Game-theoretic Problem Research Articles

Multi-Principal Multi-Agent Contract Design: Theory and Application to Device-to-Device Communications

How to stimulate the devices to participate is a key problem in the device-to-device (D2D) communications, especially when there are multiple base stations in practice. On one hand, the base station needs to lower the price to compete with other base stations for attracting more devices. On the other hand, the base station needs to increase the price to obtain more benefit. In this paper, we propose an optimal multiprincipal multiagent contract design to tackle such a challenge. Specifically, we formulate the multiprincipal contract design problem as a game theoretic optimization problem, where the objective of each principle (base station) through contract design is to maximize its overall utility obtaining from the trade with agents (devices) subject to the individual rationality and incentive compatibility constraints. By solving the game theoretic optimization problems, we can obtain the equilibrium contract where the contracts of different principals reach an equilibrium and any deviation from a single principal will lead to the degradation of its own utility. Moreover, under the equilibrium, both the individual rationality and incentive compatibility constraints are satisfied, i.e., all agents will choose the corresponding contract according to their types to reach the optimal nonnegative utilities. Simulation results show that compared with the monoprincipal contract design, both the utilities of devices and the social welfare can be improved with the multiprincipal contract design.

On Dynamic Recovery of Cloud Storage System Under Advanced Persistent Threats

Advanced persistent threat (APT) for data theft poses a severe threat to cloud storage systems (CSSs). An APT actor may steal valuable data from the target CSS even in a strategic fashion. To protect a CSS from APT, the cloud defender has to dynamically allocate the limited security resources to recover the compromised storage servers, aiming at mitigating his total loss. This paper addresses this dynamic cloud storage recovery (DCSR) problem by employing differential game theory. First, by introducing an expected state evolution model capturing the CSS's expected state evolution process under a combination of attack strategy and recovery strategy, we measure the APT attacker's net benefit and the cloud defender's total loss. On this basis and in the worst-case situation where the cloud defender assumes that the APT attacker has full knowledge of his expected loss, we reduce the DCSR problem to a differential game-theoretic problem (the DCSR* problem) to characterize the strategic interactions between the two parties. Second, we derive a necessary condition for Nash equilibrium of the DCSR* problem and thereby introduce the concept of competitive strategy profile. Next, we study the structural properties of the competitive strategy profile, followed by some numerical examples. Then, we conduct extensive comparative experiments to exhibit that the competitive strategy profile is superior to a large number of randomly generated strategy profiles in the sense of Nash equilibrium solution concept. Finally, we briefly analyze the practicability (scalability and feasibility) of this paper. Our findings will be helpful to enhance the APT defense capabilities of the cloud defender.

Platform modelling and scheduling game with multiple intelligent cloud-computing pools for big data

ABSTRACTWe develop a generic game platform that can be used to model various real-world systems with multiple intelligent cloud-computing pools and parallel-queues for resources-competing users. Inside the platform, the software structure is modelled as Blockchain. All the users are associated with Big Data arrival streams whose random dynamics is modelled by triply stochastic renewal reward processes (TSRRPs). Each user may be served simultaneously by multiple pools while each pool with parallel-servers may also serve multi-users at the same time via smart policies in the Blockchain, e.g. a Nash equilibrium point myopically at each fixed time to a game-theoretic scheduling problem. To illustrate the effectiveness of our game platform, we model the performance measures of its internal data flow dynamics (queue length and workload processes) as reflecting diffusion with regime-switchings (RDRSs) under our scheduling policies. By RDRS models, we can prove our myopic game-theoretic policy to be an asymptotic Pareto minimal-dual-cost Nash equilibrium one globally over the whole time horizon to a randomly evolving dynamic game problem. Iterative schemes for simulating our multi-dimensional RDRS models are also developed with the support of numerical comparisons.

