The invisible polluter: Can regulators save consumer surplus?

Consider an electricity market populated by competitive agents using thermal generating units. Such generation involves the emission of pollutants, on which a regulator might impose constraints. Transmission capacities for sending energy may naturally be restricted by the grid facilities. Both pollution standards and trans mission capacities can impose several constraints upon the joint strategy space of the agents. We propose a coupled constraints equilibrium as a solution to the regulator’s problem of avoiding both congestion and excessive pollution. Using the coupled constraints’ Lagrange multipliers as taxation coefficients the regulator can compel the agents to obey the multiple constraints. However, for this modification of the players’ payoffs to induce the required behaviour a coupled constraints equilibrium needs to exist and must also be unique. A three-node market example with a dc model of the transmission line constraints described in [8] and [2] possesses these properties. We extend it here to utilise a two-period load duration curve and, in result, obtain a two-period game. The implications of the game solutions obtained for several weights, which the regulator can use to vary the level of generators’ responsibilities for the constraints’ satisfaction, for consumer and producer surpluses will be discussed.

Can planners control competitive generators?

Consider an electricity market populated by competitive agents using thermal generating units. Generation often emits pollution which a planner may wish to constrain through regulation. Furthermore, generators’ ability to transmit energy may be naturally restricted by the grid’s facilities. The existence of both pollution standards and transmission constraints can impose several restrictions upon the joint strategy space of the agents. We propose a dynamic, game-theoretic model capable of analysing coupled constraints equilibria (also known as generalised Nash equilibria). Our equilibria arise as solutions to the planner’s problem of avoiding both network congestion and excessive pollution. The planner can use the coupled constraints’ Lagrange multipliers to compute the charges the players would pay if the constraints were violated. Once the players allow for the charges in their objective functions they will feel compelled to obey the constraints in equilibrium. However, a coupled constraints equilibrium needs to exist and be unique for this modification of the players’ objective functions ..[there was a “to” here, incorrect?].. induce the required behaviour. We extend the three-node dc model with transmission line constraints described in [10] and [2] to utilise a two-period load duration curve, and impose multi-period pollution constraints. We discuss the economic and environmental implications of the game’s solutions as we vary the planner’s preferences.

On Distributive Subalgebras of Qualitative Spatial and Temporal Calculi

Qualitative calculi play a central role in representing and reasoning about qualitative spatial and temporal knowledge. This paper studies distributive subalgebras of qualitative calculi, which are subalgebras in which (weak) composition distributives over nonempty intersections. It has been proven for RCC5 and RCC8 that path consistent constraint network over a distributive subalgebra is always minimal and globally consistent (in the sense of strong $n$-consistency) in a qualitative sense. The well-known subclass of convex interval relations provides one such an example of distributive subalgebras. This paper first gives a characterisation of distributive subalgebras, which states that the intersection of a set of $n\geq 3$ relations in the subalgebra is nonempty if and only if the intersection of every two of these relations is nonempty. We further compute and generate all maximal distributive subalgebras for Point Algebra, Interval Algebra, RCC5 and RCC8, Cardinal Relation Algebra, and Rectangle Algebra. Lastly, we establish two nice properties which will play an important role in efficient reasoning with constraint networks involving a large number of variables.Comment: Adding proof of Theorem 2 to appendi