Viswanadha Reddy Puduru

In this letter, we study a class of linear-quadratic mean-field-type difference games with coupled affine inequality constraints. We show that the mean-filed-type equilibrium can be characterized by the existence of a multiplier process which satisfies some implicit complementarity conditions. Further, we show that the equilibrium strategies can be computed by reformulating these conditions as a single large-scale linear complementarity problem. We illustrate our results with an energy storage problem arising in the management of microgrids.

In this paper, we study how an oligopolist influences the coalition structure in federated cloud markets. Specifically, we use cooperative game theory to model the circumstances under which a cloud provider prefers to join a cloud federation vis-a-vis consider taking a price offer made by an oligopolist.

We characterize open-loop and feedback Nash equilibria for a class of constrained linear–quadratic multistage games having the following features: (a) The control variables are of two types, namely, control variables that enter the dynamics, but are not constrained, and control variables that are part of state-control constraints, but do not enter the dynamics; (b) The parameter values are uncertain, with the stochastic process being described by a event tree. This paper takes stock on Reddy and Zaccour (2015, 2017) where the same class of games was considered, but in a deterministic setting. Here, we follow the same approaches and rewrite the results in these two papers in a stochastic setting.

In this paper, we propose a multi-cloud marketplace model for Infrastructure-as-a-Service (IaaS) layer with multiple cloud providers, intermediate brokers and end users. The brokers service end users subscribed to them by aggregating resources (virtual machines) from cloud providers while maximizing their profits. Similarly cloud providers (producers) allocate their supply of virtual machines to brokers (consumers) so as to maximize their profits. We define the notion of social welfare in this market structure and study two trading schemes. The first scheme involves centralized control which aims at maximizing social welfare but may contain unstable producer-consumer pairs who have an incentive to deviate from the current allocation. The second scheme eliminates such unstable pairs by using a generalization of stable matching algorithm but may lead to sub-optimal social welfare. The stable matching algorithm we proposed in this paper is a particular way of generalizing the original Gale-Shapley algorithm.

In this article, we study a target-attacker-defender (TAD) differential game involving one attacker, one target, and multiple defenders. We consider two variations where (a) the attacker and the target have unlimited observation range and the defenders are visibility constrained (b) only the attacker has unlimited observation range and the remaining players are visibility constrained. We model the players' interactions as a dynamic game with asymmetric information. Here, the visibility constraints of the players induce a visibility network, which encapsulates the visibility information during the evolution of the game. Based on this observation, we introduce network adapted feedback or implementable strategies for visibility constrained players. Using the inverse game theory approach, we obtain network adapted feedback Nash equilibrium strategies. We introduce a consistency criterion for selecting a subset (or refinement) of network adapted feedback Nash strategies, and provide an optimization-based approach for computing them. Finally, we illustrate our results with numerical experiments.

This letter is concerned with the distributed control of networked multi-agent systems (MAS) with linear time-invariant dynamics and quadratic performance measures. As the MAS is networked, the information available to agents is restricted, and as a result, the full-state feedback controllers are not implementable. Using game theoretic framework, we model the distributed control problem as a networked differential game. We develop the notion of network adapted guaranteed cost equilibrium (NAGCE). The NAGCE controllers are distributed and achieve a given upper bound on the individual cost of agents while retaining an equilibrium property. We provide linear matrix inequality (LMI) based conditions for the existence of these controllers, and also provide an algorithm for synthesizing them. Finally, the proposed design methods are illustrated using numerical examples.

A simple sufficient condition is proved for symmetric Markov subgame perfect Nash equilibria in public-good differential games with a single state variable. The condition admits equilibria in feedback strategies that have discontinuous dependence on the state variable. The application of the condition is demonstrated in the Dockner–Long model for international pollution control. The existence is shown of equilibria that are arbitrarily close to Pareto dominance for all initial conditions. In the limit as the discount rate tends to 0, the equilibrium strategies differ from the optimal strategies under full coordination, but nevertheless the agents’ payoffs do converge to those obtained from the coordinated (first-best) solution. For positive values of the discount rate, the supremal value function associated with the globally Pareto dominant equilibrium is a continuously differentiable function that is not a solution of the Hamilton–Jacobi–Bellman equation.

We study a class of deterministic two-player nonzero-sum differential games where one player uses piecewise-continuous controls to affect the continuously evolving state, while the other player uses impulse controls at certain discrete instants of time to shift the state from one level to another. The state measurements are made at some given instants of time, and players determine their strategies using the last measured state value. We provide necessary and sufficient conditions for the existence of sampled-data Nash equilibrium for a general class of differential games with impulse controls. We specialize our results to a scalar linear-quadratic differential game and show that the equilibrium impulse timing can be obtained by determining a fixed point of a Riccati-like system of differential equations with jumps coupled with a system of nonlinear equality constraints. By reformulating the problem as a constrained nonlinear optimization problem, we compute the equilibrium timing, and level of impulses. We find that the equilibrium piecewise continuous control and impulse control are linear functions of the last measured state value. Using a numerical example, we illustrate our results.

We study a class of discounted autonomous infinite horizon optimal control problems where the state dynamics may undergo discontinuous changes when the state crosses from one region of the state space to another. Assuming the state and control space are one-dimensional, we provide structural results of the candidate optimal solutions. In particular, we show that candidate optimal state trajectories are monotonic. Further, we prove a theorem on absence of limit cycles, generalizing the Bendixson criterion to a hybrid context. Using these results, we derive necessary and sufficient conditions for the existence of tipping points for this class of problems. A tipping point is an initial condition starting from which there exist multiple candidate optimal solutions with different qualitative behaviors. Next, we specialize these results for piecewise linear quadratic models to obtain an analytic characterization of tipping points in terms of the model parameters.

In this paper, we study how an oligopolist influences the coalition structure in federated cloud markets. Specifically, we use cooperative game theory to model the circumstances under which a cloud provider prefers to join a cloud federation vis-a-vis consider taking a price offer made by an oligopolist. We consider two price offering strategies for an oligopolist: non-adaptive and adaptive. In non-adaptive strategy, an oligopolist makes a price offer to all the cloud providers simultaneously. It can be noted that the oligopolist can buy-out all the cloud providers by making a price offer which is equal to a core allocation and the total price offer made by the oligopolist is equal to the value of the grand coalition. In adaptive strategy, the oligopolist approaches the cloud providers one after another in a sequential manner. We show that by using the adaptive strategy, the oligopolist can buy-out all the cloud providers at a total price offer which is less than that of the non-adaptive strategy.