Imperfect information in Reactive Modules games

Reactive Modules is a high-level modelling language for concurrent, distributed, and multi-agent systems, which is used in a number of practical model checking tools. Reactive Modules Games are a game-theoretic extension of Reactive Modules, in which system components are assumed to act strategically in an attempt to satisfy a temporal logic formula representing their individual goal. Reactive Modules Games with perfect information have been extensively studied, and the complexity of game theoretic decision problems relating to such games (such as the existence of Nash equilibria) have been comprehensively classified. In this article, we study Reactive Modules Games in which agents have only partial visibility of their environment.

Synthesis from component libraries with costs

Synthesis is the automated construction of a system from its specification. In real life, hardware and software systems are rarely constructed from scratch. Rather, a system is typically constructed from a library of components. Lustig and Vardi formalized this intuition and studied LTL synthesis from component libraries. In real life, designers seek optimal systems. In this paper we add optimality considerations to the setting. We distinguish between quality considerations (for example, size – the smaller a system is, the better it is), and pricing (for example, the payment to the company who manufactured the component). We study the problem of designing systems with minimal quality-cost and price. A key point is that while the quality cost is individual – the choices of a designer are independent of choices made by other designers that use the same library, pricing gives rise to a resource-allocation game – designers that use the same component share its price, with the share being proportional to the number of uses (a component can be used several times in a design). We study both closed and open settings, and in both we solve the problem of finding an optimal design. In a setting with multiple designers, we also study the game-theoretic problems of the induced resource-allocation game.

Adaptation, coordination, and local interactions via distributed approachability

This paper investigates the relation between cooperation, competition, and local interactions in large distributed multi-agent systems. The main contribution is the game-theoretic problem formulation and solution approach based on the new framework of distributed approachability, and the study of the convergence properties of the resulting game model. Approachability theory is the theory of two-player repeated games with vector payoffs, and distributed approachability is here presented for the first time as an extension to the case where we have a team of agents cooperating against a team of adversaries under local information and interaction structure. The game model turns into a nonlinear differential inclusion, which after a proper design of the control and disturbance policies, presents a consensus term and an exogenous adversarial input. Local interactions enter into the model through a graph topology and the corresponding graph-Laplacian matrix. Given the above model, we turn the original questions on cooperation, competition, and local interactions, into convergence properties of the differential inclusion. In particular, we prove convergence and exponential convergence conditions around zero under general Markovian strategies. We illustrate our results in the case of decentralized organizations with multiple decision-makers.

Coordination Between the Sexes Constrains the Optimization of Reproductive Timing in Honey Bee Colonies

Honeybees are an excellent model system for examining how trade-offs shape reproductive timing in organisms with seasonal environments. Honeybee colonies reproduce two ways: producing swarms comprising a queen and thousands of workers or producing males (drones). There is an energetic trade-off between producing workers, which contribute to colony growth, and drones, which contribute only to reproduction. The timing of drone production therefore determines both the drones’ likelihood of mating and when colonies reach sufficient size to swarm. Using a linear programming model, we ask when a colony should produce drones and swarms to maximize reproductive success. We find the optimal behavior for each colony is to produce all drones prior to swarming, an impossible solution on a population scale because queens and drones would never co-occur. Reproductive timing is therefore not solely determined by energetic trade-offs but by the game theoretic problem of coordinating the production of reproductives among colonies.

Counting Derangements and Nash Equilibria

The maximal number of totally mixed Nash equilibria in games of several players equals the number of block derangements, as proved by McKelvey and McLennan. On the other hand, counting the derangements is a well-studied problem. The numbers are identified as linearization coefficients for Laguerre polynomials. MacMahon derived a generating function for them as an application of his master theorem. This article relates the algebraic, combinatorial, and game-theoretic problems that were not connected before. New recurrence relations, hypergeometric formulas, and asymptotics for the derangement counts are derived. An upper bound for the total number of all Nash equilibria is given.

