Best-response Strategies Research Articles

Dissecting Mining Pools of Bitcoin Network: Measurement, Analysis and Modeling

Bitcoin network is one of the most popular blockchain systems. Mining pools are the main components of the Bitcoin network that invest a large amount of computing power to maximize their expected mining payoffs, which guarantees the security of the Bitcoin network. Although many existing works about mining pools are available, the long-term evolution of mining pools, and their effects on both the Bitcoin system and end-users, remain to be investigated. To fill this gap, we trace over 2.54 hundred thousand blocks from Feb 2016 to Nov 2020 and collect over 12 million unconfirmed transactions from Mar 2018 to Nov 2020. We then conduct a broad range of analyses, including the pool evolution, labeled transactions, and labeled blocks. We make the following observations from our measured data: 1) A few mining pools control most of the peer-to-peer network's computing power. 2) The long-term computing power of top mining pools grows exponentially while its <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">continuous-time mining strategy</i> decreases linearly. 3) The computing power of the Bitcoin network converges to the Nash equilibrium. We then propose game-based strategies for mining activity analysis, i.e., the best-response strategies for mining pools when the mining revenue increases or decreases sharply. Moreover, we study the transaction fee dilemma of mining pools and the transaction fee strategies for end-users. Our models and analysis can help to understand and improve the Bitcoin system quantitatively.

Kernel Structure Design for Data-Driven Probabilistic Load Flow Studies

In power system analysis, probabilistic load flow (PLF) accounts for uncertainties stemming from power entities such as renewable generation systems and consumer demands. In this paper, we present a Gaussian Process (GP) emulator for enabling data-driven PLF on practical distribution networks (DNs) without requiring knowledge of underlying system parameters. The main novelty of our proposal lies in the kernel design process. An ideal kernel allows for greater efficiency during training and inferencing stages without being subject to common issues that include overfitting to the training dataset and poor accuracies. In this proposal, the kernel selection process is formulated as a bi-level optimization problem. This is a very difficult problem to solve as it is composed of discrete variables and non-convex constraints. We overcome these issues by proposing a best-response strategy refinement process to identify an efficient kernel configuration in an iterative manner. The convergence properties of this iterative algorithm and the approximating capabilities of the resulting GP emulator are established using potential game theoretic constructs, universal approximation theorem and representer theorem. The performance of the proposed emulator is then showcased via comprehensive simulations conducted on practical DNs and comparisons with the state-of-the-art.

Diffusion in large networks

We investigate the phenomenon of diffusion in a countably infinite society of individuals interacting with their neighbors in a network. At a given time, each individual is either active or inactive. The diffusion is driven by two characteristics: the network structure and the diffusion mechanism represented by an aggregation function. We distinguish between two diffusion mechanisms (probabilistic, deterministic) and focus on two types of aggregation functions (strict, Boolean). Under strict aggregation functions, polarization of the society cannot happen, and its state evolves towards a mixture of infinitely many active and infinitely many inactive agents, or towards a homogeneous society. Under Boolean aggregation functions, the diffusion process becomes deterministic and the contagion model of Morris (2000) becomes a particular case of our framework. Polarization can then happen. Our dynamics also allows for cycles in both cases. The network structure is not relevant for these questions, but is important for establishing irreducibility, at the price of a richness assumption: the network should contain at least one complex star and have enough space for storing local configurations. Our model can be given a game-theoretic interpretation via a local coordination game, where each player would apply a best-response strategy in a random neighborhood.

Stability analysis of multiplayer games on adaptive simplicial complexes.

We analyze the influence of multiplayer interactions and network adaptation on the stability of equilibrium points in evolutionary games. We consider the Snowdrift game on simplicial complexes. In particular, we consider as a starting point the extension from only two-player interactions to coexistence of two- and three-player interactions. The state of the system and the topology of the interactions are both adaptive through best-response strategies of nodes and rewiring strategies of edges, respectively. We derive a closed set of low-dimensional differential equations using pairwise moment closure, which yields an approximation of the lower moments of the system. We numerically confirm the validity of these moment equations. Moreover, we demonstrate that the stability of the fixed points remains unchanged for the considered adaption process. This stability result indicates that rational best-response strategies in games are very difficult to destabilize, even if higher-order multiplayer interactions are taken into account.

