Game-theoretic Interaction Research Articles

A Three-branch Jointed Feature and Topology Decoder guided by game-theoretic interactions for temporomandibular joint segmentation

Segmentation of the temporomandibular joint (TMJ) disc and condyle from magnetic resonance imaging (MRI) is a crucial task in TMJ internal derangement research. The automatic segmentation of the disc structure presents challenges due to its intricate and variable shapes, low contrast, and unclear boundaries. Existing TMJ segmentation methods often overlook spatial and channel information in features and neglect overall topological considerations, with few studies exploring the interaction between segmentation and topology preservation. To address these challenges, we propose a Three-Branch Jointed Feature and Topology Decoder (TFTD) for the segmentation of TMJ disc and condyle in MRI. This structure effectively preserves the topological information of the disc structure and enhances features. We introduce a cross-dimensional spatial and channel attention mechanism (SCIA) to enhance features. This mechanism captures spatial, channel, and cross-dimensional information of the decoded features, leading to improved segmentation performance. Moreover, we explore the interaction between topology preservation and segmentation from the perspective of game theory. Based on this interaction, we design the Joint Loss Function (JLF) to fully leverage the features of segmentation, topology preservation, and joint interaction branches. Results on the TMJ MRI dataset demonstrate the superior performance of our TFTD compared to existing methods.

Interpretability of Neural Networks Based on Game-theoretic Interactions

Interpretability of Neural Networks Based on Game-theoretic Interactions

Maximum-Entropy Multi-Agent Dynamic Games: Forward and Inverse Solutions

In this article, we study the problem of multiple stochastic agents interacting in a dynamic game scenario with continuous state and action spaces. We define a new notion of stochastic Nash equilibrium for boundedly rational agents, which we call the entropic cost equilibrium (ECE). We show that ECE is a natural extension to multiple agents of maximum entropy optimality for a single agent. We solve both the “forward” and “inverse” problems for the multi-agent ECE game. For the forward problem, we provide a Riccati algorithm to compute closed-form ECE feedback policies for the agents, which are exact in the linear-quadratic-gaussian case. We give an iterative variant to find locally ECE feedback policies for the nonlinear case. For the inverse problem, we present an algorithm to infer the cost functions of the multiple interacting agents given noisy, boundedly rational input and state trajectory examples from agents acting in an ECE. The effectiveness of our algorithms is demonstrated in a simulated multi-agent collision avoidance scenario, and with data from the INTERACTION traffic dataset. In both cases, we show that, by taking into account the agents' game theoretic interactions using our algorithm, a more accurate model of agents' costs can be learned, compared with standard inverse optimal control methods.

FCP-Net: A Feature-Compression-Pyramid Network Guided by Game-Theoretic Interactions for Medical Image Segmentation.

Medical image segmentation is a crucial step in diagnosis and analysis of diseases for clinical applications. Deep convolutional neural network methods such as DeepLabv3+ have successfully been applied for medical image segmentation, but multi-level features are seldom integrated seamlessly into different attention mechanisms, and few studies have fully explored the interactions between medical image segmentation and classification tasks. Herein, we propose a feature-compression-pyramid network (FCP-Net) guided by game-theoretic interactions with a hybrid loss function (HLF) for the medical image segmentation. The proposed approach consists of segmentation branch, classification branch and interaction branch. In the encoding stage, a new strategy is developed for the segmentation branch by applying three modules, e.g., embedded feature ensemble, dilated spatial mapping and channel attention (DSMCA), and branch layer fusion. These modules allow effective extraction of spatial information, efficient identification of spatial correlation among various features, and fully integration of multi-receptive field features from different branches. In the decoding stage, a DSMCA module and a multi-scale feature fusion module are used to establish multiple skip connections for enhancing fusion features. Classification and interaction branches are introduced to explore the potential benefits of the classification information task to the segmentation task. We further explore the interactions of segmentation and classification branches from a game theoretic view, and design an HLF. Based on this HLF, the segmentation, classification and interaction branches can collaboratively learn and teach each other throughout the training process, thus applying the conjoint information between the segmentation and classification tasks and improving the generalization performance. The proposed model has been evaluated using several datasets, including ISIC2017, ISIC2018, REFUGE, Kvasir-SEG, BUSI, and PH2, and the results prove its competitiveness compared with other state-of-the-art techniques.

