Many-to-many allocations in systems of self-interested agents: Some dominant strategy solutions
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In a multi-agent system where each agent acts in its respective self-interest, the problem of many-to-many allocations is explored. The question for the regulator making the allocations is: what should be the allocation protocol when there are many resource provider agents and many resource seeker agents? A regulator, given that it cannot force an agent to choose a specific strategy, must design a protocol that supports its agenda. Motivated by the needs in the emerging electricity networks, this thesis considers the problem under incomplete information, i.e., when the type, the abstraction of an agent's particulars which influence the agent's strategy choice, of any specific agent is not known. Two kinds of allocation models are developed, namely, (i) one based on bilateral agreements, and (ii) one based on use of incentives to influence the strategy choices. The models are presented in the electricity distribution contexts. With a nominal role for the regulator, the thesis explored a multi-cycle model and a single-cycle model in which the allocations result from a series of bilateral bargaining encounters. The possibility of multiple equilibria in these models implies an unpredictable outcome, as the agents are uncertain of the specific equilibrium selection. This motivates the pursuit of a dominant strategy solution. Providing a stronger role for the regulator, the conditions for dominant strategy solution are identified in a single-cycle model. In this bilateral encounter and bargaining model, influencing a set of resource providers to pursue a specific strategy results in dominant strategy equilibrium. Given the parameters of the model, each agent can determine its respective dominant strategy by using the commonly known probability distribution of agents' types. Relaxing the requirement that the agents know the probability distribution of agents' types, the model of a regulator empowered to provide incentives to influence agents' strategy choices is adopted. A many-to-many allocation procedure is composed using two one-to-many allocation mechanisms. The conditions under which a system of incentives leads to a dominant strategy solution, are identified.