Evolution Strategies for Approximate Solution of Bayesian Games

We address the problem of solving complex Bayesian games, characterized by high-dimensional type and action spaces, many (&gt; 2) players, and general-sum payoffs. Our approach applies to symmetric one-shot Bayesian games, with no given analytic structure. We represent agent strategies in parametric form as neural networks, and apply natural evolution strategies (NES) [wierstra2014natural] for deep model optimization. For pure equilibrium computation, we formulate the problem as bi-level optimization, and employ NES in an iterative algorithm to implement both inner-loop best response optimization and outer-loop regret minimization. In simple games including first- and second-price auctions, it is capable of recovering known analytic solutions. For mixed equilibrium computation, we adopt an incremental strategy generation framework, with NES as strategy generator producing a finite sequence of approximate best-response strategies. We then calculate equilibria over this finite strategy set via a model-based optimization process. Both our pure and mixed equilibrium computation methods employ NES to efficiently search for strategies over the functional space, given only black-box simulation access to noisy payoff samples. We experimentally demonstrate the efficacy of all methods on two simultaneous sealed-bid auction games with distinct type distributions, and observe that the solutions exhibit qualitatively different behavior in these two environments.

Dynamic Learning in Strategic Pricing Games

In monopoly pricing situations, firms should optimally vary prices to learn demand. The variation must be sufficiently high to ensure complete learning. In competitive situations, however, varying prices provides information to competitors and may reduce the value of learning. Such situations may arise in the pricing of new products such as pharmaceuticals and digital goods. This paper shows that firms in competition can learn efficiently in certain equilibrium actions which involve adding noise to myopic estimation and best-response strategies. The paper then discusses how this may not be the case when actions reveal information quickly to competitors. The paper provides a setting where this effect can be strong enough to stop learning so that firms optimally reduce any variation in prices and choose not to learn demand. The result can be that the selling firms achieve a collaborative outcome instead of a competitive equilibrium. The result has implications for policies that restrict price changes or require disclosures.

Stochastic Channel Access in Underwater Networks With Statistical Interference Modeling

Designing efficient medium access control protocols for underwater acoustic sensor networks (UW-ASNs) is a major challenge because of the spatial and temporal interference uncertainty caused by asynchronous transmissions and by the low propagation speed of sound. To address these challenges, in this article we propose a new approach for distributed underwater medium access based on lightweight and asynchronous distributed algorithms that optimize the access probability profile over a series of time slots based on a new statistical physical interference model. The latter is based on measuring the level of interference at multiple instants of time in each time slot in order to capture the effects of temporal uncertainty and of unaligned interference. At each measurement instant, the statistical properties of time-varying interference are represented by a Gamma probability distribution. The model is validated through extensive channel measurement experiments conducted with an underwater acoustic testbed in Lake LaSalle. Based on this model, we formulate the problem of queue-aware stochastic channel access. The objective is to maximize the sum throughput of a set of concurrent and mutually interfering source-destination pairs by letting the transmitters adjust their own transmission probability profiles, without collaborating with each other, over a series of time slots based on a statistical characterization of interference obtained through past observations. We propose an iterative distributed solution algorithm for this problem based on a best-response strategy. At each iteration, each node individually solves a non-convex optimization problem of logarithmic complexity. The performance of the proposed distributed algorithm is evaluated by comparing it with two alternative distributed schemes and with the global optimum obtained through a newly-developed centralized globally optimal solution algorithm. Results indicate that by jointly taking the queueing and multi-slot optimization into consideration considerable improvement in terms of sum-throughput can be achieved by the proposed distributed algorithm.

