Citizens’ motivation and benefits distribution in co-production of public services. A cooperative game theory approach

Miklós Rosta, Anna Radványi

Our study is focusing on the coproduction between public service providers and groups of the service users that can be represented by civil organizations. We try to suggest a methodology to solve the problem of distributing the benefits of coproduction and also give a well-grounded answer to the following question: by what amount should the state motivate the citizens in order to have them actively participate in the production of public services? Our results are valid for all kind of cooperation forms which is defined by Pestoff – Osborne – Brandsen (2006) and Verschuere – Brandsen – Pestoff (2012) like co-governance, co-management, co-production, co-construction, co-policy making or co-evaluation.

The applied methodology is the cooperative game theory which is a very young discipline, the first publications date back to the 1930s, since then cooperative game theory has become increasingly important and popular. The winners of the Nobel Memorial Prize in Economic Science inthe year 2012 were two scientists (Alvin E. Roth and Lloyd S. Shapley) whose research area is game theory; specifically Shapley’s is cooperative game theory.

Cooperative game theory provides tools for modeling situations where several participants can cooperate. The participants (‘players’) can form groups, so called ‘coalitions’ and these coalitions might reach more benefit than if the players would act individually. The coalitions can be perceived as agreements with contracts, i.e. if a member of a coalition violates the contract, he would get a penalty so it is not worth for him to exit the coalition.Besides modeling the coalition formation, one of the most important questions of cooperative game theory is how to divide the common reached benefit of a coalition among the players. The Shapley value is one of the most famous solution concepts, which gives a ‘fair’ allocation of the value of the grand coalition.

We try to demonstrate the usefulness of our methodology by using an example from Hungary where the above method is validly used to represent the situation of the overnight public transport in Budapest. A Hungarian civil organization called VEKE (Urban and Suburban Transit Association)has developed and completed the optimization of the night routes and it made this available free of charge to the BKV (Budapest Transport Company). We would like to quantify the common reached benefits with and without the assistance of this non-profit organization. Probably this operationalization is the most difficult and complex part of our research. We have conducted several interviews with members of the non-profit organization (‘VEKE’) to determine how to measure their success. Additionally, we have received relevant data from the Centre for Budapest Transport (BKK) which is supervise the public transport in Budapest. These data help us to make the benefit of BKV and the population of Budapest measurable.

In the presented situation we have two coalitions with a non-zero value:the coalition consisting of BKV and the population; and the coalition consisting of BKV, the population,and VEKE. In order to be able to use the methods and solutions of the cooperative game theory we need to express the valueeach coalition with only one number. This number should express the measured benefit more precisely. Of course, this is a difficult question. In our talk we would like to present the statistical methods we used to generate indexes that represent the appropriate benefits. The indexes express the social welfares of the different situations before and after the introduction of the overnight public transport. We will also talk about the difficulties of the modeling.

With the generated indexes we could define the values of the coalitions and therefore we could calculate the Shapley value of each participant. Thereby we give a solution for the allocation of social welfare among the actors of the society. This result demonstrates the impact of a non-profit organization on a society. We can also analyze how profitable it can be for the state to support a non-profit organization if they keep the increase of social welfare in mind.