Biblio

We consider a mechanism design problem for strategic agents with multi-dimensional private information and uncertainty in their utility/cost functions. We show that the optimal mechanism is a menu of contracts that can be implemented as a nonlinear pricing scheme. We illustrate the result by considering an optimal energy procurement mechanism from a strategic seller with conventional (deterministic) and renewable (random) plants. We address the problem of risk-sharing and ex post voluntary participation (commitment) under uncertainty.

An analytical approach for a dynamic cyber-security problem that captures progressive attacks to a computer network is presented. We formulate the dynamic security problem from the defender’s point of view as a supervisory control problem with imperfect information, modeling the computer network’s operation by a discrete event system. We consider a min-max performance criterion and use dynamic programming to determine, within a restricted set of policies, an optimal policy for the defender. We study and interpret the behavior of this optimal policy as we vary certain parameters of the supervisory control problem.

In the restructured electricity industry, electricity pooling markets are an oligopoly with strategic producers possessing private information (private production cost function). We focus on pooling markets where aggregate demand is represented by a non-strategic agent. We consider demand to be elastic. We propose a market mechanism that has the following features. (F1) It is individually rational. (F2) It is budget balanced. (F3) It is price efficient, that is, at equilibrium the price of electricity is equal to the marginal cost of production. (F4) The energy production profile corresponding to every nonzero Nash equilibrium of the game induced by the mechanism is a solution of the corresponding centralized problem where the objective is the maximization of the sum of the producers' and consumers' utilities. We identify some open problems associated with our approach to electricity pooling markets.

The defense of computer networks from intruders is becoming a problem of great importance as networks and devices become increasingly connected. We develop an automated approach to defending a network against continuous attacks from intruders, using the notion of Bayesian attack graphs to describe how attackers combine and exploit system vulnerabilities in order to gain access and progress through a network. We assume that the attacker follows a probabilistic spreading process on the attack graph and that the defender can only partially observe the attacker’s capabilities at any given time. This leads to the formulation of the defender’s problem as a partially observable Markov decision process (POMDP). We define and compute optimal defender countermeasure policies, which describe the optimal countermeaSure action to deploy given the current information.

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We analyze a dynamic oligopoly model with strategic sellers and buyers/consumers over a finite horizon. Each seller has private information described by a finite-state Markov process; the Markov processes describing the sellers' information are mutually independent. At the beginning of each time/stage t the sellers simultaneously post the prices for their good; subsequently, consumers make their buying decisions; finally, after the buyers' decisions are made, a public signal, indicating the buyers' consumption experience from each seller's good becomes available and the whole process moves to stage t + 1. The sellers' prices, the buyers' decisions and the signal indicating the buyers' consumption experience are common knowledge among buyers and sellers. This dynamic oligopoly model arises in online shopping and dynamic spectrum sharing markets. The model gives rise to a stochastic dynamic game with asymmetric information. Using ideas from the common information approach, we prove the existence of common information based equilibria. We obtain a sequential decomposition of the game and we provide a backward induction algorithm to determine common information-based equilibria that are perfect Bayesian equilibria. We illustrate our results with an example.

We formulate and analyze a general class of stochastic dynamic games with asymmetric information arising in dynamic systems. In such games, multiple strategic agents control the system dynamics and have different information about the system over time. Because of the presence of asymmetric information, each agent needs to form beliefs about other agents’ private information. Therefore, the specification of the agents’ beliefs along with their strategies is necessary to study the dynamic game. We use Perfect Bayesian equilibrium (PBE) as our solution concept. A PBE consists of a pair of strategy profile and belief system. In a PBE, every agent’s strategy should be a best response under the belief system, and the belief system depends on agents’ strategy profile when there is signaling among agents. Therefore, the circular dependence between strategy profile and belief system makes it difficult to compute PBE. Using the common information among agents, we introduce a subclass of PBE called common information based perfect Bayesian equilibria (CIB-PBE), and provide a sequential decomposition of the dynamic game. Such decomposition leads to a backward induction algorithm to compute CIB-PBE. We illustrate the sequential decomposition with an example of a multiple access broadcast game. We prove the existence of CIBPBE for a subclass of dynamic games.

We consider mechanism design problems for strategic agents with multi-dimensional private information and uncertainty in their utility/cost function. We show that the optimal mechanism with firm allocation can be implemented as a nonlinear pricing scheme, and the optimal mechanism with random allocation can be implemented as a menu of nonlinear pricing schemes.We provide two examples to demonstrate the results: an optimal energy procurement mechanism from a strategic seller with renewable (random) generation, and the design of an optimal demand response program for a network of heterogeneous loads.

With the increased level of distributed generation and demand response comes the need for associated mechanisms that can perform well in the face of increasingly complex deregulated energy market structures. Using Lagrangian duality theory, we develop a decentralized market mechanism that ensures that, under the guidance of a market operator, self-interested market participants: generation companies (GenCos), distribution companies (DistCos), and transmission companies (TransCos), reach a competitive equilibrium. We show that even in the presence of informational asymmetries and nonlinearities (such as power losses and transmission constraints), the resulting competitive equilibrium is Pareto efficient.

In the restructured electricity industry, Generation Expansion Planning (GEP) is an oligopoly of strategic Generation Companies (GenCos) with private information investing in a highly uncertain environment. Strategic planning and uncertainties can result in market manipulation and underinvestment (short-term planning). We present a forward moving approach to the problem of investment expansion planning in the restructured electricity industry. This approach accounts for technological, political and environmental uncertainties in the problem's environment and leads to long-term planning. At each step of the approach we present a block investment market mechanism that has the following features. (F1) It is individually rational. (F2) It is budget balanced. (F3) The expansion and production allocations corresponding to the unique Nash Equilibrium (NE) of the game induced by the mechanism are the same as those that maximize the sum of utilities of the producers and the demand. (F4) It is price efficient that is, the price for electricity at equilibrium is equal to the marginal utility of the demand and to the marginal cost of production by producers with free capacity.

We formulate and analyze dynamic games with d-step (d ≥ 1) delayed sharing information structure. The resulting game is a dynamic game of asymmetric information with hidden actions, imperfect observations, and controlled and interdependent system dynamics. We adopt common in- formation based perfect Bayesian equilibrium (CIB-PBE) as the solution concept, and provide a sequential decomposition of the dynamic game. Such a decomposition leads to a backward induction algorithm to compute CIB-PBEs. We discuss the features of our approach to the above class of games and address the existence of CIB-PBEs.

In the restructured electricity industry, Generation Expansion Planning (GEP) is an oligopoly of strategic Generation Companies (GenCos) with private information investing in a highly uncertain environment. Strategic planning and uncertainties can result in market manipulation and underinvestment (short-term planning). We present a forward moving approach to the problem of investment expansion planning in the restructured electricity industry. This approach accounts for technological, political and environmental uncertainties in the problem’s environment and leads to long-term planning. At each step of the approach we present a block investment market mechanism that has the following features. (F1) It is individually rational. (F2) It is budget balanced. (F3) The expansion and production allocations corresponding to the unique Nash Equilibrium (NE) of the game induced by the mechanism are the same as those that maximize the sum of utilities of the producers and the demand. (F4) It is price efficient that is, the price for electricity at equilibrium is equal to the marginal utility of the demand and to the marginal cost of production by producers with free capacity.