Biased-Belief Equilibrium

We investigate how distorted, yet structured, beliefs can persist in strategic situations. Specifically, we study two-player games in which each player is endowed with a biased-belief function that represents the discrepancy between a player’s beliefs about the opponent’s strategy and the actual strategy. Our equilibrium condition requires that (i) each player choose a best-response strategy to his distorted belief about the opponent’s strategy, and (ii) the distortion functions form best responses to one another. We obtain sharp predictions and novel insights into the set of stable outcomes and their supporting stable biases in various classes of games. (JEL C73, D83)

A Dilemma in the Communication of a UAV with its Controller

In this paper, we investigate a dilemma of employing silent mode and communication mode by an unmanned aerial vehicle (UAV) in communication with its controller. In many applications, a UAV communicates with a controller to receive instructions or accurate positioning, but such active communication poses a threat that the UAV can be hijacked through spoofing. On the other hand, during a silent mode (when the UAV does not communicate with the controller), the UAV is safe from spoofing, but is not receiving updates or other important data, and can degrade the overall UAV mission. To gain insight into the UAV risk versus benefit tradeoff, a simple game-theoretic model is presented. Additionally, this paper investigates how incomplete information about the capability of the controller to quickly learn the adversary’s attack and adjust its strategy accordingly can impact the equilibrium strategies. In contrast to regular-type capability, when both the rivals maximize their payoffs simultaneously, the capability of the controller to quickly learn is modeled by having the controller apply the best-response strategy. We model this problem using a Bayesian game, where the adversary knows only a priori probabilities about what capability the controller has. Dependence of the equilibrium strategies on these a priori probabilities is illustrated.

Recommender systems with selfish users

Recommender systems are a fundamental component of contemporary social-media platforms and require feedback submitted from users in order to fulfill their goal. On the other hand, the raise of advocacy about user-controlled data repositories supports the selective submission of data by user through intelligent software agents residing at the user end. These agents are endowed with the task of protecting user privacy by applying a “soft filter” on personal data provided to the system. In this work, we pose the question: “how should the software agent control the user feedback submitted to a recommender system in a way that is most privacy preserving, while the user still enjoys most of the benefits of the recommender system?”. We consider a set of such agents, each of which aims to protect the privacy of its serving user by submitting to the recommender system server a version of her real rating profile. The fact that issued recommendations to a user depend on the collective rating profiles by all agents gives rise to a novel game-theoretic setup that unveils the trade-off between privacy preservation of each user and the quality of recommendation they receive. Privacy is quantified through a distance metric between declared and an “initial” random rating profile; the latter is assumed to provide a “neutral” starting point for the disclosure of the real profile. We allow different users to have different perception of their privacy through a user-dependent utility function of this distance. The quality of recommendations for each user depends on submitted ratings of all users, including the ratings of the user to whom the recommendation is provided. We prove the existence of a Nash equilibrium point (NEP), and we derive conditions for that. We show that user strategies converge to the NEP after an iterative best-response strategy update sequence that involves circulation of aggregate quantities in the system and no revelation of real ratings. We also present various modes of user cooperation in rating declaration, by which users mutually benefit in terms of privacy. We evaluate and compare cooperative and selfish strategies in their performance in terms of privacy preservation and recommendation quality through real movie datasets.

A Game-Theoretic Analysis of Reallocation Mechanisms for Airport Landing Slots

As airport arrival capacities increasingly constrain the air transportation system, there is a need for mechanisms by which airlines can exchange landing slots amongst each other. We analyze two such mechanisms, scaled airline preferences and two-for-two trades, from a game-theoretic perspective. This paper investigates the extent to which strategic behavior on part of the airlines can impact the performance of each mechanism. In addition to increasing system efficiency, the reallocation mechanisms should exhibit desirable fairness and incentive properties, notions that we formally investigate in this paper. We show that neither mechanism has good incentive properties, and we develop simple, non-truthful strategies that airlines can use. Our empirical results show that for the scaled airline preferences mechanism, the best performing strategy depends greatly on the extent to which fairness is enforced. For the two-for-two trades mechanism, a simple threshold strategy can yield significant cost savings relative to the best-response strategy, and system efficiency increases when all airlines use the threshold strategy in equilibrium.