Local Computation Mechanism Design

We introduce the notion of local computation mechanism design —designing game-theoretic mechanisms that run in polylogarithmic time and space. Local computation mechanisms reply to each query in polylogarithmic time and space, and the replies to different queries are consistent with the same global feasible solution. When the mechanism employs payments, the computation of the payments is also done in polylogarithmic time and space. Furthermore, the mechanism needs to maintain incentive compatibility with respect to the allocation and payments. We present local computation mechanisms for two classical game-theoretical problems: stable matching and job scheduling. For stable matching, some of our techniques may have implications to the global (non-LCA (Local Computation Algorithm)) setting. Specifically, we show that when the men’s preference lists are bounded, we can achieve an arbitrarily good approximation to the stable matching within a fixed number of iterations of the Gale-Shapley algorithm.

A Class of Control Problems Under Uncertainty

We consider a class of nonlinear game-theoretical control problems for a dynamical system with uncertain parameters, a free termination time, and a Bolza functional in the form of a power function of the control parameter. A control is proposed in the class of countercontrols on which the objective functional attains a guaranteed value that depends on the realized uncertainty. Calculation results using test model parameters are reported for the control and the functional values.

Hospital Stockpiling Problems with Inventory Sharing

Hospitals are typically optimized to operate near capacity, and there are serious concerns that our healthcare system is not prepared for the next pandemic. Stockpiles of different supplies, e.g., personal protective equipments (PPE) and medical equipment, need to be maintained in order to be able to respond to any future pandemics. Large outbreaks occur with a low probability, and such stockpiles require big investments. Further, hospitals often have mutual sharing agreements, which makes the problem of stockpiling decisions a natural game-theoretical problem. In this paper, we formalize hospital stockpiling as a game-theoretical problem. We use the notion of pairwise Nash stability as a solution concept for this problem, and characterize its structure. We show that stable strategies can lead to high unsatisfied demands in some scenarios, and stockpiles might not be maintained at all nodes. We also show that stable strategies and the social optimum can be computed efficiently.

A packet dropping mechanism for efficient operation of M/M/1 queues with selfish users

We consider a fundamental game theoretic problem concerning selfish users contributing packets to an M/M/1 queue. In this game, each user controls its own input rate so as to optimize a desired tradeoff between throughput and delay. We first show that the original game has an inefficient Nash Equilibrium (NE), with a Price of Anarchy (PoA) that scales linearly or worse in the number of users. In order to improve the outcome efficiency, we propose an easily implementable mechanism design whereby the server randomly drops packets with a probability that is a function of the total arrival rate. We show that this results in a modified M/M/1 queueing game that is an ordinal potential game with at least one NE. In particular, for a linear packet dropping function, which is similar to the Random Early Detection (RED) algorithm used in Internet Congestion Control, we prove that there is a unique NE. We also show that the simple best response dynamic converges to this unique equilibrium. Finally, for this scheme, we prove that the social welfare (expressed either as the summation of utilities of all players, or as the summation of the logarithm of utilities of all players) at the equilibrium point can be arbitrarily close to the social welfare at the global optimal point, i.e. the PoA can be made arbitrarily close to 1. We also study the impact of arrival rate estimation error on the PoA through simulations.

A game theoretic analysis of firms' entry mode decisions

Limited research has been completed using formal modelling to investigate a firm's entry mode decisions. Addressing this issue, we formulate Dunning's eclectic model as a game theoretic problem. We develop a novel three-stage game theory model to investigate the relationships and nuances of the core constructs of the eclectic model, i.e., ownership advantage, location advantage and internalisation (OLI). We develop an equilibrium solution to identify the optimal entry decisions for firms entering new markets using a two firm-two country scenario when parameters including ownership advantage of firms, market size, production cost and country risks are varied. The results obtained provide insight for future research as well as having significant practical implications.

