Journées de l'optimisation 2007 Optimizations days

This presentation deals with a class of stochastic control systems with one or many agents. One will follow different developments linking the theory of infinite horizon control, the theory of Markov decision processes, the theory of Markov games and the theory of singularly perturbed control systems. One will see how this formalism permits a new approach to a class of socioeconomic models.

In a previous paper, bimatrix games were expressed as parametric linear mixed $0-1$ programs and the E$\chi$MIP algorithm was proposed to enumerate all their extreme Nash equilibria. We propose new perfect and proper refinement approaches for the set of all extreme Nash equilibria.

In a number of industries, certain suppliers essentially detain a monopoly control on the production technology of key components (e.g., airplane industry, aerospace industry, car industry, computer industry, etc). It then becomes inevitable that the manufacturers in these industries have common suppliers. In their collaboration with suppliers, the manufacturers notably engage in improving the quality of their existing products. Since the manufacturers are competitors, neither would like to see its effort in quality improvement being taken advantage of by the other. However due to the inevitable fact that the two firms share a common supplier who is cooperating with both firms, it seems rather difficult, if not impossible to keep the fruit of such input strictly separate. In this paper, a non-cooperative dynamic game is formulated in which a single supplier collaborates with two competing manufacturers in improving the quality of their respective products. Assuming a finite planning horizon, the paper notably analyzes how each party allocates resources for quality improvement.

This paper proposes an analytical framework for resource allocation between social relationship and transactional marketing efforts for a firm that aims at maximizing customer lifetime value (CLV) in the context of a single relational exchange allowing different levels of opportunism and trust between partners. Several issues including, the relationship between the buyer’s commitment and CLV, the evolution of CLV over time, the influence of mutual trust on marketing policies, customer acquisition and retention costs, are investigated. Some of our main findings follow. The absence of mutual trust between partners leads to commitment-independent social relationship and transactional marketing policies; while when mutual trust dominates propensities to opportunism and the seller discounts gently future cash flows; it is optimal to implement commitment-dependent policies. Contrary to the basic principles of relationship marketing, we found that committed customers as well as longer relationships do not always generate better cash flows, especially when buyers look for superior current value proposition in each purchase opportunity. Also customer acquisition and retention costs are identical in the absence of mutual trust. Maintaining current customers is cheaper than acquiring new ones only if mutual trust overcomes propensities to opportunism and the seller is farsighted.