Topics In Demand management

Abstract

This thesis is divided into two parts. Part I deals with demand management. For goods with no substitutes, under supply constraints, fairness considerations introduce negative externalities and lead to a market failure. One example of such a good with no substitutes is water. In case of a market failure, it is necessary to design coordination mechanisms called contracts which provide the right incentives for coordination. As “repetition can yield coordination”, the aim in this part is to design price based dynamic demand management contracts which, under supply constraints, mitigate the market failure. In these contracts, we consider complete information settings; and use the status quo proposition as a fairness criterion for designing them. The contracts are designed as almost noncooperative dynamic games, within the agency theory framework, where the agent (the consumer) is induced to consume at a specified consumption level based on the incentive mechanism offered by the principal (the producer). These contracts use the solution concept of sub-game perfect Nash equilibrium (SPNE) to compute the price (mal-incentive) that acts as a credible threat for deviation from the specified consumption level. In these contracts, unlike the dynamic contracts with asymmetric information, the penalty for deviation is proportional to the amount of deviation. First, we consider a two-period demand management contract for a single consumer satisfying the status quo proposition. Under the assumption that the gain to the consumer and the loss to the producer by deviation is small, the contract is shown to be economically efficient. It is shown that, in the finite horizon, a fair demand management contract cannot be efficient. The demand management contract is homeomorphic to finite horizon alternating bargaining model. In the finite horizon alternating bargaining model, there is a unique SPNE, in which the player who offers last is always at an advantageous position. In the two-period contract, the assumption considered attenuates the last mover advantage and leads to the efficiency. We have shown that one possible way to achieve efficiency, without the assumption, is to make the agents uncertain about the period of interaction. This possibility can be included in an infinite horizon contract. Hence, next, we design an infinite horizon contract for a single consumer. It is proved that this contract is economically efficient and provides revenue sufficiency. The sensitivity analysis of the contract shows that the discounting rate measures the aversion to conservation characteristics of the consumer. The analysis of the contract shows that a sufficiently time-patient consumer is not penalized for the deviation, as the consumer himself is aware of conservation requirements. This result is similar to the results for the present-biased preferences in behavioral economics. Lastly, the infinite horizon contract is extended to two consumers case which internalizes the externality a consumer causes to another. In the two consumer case, consumers are strategically noninteracting; and it is shown that the producer acts as a budget balancer. These contracts are also shown to be economically efficient. The demand management contracts achieve both the procedural and end-state fairness. Also, the infinite horizon contracts are homeomorphic to infinite horizon alternating bargaining model. The efficiency of infinite horizon contracts is due to their homeomorphism with the alternating bargaining process as they exhaust all possible mutual gains from exchange. In the two-period model, the bargaining process is constrained and hence all possible mutual gains are not eliminated, leading to the inefficiency. In part II of the thesis, we discuss the notions of exchangeability in the Shapley value. The Shapley value is a probabilistic value for the transferable utility (TU) cooperative games, in which each player subjectively assigns probabilities to the events which define their positions in the game. In this part, the objective have been to explore the aspect of subjective probability which leads to the uniqueness of the Shapley value. This aspect of subjective probability is known as exchangeability. We derive the Shapley value using de Finetti’s theorem. We also show that, in the Shapley value, each player’s prospects of joining a t-player game as the last member of the game is a moment sequence of the uniquely determined uniform distribution. We stress on finite exchangeability; and deduce that, with finite exchangeability, the Shapley value is the only value in which the probability assignment is a unique mixture of independent and identical distributions. It is concluded that, in both the finite and infinite exchangeable cases, the uniqueness of probability assignment in the Shapley value is due to exchangeability and the mixing with the uniform distribution.