From "In" to "Over": Behavioral Experiments on Whole-Network Computation

We report on a series of behavioral experiments in human computation on three different tasks over networks: graph coloring, community detection (or graph clustering), and competitive contagion. While these tasks share similar action spaces and interfaces, they capture a diversity of computational challenges: graph coloring is a search problem, clustering is an optimization problem, and competitive contagion is a game-theoretic problem. In contrast with most of the prior literature on human-subject experiments in networks, in which collectives of subjects are embedded "in" the network, and have only local information and interactions, here individual subjects have a global (or "over") view and must solve "whole network" problems alone. Our primary findings are that subject performance is impressive across all three problem types; that subjects find diverse and novel strategies for solving each task; and that collective performance can often be strongly correlated with known algorithms.

Marginal Pricing of Transmission Services Using Min-Max Fairness Policy

We consider the problem of allocating the cost of a transmission system among load and generator entities. It is a known instance of the classical cooperative game theoretic problem. To solve this problem is a formidable task, as we are dealing with a combinatorial game with transferable utilities. This is an NP hard problem. Therefore, it suffers from the curse of dimensionality. Marginal pricing is a pragmatic alternative to solve this problem since both Kirchhoff current law and voltage law are strictly adhered to. However, the generic complexity of cooperative game theoretic problems cannot be just wished away. It now manifests as the difficulty in choosing an economic slack bus, which may even be dispersed. We propose the application of min-max fairness policy to solve this problem and give an algorithm which will run in polynomial time. During network cost allocation, min-max fairness policy minimizes the maximum regret among participating entities at each step. Maximum regret is measured in terms of price, and lexicographic application of this principle leads to a fair and unique equilibrium price vector. Results on a large network demonstrate fairness as well as tractability of the proposed approach.

Applications of Algebra for Some Game Theoretic Problems

In this paper we present applications of polynomial algebra for the problem of computing Nash equilibria of a subclass of finite normal form games.We characterize Nash equilibria of a normal form game as solutions to a system of polynomial equations and define the subclass of games under consideration. We present an algebraic method for deciding membership decision to the subclass of games. A method based on group action to compute all Nash equilibria of the subclass of games is presented with examples to show working of the methods. We also present some related results and discuss properties of the subclass of games.

An Efficient Speedup Strategy for Constant Sum Game Computations

Large classes of game theoretic problems seem to defy attempts of finding polynomial-time algorithms while analyzing large amounts of data. This premise leads naturally to the possibility of using efficient parallel computing implementations when seeking exact solutions to some of these problems. Although alpha beta algorithms for more than one-player game-tree searches show moderate parallel performance, this paper sets forth an alpha beta strategy enhanced with transposition tables in order to offer satisfactory speedups on high performance servers. When the access to the transposition tables is done in low constant delay time, the achieved speedups should approach the theoretical upper bounds of the code parallelism. We tested the strategy on a well-known combinatorial game.Keywords: Constant Sum Games, Game Computation Parallelization Strategies1IntroductionHigh-performance parallel computing is being increasingly used in computational science to solve large-scale algorithmically intensive problems. Recent technological advances in processor development gave rise to a large range of unexpansive chips with tens or even hundreds of cores. These multi-core chips enhanced with simultaneous multithreading, dedicated fast access memory and manifold specific cores, promise additional performance and efficiency gains [1] [2], especially in processing computational science applications.Large classes of game theoretic problems seem to defy attempts of finding polynomialtime algorithms [3-7], requiring super-polynomial time algorithmic schemes and, thereby, being computationally intensive. Furthermore, large quantities of data can potentially be generated, analyzed and stored while exploring exponentially growing game trees.These premises lead naturally to the possibility of applying highly parallel computational implementations when aiming to find exact solutions for many game theory problems. We propose a speedup strategy to allow constant sum games computations to take full advantage of the parallelism and the efficient scheduling strategies implemented on these architectures [8] [9], This way, we obtain fast and accurate sub-game utility estimations by scaling up the amount of required resources and accelerating the dissemination of intermediate results.This paper is organized as follows: section 2 is devoted to presenting the underlying game theoretic concepts used in this research and related algorithmic complexity aspects. The speedup strategy for constant sum games is expounded in the third section. A case study together with its experimental plan is detailed in section 4. Results and conclusions are presented in sections 5 and 6.2 Overview of relevant Game Theory ConceptsThe current section starts off by briefly restating the definitions of the main concepts used throughout the paper, and proceeds by expounding the underlying considerations on the algorithmic complexity of game equilibria computations.Brief Overview of underlying game theoretic ConceptsA finite perfect-information game in extensive form is defined as a tuple G = (JV, A, H, Z, χ, p, a, u) where:* N is the finite set of rational players;* A is the set of possible actions of the players;* H is the set of choice nodes;* χ: H -> 2a is the choice function;* p: H -> N is the player function which indicates player to perform the move at some given choice node;* σ: H x A -> H U Z is the successor function. This function maps pairs of choice nodes and possible actions to other successor terminal or choice nodes;* u = (u1; ...,U|N|), whereu?:Z -> R is a utility function for the player i on the terminal nodes Z,* Z is the set of terminal nodes in the game three. Each terminal node of the game tree has an N-tuple of payoffs, one for each player at the end of every possible play.Each player has a utility function defined for every game outcome. …

