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Heterogeneous Computing (HC) systems achieve high performance by networking together computing resources of diverse nature. The issues of task assignment and scheduling are critical in the design and performance of such systems. In this thesis, an auction based game theoretic framework is developed for dynamic task scheduling in HC systems. Based on the proposed game theoretic model, a new dynamic scheduling algorithm is developed that uses auction based strategies. The dynamic scheduling algorithm yields schedules with shorter completion times than static schedulers while incurring higher scheduling overhead. Thus, a second scheduling algorithm is proposed which uses an initial schedule generated with a learning automaton based algorithm, and then heuristics are used to identify windows of tasks within the application that can be rescheduled dynamically during run time.

The optimal allocation of the resources to the emergency locations in the event of multiple crises in an urban environment is an intricate problem, especially when the available resources are limited. In such a scenario, it is important to allocate emergency response units in a fair manner based on the criticality of the crisis events and their requests. In this research, a crisis management tool is developed which incorporates a resource allocation algorithm. The problem is formulated as a game theoretic framework in which the crisis events are modeled as the players, the emergency response centers as the resource locations with emergency units to be scheduled and the possible allocations as strategies. The pay-off is modeled as a function of the criticality of the event and the anticipated response times. The game is played assuming a specific region within a certain locality of the crisis event to derive an optimal allocation. If a solution is not feasible, the perimeter of the locality in consideration is increased and the game is repeated until convergence. Experimental results are presented to illustrate the efficacy of the proposed methodology and metrics are derived to quantify the fairness of the solution. A regression analysis has been performed to identify the statistical significance of the results.

The problem of resource allocation and management in the context of multiple crises occurring in an urban environment is challenging. In this thesis, the problem is formulated using game theory and a solution is developed based on the Nash equilibrium to optimize the allocation of resources to the different crisis events in a fair manner considering several constraints such as the availability of resources, the criticality of the events, the amount of resources requested etc. The proposed approach is targeted at managing small to medium level crisis events occurring simultaneously within a specific pre-defined perimeter with the resource allocation centers being located within the same fixed region. The objective is to maximize the utilization of the emergency response units while minimizing the response times. In the proposed model, players represent the crisis events and the strategies correspond to possible allocations. The choice of strategies by each player impacts the decisions of the other players. The Nash equilibrium condition will correspond to the set of strategies chosen by all the players such that the resource allocation optimal for a given player also corresponds to the optimal allocations of the other players. The implementation of the Nash equilibrium condition is based on the Hansen's combinatorial theorem based approximation algorithm. The proposed solution has been implemented using C++ and experimental results are presented for various test cases. Further, metrics are developed for establishing the quality and fairness of the obtained results.

This paper studies the problem of multi-period pricing for perishable products in a competitive (oligopolistic) market. We study non cooperative Nash equilibrium policies for sellers. At the beginning of the time horizon, the total inventories are given and additional production is not an available option. The analysis for periodic production-review models, where production decisions can be made at the end of each period at some production cost after incurring holding or backorder costs, does not extend to this model. Using results from game theory and variational inequalities we study the existence and uniqueness of equilibrium policies. We also study convergence results for an algorithm that computes the equilibrium policies. The model in this paper can be used in a number of application areas including the airline, service and retail industries. We illustrate our results through some numerical examples. / Singapore-MIT Alliance (SMA)

General Game Playing (GGP) deals with the design of players that are able to play any discrete, deterministic, complete information games. For many games like chess, designers develop a player using a specially designed algorithm and tune all the features of the algorithm to play the game as good as possible. However, a general game player knows nothing about the game that is about to be played. When the game begins, game description is given to the players and they should analyze it and decide on the best way to play the game. In this thesis, we focus on two-player constant-sum simultaneous move games in GGP and how this class of games can be handled. Rock-paper-scissors can be considered as a typical example of a simultaneous move game. We introduce the CFR algorithm to the GGP community for the first time and show its effectiveness in playing simultaneous move games. This is the first implementation of CFR outside the poker world. We also improve the UCT algorithm, which is the state of the art in GGP, to be more robust in simultaneous move games. In addition, we analyze how UCT performs in simultaneous move games and argue that it does not converge to a Nash equilibrium. We also compare the usage of UCT and CFR in this class of games. Finally, we discuss about the importance of opponent modeling and how a model of the opponent can be exploited by using CFR.