A Stochastic Game Model for Evaluating the Impacts of Security Attacks Against Cyber-Physical Systems

A quantitative security evaluation in the domain of cyber-physical systems (CPS), which operate under intentional disturbances, is an important open problem. In this paper, we propose a stochastic game model for quantifying the security of CPS. The proposed model divides the security modeling process of these systems into two phases: (1) intrusion process modeling and (2) disruption process modeling. In each phase, the game theory paradigm predicts the behaviors of the attackers and the system. By viewing the security states of the system as the elements of a stochastic game, Nash equilibriums and best-response strategies for the players are computed. After parameterization, the proposed model is analytically solved to compute some quantitative security measures of CPS. Furthermore, the impact of some attack factors and defensive countermeasures on the system availability and mean time-to-shutdown is investigated. Finally, the proposed model is applied to a boiling water power plant as an illustrative example.

Biased-Belief Equilibrium

We investigate how distorted, yet structured, beliefs can persist in strategic situations. Specifically, we study two-player games in which each player is endowed with a biased-belief function that represents the discrepancy between a player’s beliefs about the opponent's strategy and the actual strategy. Our equilibrium condition requires that: (1) each player choose a best-response strategy to his distorted belief about the opponent's strategy, and (2) the distortion functions form best responses to one another. We obtain sharp predictions and novel insights into the set of stable outcomes and their supporting stable biases in various classes of games.

A Game-Theoretic Analysis of Reallocation Mechanisms for Airport Landing Slots

As airport arrival capacities increasingly constrain the air transportation system, there is a need for mechanisms by which airlines can exchange landing slots amongst each other. We analyze two such mechanisms, scaled airline preferences and two-for-two trades, from a game-theoretic perspective. This paper investigates the extent to which strategic behavior on part of the airlines can impact the performance of each mechanism. In addition to increasing system efficiency, the reallocation mechanisms should exhibit desirable fairness and incentive properties, notions that we formally investigate in this paper. We show that neither of these mechanisms has good incentive properties, and we develop simple, non-truthful strategies that airlines can use. Our empirical results show that for the scaled airline preferences mechanism, the best performing strategy depends greatly on the extent to which fairness is enforced. For the two-for-two trades mechanism, a simple threshold strategy can yield significant cost savings relative to the best-response strategy, but system efficiency decreases when all airlines use a threshold strategy.

The Value of Cooperation: Minimizing User Costs in Multi-Broker Mobile Cloud Computing Networks

We study the problem of user cost minimization in mobile cloud computing (MCC) networks. We consider a MCC model where multiple brokers assign cloud resources to mobile users. The model is characterized by an heterogeneous cloud architecture (which includes a public cloud and a cloudlet) and by the heterogeneous pricing strategies of cloud service providers. In this setting, we investigate two classes of cloud reservation strategies, i.e., a competitive strategy, and a compete-then-cooperate strategy as a performance bound. We first study a purely competitive scenario where brokers compete to reserve computing resources from remote public clouds (which are affected by long delays) and from local cloudlets (which have limited computational resources but short delays). We provide theoretical results demonstrating the existence of disagreement points (i.e., the equilibrium reservation strategy that no broker has incentive to deviate unilaterally from) and convergence of the best-response strategies of the brokers to disagreement points. We then consider the scenario in which brokers agree to cooperate in exchange for a lower average cost of resources. We formulate a cooperative problem where the objective is to minimize the total average price of all brokers, under the constraint that no broker should pay a price higher than the disagreement price (i.e., the competitive price). We design new globally optimal solution algorithm to solve the resulting non-convex cooperative problem, based on a combination of the branch and bound framework and of advanced convex relaxation techniques . The resulting optimal solution provides a lower bound on the achievable user cost without complete collusion among brokers. Compared with pure competition, we found that (i) noticeable cooperative gains can be achieved over pure competition in markets with a few brokers only, and (ii) the cooperative gain is only marginal in crowded markets, i.e., with a high number of brokers, hence there is no clear incentive for brokers to cooperate.

