Learning Stackelberg-Nash Equilibria in Games with Incomplete Information for Public Policy Design: Applications to Forest Insurance under Multiple Risks

Context and challenges

Insurance is an important tool for managing and providing cover against multiple risks and their consequences in the context of climate change. This tool exists in the forestry sector because private forests are considered to be insurable assets against climate-related risks such as storms and wildfires, the two main risks today. However, in France, the forest insurance market is characterized by low demand and limited supply. This situation raises many questions about the reasons for the low use of insurance, how the current insurance system should be adapted to address these multiple risks, and the potential role of public authorities. Furthermore, very little data is currently available to properly analyze this market, which makes modeling critically important.

Goals

The aim of this thesis is to provide a multi-actor model based on game theory and reinforcement learning, which will serve as a tool for identifying and analyzing the strategies of private and public decision-makers in a context of multiple risks, in order to propose recommendations to the relevant parties (including public authorities). The model is a leader-follower game in which the public decision-maker (leader) implements public policies that influence the behavior of private actors (followers). A key research challenge is the calculation of Stackelberg-Nash equilibria in a context where the parameters of other actors (such as the risk aversion of forest owners or the fixed costs of insurers) are partially unknown.

This subject deals with the calculation of equilibria in single-leader, multiple-follower games with incomplete information. The example of forest insurance lends itself to a family of games that model the strategic interactions among forest owners, insurers, and the State. Forest owners, motivated by short-term objectives, interact with strategic insurers who, in turn, are influenced by public policies proposed by the State. This framework allows for the analysis of insurance incentive mechanisms in a context of multiple risks and uncertainty.

The methodological research question (in algorithmic game theory) of this thesis lies in the proposal of novel algorithms for computing Stackelberg-Nash equilibria. Since players do not necessarily have any knowledge of the parameters of other players, this thesis will be placed within the context of “games with incomplete information” [Harsanyi, 1968] and within a sequential decision-making framework, in which the players can adapt their strategies (by adapting contract proposals to those of other insurers, adjusting State incentives in response to the observed proportion of insured foresters, etc.). This makes the problem of defining incentives more complex. Within this framework, a dynamic model will be proposed for which multi-agent reinforcement learning algorithms can be implemented.

INRAE structure