Abstract B010: Ecological epistasis can drastically alter evolutionary trajectories on genotypic fitness landscapes, maintaining, masking or mimicking genetic selection in evolutionary simulations

Abstract The evolution of drug resistance is broadly understood in terms of the evolution and survival of the genotype that is "fittest" under treatment. There are many computational evolutionary models built upon the assumption that under treatment, cancer cells with the fittest genotype persist and ultimately prevail. Many of these models lack sufficient complexity to predict tumor evolution in the clinic. In particular, the standard Wright-Fisher approach taken from population genetics neither considers nor accurately predicts the heterogeneity that we see in patients and cell-cell interactions are not included. To combat this we develop a model of evolution that incorporates average cell-cell interactions by adding game theoretic interactions to a Wright-Fisher model with mutation and use this to explore and model cases of interest. In our agent-based model we start with N wildtype cells and represent the genotype of each cell with a binary string of n alleles. We represent mutations to the genotype as transitions from 0 to 1 and vice-versa in an allele and each unique genotype is a cell type. Each cell in the non-spatial, well-mixed agent-based model can be selected to reproduce with probability p proportional to the fitness of its genotype and each daughter cell can undergo mutation with probability μ. At each new time step we modify the fitness of each cell type, using the multiplication of the payoff matrix with the cell type frequency vector to reflect the average fitness benefits and costs of cell-cell interactions. We vary the payoff matrices for up to 4 alleles (16 possible genotypes) and show how the addition of these ecological game interactions between different cell populations can modify evolutionary trajectories. We find, for example, that with certain strengths of game interactions, the evolution on an initially selective genotypic landscape can mimic neutral landscapes and vice versa. We term this addition of ecological game interactions to genotypic landscapes "ecological epistasis". We derive mathematical expressions for the equilibrium population distribution in the single allele (two genotype) with arbitrary games case. We also derive expressions for the payoff matrices required to mimic selective games and to make selective landscapes neutral. Furthermore we derive an expression for the curvature of the resultant population distribution, producing a "game signature” with which to probe temporal evolutionary data for the presence of games. This model emphasizes that the emergence of a dominant cell-type can be caused by both ecological and genotypic factors and conversely that the genotypic landscape does not need to be neutral for heterogeneity to persist. Due to the multiclonal and heterogeneous nature of tumors and their microenvironment, these results are of key importance in considering treatment approaches and interpreting existing patient data. We highlight how game interactions may explain heterogeneous patient outcomes and contradicting results on the fitness of cancer genotypes in the literature. Citation Format: Steph J. Owen, Michael Hinczewski, Jacob G. Scott. Ecological epistasis can drastically alter evolutionary trajectories on genotypic fitness landscapes, maintaining, masking or mimicking genetic selection in evolutionary simulations [abstract]. In: Proceedings of the AACR Special Conference on the Evolutionary Dynamics in Carcinogenesis and Response to Therapy; 2022 Mar 14-17. Philadelphia (PA): AACR; Cancer Res 2022;82(10 Suppl):Abstract nr B010.

Game-environment feedback dynamics in growing population: Effect of finite carrying capacity

The tragedy of the commons (TOC) is an unfortunate situation where a shared resource is exhausted due to uncontrolled exploitation by the selfish individuals of a population. Recently, the paradigmatic replicator equation has been used in conjunction with a phenomenological equation for the state of the shared resource to gain insight into the influence of the games on the TOC. The replicator equation, by construction, models a fixed infinite population undergoing microevolution. Thus, it is unable to capture any effect of the population growth and the carrying capacity of the population although the TOC is expected to be dependent on the size of the population. Therefore, in this paper, we present a mathematical framework that incorporates the density dependent payoffs and the logistic growth of the population in the eco-evolutionary dynamics modeling the game-resource feedback. We discover a bistability in the dynamics: a finite carrying capacity can either avert or cause the TOC depending on the initial states of the resource and the initial fraction of cooperators. In fact, depending on the type of strategic game-theoretic interaction, a finite carrying capacity can either avert or cause the TOC when it is exactly the opposite for the corresponding case with infinite carrying capacity.

A game-theoretic model of water theft during a drought

We study water use by two geographically proximate farmers in a particular region during a drought. The two farmers each have an endowment of time that can be used either to produce water or to steal water. The price of water is exogenously given. The goal of the two farmers is to maximize their wealth from water production and water theft. In this setting, we perform three tasks. First, we determine the Nash equilibrium of the game-theoretic interaction between the two farmers. Second, we study how this equilibrium depends on the ease with which water can be stolen. Finally, we show how the preceding equilibrium is impacted when there is no water theft and then we determine the maximum amount that a farmer would be willing to pay to prevent theft.

To Infinity and Beyond: Financing Platforms With Uncapped Crypto Tokens

Problem: Initial Coin Offerings (ICOs) are an emerging form of crowdfunding for blockchain-based startups. While ICO design varies greatly in practice, many service-based platforms (e.g., Ethereum), use structures that forego limits on token supply, subjecting early investors to dilution risk. In this paper, we examine the conditions under which such ICOs are optimal and provide guidance for their optimal design. Relevance: Despite their popularity in practice, uncapped ICOs are understudied and not as well understood as their capped counterparts. Methodology: We model game-theoretic interactions among various stakeholders in an infinite-horizon setting with network effects, taking account of operational details. Results: We show that uncapped ICOs weakly dominate capped ones in the context of service platforms. In terms of design, a platform commission and regulation are generally substitutes when it comes to overcoming moral hazard, but can also be combined to make ICOs more accessible, especially for platforms with high initial setup costs. ICO accessibility can also be increased by employing a dual token offering (security & transaction tokens), at the cost of reduced expected profit. Implications: The paper provides a theoretical underpinning for the use of uncapped ICOs in practice. At a high level, it shows that ICOs succeed more easily in the presence of regulation, and platforms with low (high) setup costs should preferably issue utility (dual token) type ICOs.