Game theory-based mode cooperative selection mechanism for device-to-device visible light communication

Various patterns of device-to-device (D2D) communication, from Bluetooth to Wi-Fi Direct, are emerging due to the increasing requirements of information sharing between mobile terminals. This paper presents an innovative pattern named device-to-device visible light communication (D2D-VLC) to alleviate the growing traffic problem. However, the occlusion problem is a difficulty in D2D-VLC. This paper proposes a game theory–based solution in which the best-response dynamics and best-response strategies are used to realize a mode-cooperative selection mechanism. This mechanism uses system capacity as the utility function to optimize system performance and selects the optimal communication mode for each active user from three candidate modes. Moreover, the simulation and experimental results show that the mechanism can attain a significant improvement in terms of effectiveness and energy saving compared with the cases where the users communicate via only the fixed transceivers (light-emitting diode and photo diode) or via only D2D.

Imperfect Best-Response Mechanisms

Best-response Mechanisms, introduced by Nisan et al. (2011) provide a unifying framework for studying various distributed protocols in which the participants are instructed to repeatedly best respond to each others' strategies. Two fundamental features of these mechanisms are convergence and incentive compatibility. This work investigates convergence and incentive compatibility conditions of such mechanisms when players are not guaranteed to always best respond but they rather play an imperfect best-response strategy. That is, at every time step every player deviates from the prescribed best-response strategy according to some probability parameter. The results explain to what extent convergence and incentive compatibility depend on the assumption that players never make mistakes, and how robust such protocols are to noise or mistakes.

Thinking and Learning in the Tax Evasion Game

Equilibrium behaviour is one of the fundamental concepts of economics: that each player's strategy is a best response to their beliefs about other players' strategies (and that these beliefs are realised). It is therefore striking that one of the most utilised economic models of tax compliance (Allingham and Sandmo, 1972) lacks this property as random audit selection is not a best response for the tax administration. The game theory literature of tax compliance has solved the equilibrium under assumptions of perfect information, full rationality and representative agents (Reinganum and Wilde, 1986; Erard and Feinstein, 1994). The recent application of behavioural economics to tax compliance (Hashimzade et al., 2014) allows richer assumptions such as heterogeneity and asymmetric information to be included in agent-based models. This paper investigates the tax administration's best-response audit strategy with heterogeneous taxpayers, imperfect information and evolutionary survival of taxpayers. It finds that, under these conditions, the tax administration's best-response audit strategy is an adaptive learning approach and not a well-defined audit function. This fits with actual practice of ‘predictive analytics’ by OECD tax administrations. Behavioural game theory also predicts that when actors are information rich, adaptive learning will dominate abstract thinking.

Online ascending auctions for gradually expiring items

We consider dynamic auction mechanisms for the allocation of multiple items. Items are identical, but have different expiration times, and each item must be allocated before it expires. Buyers are of dynamic nature, and arrive and depart over time. Our goal is to design mechanisms that maximize the social welfare. We begin by showing that dominant-strategy incentive-compatibility cannot be used in this case, since any such auction cannot obtain any constant fraction of the optimal social welfare. We then design two auctions that perform well under a wide class of “semi-myopic” strategies. For every combination of such strategies, the auction is associated with a different algorithm (or allocation rule), and so we have a family of “semi-myopic” algorithms. We show that any algorithm in this family obtains at least 1/3 of the optimal social welfare. We also provide some game-theoretic justification for acting in a semi-myopic way. We suggest a new notion of “Set-Nash” equilibrium, where we cannot pinpoint a single best-response strategy, but rather only a set to which best-response strategies belong. We show that our auctions have a Set-Nash equilibrium which is all semi-myopic.

Bayesian Population Dynamics of Spreading Species

The invasion by spreading species is one of the most serious threats to biodiversity and ecosystem functioning. Despite a number of empirical and theoretical studies, there is still no general model about why or when settlement becomes an invasion. The purpose of this work is to test a model of Bayesian population dynamics relying on best-response strategies that could help in resource management and bioeconomic modeling. Given the species survival probability, our static game unveils a breaking-level probability in mixed strategies, where the best response for exotic species is to invade and the best response for native species is to resist. In a dynamic setting, we introduce a stochastic version of the balance equation based on conditional probabilities. We find that when the species survival probability and the availability of resources in the ecosystem are respectively high and low, the population rebalancing dynamics operates at a high pace.