A study on capacity allocation scheme with seasonal demand

This paper studies a game-theoretical capacity allocation problem in a two-echelon supply chain comprised of one supplier and N retailers. With demand fluctuating seasonally and significantly, supply is sufficient in low-demand periods but is insufficient in high-demand periods, especially when the supplier’s capacity decreases in high-demand periods. Retailers compete for the supplier’s capacity in high-demand periods, but do not want to absorb the supplier’s redundant capacity in low-demand periods. A turn-and-earn allocation scheme is proposed to encourage retailers to increase their order quantity in low-demand periods. Under the turn-and-earn allocation scheme, in high-demand periods, the supplier is willing to offer a guaranteed portion of supply capacity for the primary retailer. The remaining capacity in high-demand periods is allocated based on orders retailers placed in low-demand periods. In response, the retailers will decide how much they should order in low-demand periods. Then, a competitive game based on Nash equilibrium among the supplier and her retailers is analysed. In order to solve the problem of unreasonable distribution of interest caused by competition, a contract is designed to make it possible for subsidy to be transferred from the supplier to the retailers. Usually, the supplier and her primary retailer can both be better off under turn-and-earn allocation compared with fixed allocation, and the system efficiency in Nash solution is close to it in optimal solution. A numerical study is also conducted to discuss the parties’ sensitivity to different demand level and guaranteed allocation portion of capacity.

Critical infrastructure protection using secrecy – A discrete simultaneous game

In this research, critical infrastructure protection against intentional attacks is modeled as a discrete simultaneous game between the protector and the attacker, to model the situation that both players keep the information of their resource allocation secret. We prove that keeping the information regarding protection strategies secret can obtain a better effect of critical infrastructure protection than truthfully disclosing it. Solving a game theoretic problem, even in the case of two players, has been known to be intractable. To deal with this complexity, after proving that pure-strategy Nash equilibrium solutions do not exist for the proposed simultaneous game, a new approach is proposed to identify its mixed-strategy Nash equilibrium solution.

Distributed Spectrum Sharing Games Via Congestion Advertisement

Distributed spectrum sharing via congestion advertisement is modelled and studied as a game theoretic problem. A related graphical anti-coordination game problem and a suitable logit-response learning mechanism is proposed and studied. It has been shown that introducing an arbitrary small congestion advertisement term into the users utility can improve the convergence rate of the spectrum sharing game exponentially. Finally, simulation results are presented to evaluate the price of anarchy, convergence rate and phase transition properties. Received on 17 March 2013; accepted on 25 June 2013; published on 14 July 2014