Agrifood Campaign Planning

The challenge was to find ways for the players in an agricultural food supply chain to interact in ways that enable the chain to operate more efficiently. What information do they need to exchange, and what incentives need to be in place between them? What software would help the information exchange and responsive actions to take place? The problem was thought about with the UK sugar beet industry as the working example, but similar considerations, with many differences of detail, are expected to apply in other contexts

Games in Energy Markets

We study energy markets in game theoretic framework. The energy markets consist of two types of energy producers: exhaustible producer and renewable producer. An exhaustible producer produces energy with exhaustible resources, such as oil. The resource reserves of each exhaustible producer diminish due to production, and also get replenished with costly effort to explore for new resources. This exploration activity is modeled through a controlled point process that leads to stochastic increments to reserves level. A renewable producer uses renewable resources, such as solar power, to produce energy. The renewable resources are infinite, but costly in production. Each producer chooses optimal controls of production quantity and exploration effort (exhaustible producers only), in order to maximize individual profit that equals his quantity of production multiplied by market price, minus costs of production and exploration. The producers interact with each other through the energy price that is a function of aggregate production, as one's profit does not only depend on his own production quantity, but also depends on the total quantity of all other producers. We aim to study the equilibrium total production and price. In Chapter 2 we study the game between an exhaustible producer and a renewable producer under stochastic demand that switches between different regimes. We study how the regime changes and the relative cost of production, which is a proxy for market competitiveness, affect game equilibria, and compare with the case of deterministic demand. A novel feature driven by stochasticity of demand is that production may shut down during low demand to conserve reserves. In Chapter 3 we study game with a continuum of homogeneous exhaustible producers. Mean field game approach is employed to solve for an approximate Markov Nash equilibrium of the game. We develop numerical schemes to solve the resulting system of partial differential equations: a backward Hamilton-Jacobi-Bellman (HJB) equation for the game value function of a representative producer and a forward transport equation for the distribution of the reserves levels among all producers.In Chapter 4 we study a time-stationary mean field game model, in which the reserves level remains invariant due to the counteracting effects of production and exploration. We also study the impact of uncertainty in the regime that the exploration process becomes asymptotically deterministic, so that discovery of new resources happens at high frequency with small amount of each discovery

Stochastic Analysis in Finance and Insurance

This workshop brought together leading experts and a large number of younger researchers in stochastic analysis and mathematical finance from all over the world. During a highly intense week, participants exchanged during talks and discussions many ideas and laid foundations for new collaborations and further developments in the field

Empirical Framework for Cournot Oligopoly with Private Information

We propose an empirical framework for asymmetric Cournot oligopoly with private information about variable costs. First, considering a linear demand for a homogenous product with a random intercept, we characterize the Bayesian Cournot-Nash equilibrium. Then we establish the identification of the joint distribution of demand and firm-specific cost distributions. Following the identification steps, we propose a likelihood-based estimation method and apply it to the global market for crude-oil and quantify the welfare effect of private information. We also consider extensions of the model to include either product differentiation, conduct parameters, nonlinear demand, or selective entry.Comment: forthcoming, The RAND Journal of Economic

The War of Rare Earth Elements: A Dynamic Game Approach

Rare earth elements govern today’s high-tech world and are deemed to be essential for the attainment of sustainable development goals. Since the 1990s, these elements have been predominantly supplied by one single actor, China. However, due to the increasing global relevance of their availability, other countries are now encouraged to enter the market. The objective of this paper is to analyze the strategic interactions among (potential) suppliers. In particular, we are interested in (1) the optimal timing for a newcomer (e.g. the U.S.) to enter the market, (2) the incumbent’s (i.e. China’s) optimal behavior, and (3) the cost-efficiency of cooperative vs. competitive market relations. By setting up a continuous-time dynamic game model, we show that (1) the newcomer should postpone the production launch until its rare earth reserves coincide with those of the incumbent, (2) the incumbent should strive for a late market entry and therefore keep its monopolistic resource extraction at the lowest possible level, (3) compared to the payoffs under competition, cooperation leads to a Pareto improvement when started at an early stage. The findings of our model are particularly relevant for the rational strategic positioning of the two great powers, America and China