the policy pursued vis-à-vis using the primary or secondary sources.