Demand fluctuations will bias the measurement of productivity and efficiency. This dissertation described three ways to characterize the effect of demand fluctuations. First, a two-dimensional efficiency decomposition (2DED) of profitability is proposed for manufacturing, service, or hybrid production systems to account for the demand effect. The first dimension identifies four components of efficiency: capacity design, demand generation, operations, and demand consumption, using Network Data Envelopment Analysis (Network DEA). The second dimension decomposes the efficiency measures and integrates them into a profitability efficiency framework. Thus, each component's profitability change can be analyzed based on technical efficiency change, scale efficiency change and allocative efficiency change. Second, this study proposes a proactive DEA model to account for demand fluctuations and proposes input or output adjustments to maximize effective production. Demand fluctuations lead to variations in the output levels affecting measures of technical efficiency. In the short-run, firms can adjust their variable resources to address the demand fluctuates and perform more efficiently. Proactive DEA is a short-run capacity planning method, proposed to provide decision support to a firm interested in improving the effectiveness of a production system under demand uncertainty using a stochastic programming DEA (SPDEA) approach. This method improves the decision making related to short-run capacity expansion and estimates the expected value of effectiveness given demand. In the third part of the dissertation, a Nash-Cournot equilibrium is identified for an oligopolistic market. The standard assumption in the efficiency literature that firms desire to produce on the production frontier may not hold in an oligopolistic market where the production decisions of all firms will determine the market price, i.e. an increase in a firm's output level leads to a lower market clearing price and potentially-lower profits. Models for both the production possibility set and the inverse demand function are used to identify a Nash-Cournot equilibrium and improvement targets which may not be on the strongly efficient production frontier. This behavior is referred to as rational inefficiency because the firm reduces its productivity levels in order to increase profits.

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This dissertation studies the competitive dynamics between two non-identical providers competing for customers seeking low-cost and quick service. Providers have generic delay functions where, asdemand received by each provider grows, so does delay in processing customers' requests. Given a pricing or capacity decision by each provider, customers determine the proportion of demand to send to each provider by minimizing generalized cost (monetary cost plus delaycost). This problem is formulated as a bilevel optimization, with providers competing at the upper level subject to the customers' decisions at the lower level. Occurrence of Nash equilibria between the providers is studied.First studied is the providers' problem of making decisions on capacities, while competing for a single customer. Conditions are derived for one provider to claim the entire market share, and for the occurrence of an equilibrium where both providers receive positivedemand. A numerical example in which no equilibrium exists is presented. Both the inelastic and elastic demand cases are studied for this scenario. In a second model, providers make pricing decisions with capacity fixed. Under some assumptions, it is shownthat a Nash equilibrium between providers always exists and a numerical example is presented. These models are then combined, in which providers make capacity decisions where prices equilibrate based on the results from the second model.Two competing customers with demand for a homogeneous product are then introduced, where providers choose prices as they compete for customers. This model is extended to an application along a highway corridor with a high-occupancy/toll (HOT) lane in parallel with a free road and transit line. A government agency chooses the transit service frequency while a private toll operator competes by choosing a toll to charge single-occupancy vehicles who wish to use the HOT lane.This scenario is also modeled as a bilevel program. For the lower level, a new dynamic equilibration process where homogeneous users make mode choice decisions based on previous generalized costs ofusing a particular mode is developed. Two numerical examples are presented showing a unique Nash equilibrium between the providers and an example in which multiple equilibria exist.

<p>Algorithms for finding game-theoretic solutions are now used in several real-world security applications. Many of these applications are based on different but related game-theoretical models collectively known as security games. Much of the research in this area has focused on the two-player setting in which the first player (leader, defender) commits to a strategy, after which the second player (follower, attacker) observes that strategy and responds to it. This is commonly known as the Stackelberg, or leader-follower, model. If none of the players can observe the actions of the others then such a setting is called a simultaneous-move game. A common solution concept in simultaneous-move games is the Nash equilibrium (NE). In the present dissertation, we contribute to this line of research in two ways.</p><p>First, we consider new ways of modeling commitment. We propose the new model in which the leader can commit to a correlated strategy. We show that this model is equivalent to the Stackelberg model in two-player games and is different from the existing models in games with three or more players. We propose an algorithm for computing a solution to this model in polynomial time. We also consider a leader-follower setting in which the players are uncertain about whether the follower can observe. We describe an iterative algorithm for solving such games.</p><p>Second, we analyze the computational complexity of computing Stackelberg and NE strategies in security games. We describe algorithms to solve some variants of the security game model in polynomial time and prove NP-hardness of solving other variants of the model. We also extend the family of security games by allowing the attacker have multiple resources. We provide an algorithm for computing an NE of such games in polynomial time, and we show that computing a Stackelberg strategy is NP-hard.</p> / Dissertation