On Modeling Link Flooding Attacks and Defenses

The increasing popularity of Internet of Things (IoTs) is making people universally connected and thus bringing the ease of life. Because of their sheer volume, weak security, and continual operation, IoT devices, along with many computer servers, are widely compromised to launch powerful distributed denial-of-service (DDoS) attacks. The emerging link flooding attacks (LFAs) are one type of such attacks that attract significant attention in both academia and industry against the routing infrastructure. The attack traffic flows originating from bots (e.g., compromised IoT devices) are deliberately aggregated at upstream critical links and grow intensified, gradually making a network connected to the critical links disconnected. Although LFAs are far more sophisticated than traditional DDoS attacks, whether such sophistication comes without a downside has never been investigated. In this paper, by modeling link flooding attacks and defenses, we tackle a series of questions concerning the practical issues of LFAs. Specifically, from the perspective of attacks, we advance a novel notion of strike precision, and reveal that LFAs may exhibit attack interference (i.e., unexpectedly interfere the connectivity of innocent networks) which might undermine the stealthiness and persistence of LFAs. From the perspective of defenses, we make the first step to study attack intention, i.e., inversely inferring the target network to disconnect based on the identified links under attack. Furthermore, we consider a strong defender who employs traffic engineering to mitigate LFAs, and formulate the game-theoretic interactions between attackers and defenders. Our formulation demonstrates that LFAs can be effectively mitigated based on traffic engineering from a game-theoretic perspective. We also study practical issues of non-cooperative defenses (e.g., light-weight probe deployment, multi-protocol-based measurement).

Robust optimization for transmission defense against multi-period attacks with uncertainties

The power system is under increasing threat of terrorist attacks, and it is important to develop efficient methods to improve the power system resiliency for defending against the attacks. In this paper, the defense strategy of the transmission system in case of multi-period attacks considering uncertainties is investigated. The problem formulation involves a multi-stage decision process: first, the defender chooses the critical branches to harden for the purpose of minimizing the expected damage; second, the attacker may launch multiple attacks to disrupt the branches aiming to maximize the damage; third, following each of the attacks, the operator performs the optimal power re-dispatch to minimize the load shedding. A novel robust optimization-based Defender-Sequential-Attacker-Operator (DSAO) model is developed, which considers game-theoretic interactions between different agents (the defender, attacker and operator), selection of attacking targets, as well as the probabilities of attacks and correlations between attacks. A hybrid solution approach consisting of both robust optimization and stochastic programming is developed to solve the DSAO model. Case studies based on the IEEE RTS79 and 118-bus systems validate the proposed approach. In addition, detailed comparisons are made with the explicit enumeration method and the recent trilevel defender-attacker-defender (DAD) model, which demonstrates the accuracy and computational efficiency of the proposed approach.

Applications of Utility Functions to Modeling of Expectations Are Non-Robust, Are ‘Out of Whack’

This research note provides clear, unambiguous rationalization for the normative that applications of utility functions to modeling of expectations are non-robust, are, in relation to best practice, out of whack. With this inference in tow, all formal theoretical studies that apply utility functions to modeling of any of Game Theoretic Interactions (GTIs), General Equilibriums (GEs) - as distinct from models of General Disequilibrium - or Rational Expectations Equilibriums (REEs), all of which are exercises in modeling of expectations, are non-robust, as such out of whack with best practice. With allusions to successful implementations in context of markets for managed funds, markets for IPOs, modeling of preferences, and labor markets in tow, the note provides an introduction to effectiveness of probability measures as robust alternatives for modeling of expectations.

Combining network theory with corporate governance: Converging models for connected stakeholders

Traditional corporate governance patterns are based on the interaction among composite stakeholders and the various forms of separation between ownership and control. Stakeholders cooperate around the Coasian firm represented by a nexus of increasingly complex contracts. These well-known occurrences have been deeply investigated by growing literature and nurtured by composite empirical evidence. Apparently, unrelated network theory is concerned with the study of graphs as a representation of (a)symmetric relations between discrete objects (nodes connected by links). Network theory is highly interdisciplinary, and its versatile nature is fully consistent with the complex interactions of (networked) stakeholders, even in terms of game-theoretic patterns. The connection between traditional corporate governance issues and network theory properties is, however, still under-investigated. Hence the importance of an innovative reinterpretation that brings to “network governance”. Innovation may, for instance, concern the principal-agent networked relationships and their conflicts of interest or the risk contagion and value drivers – three core governance issues. Networks and their applications (like blockchains, P2P platforms, game-theoretic interactions or digital supply chains) foster unmediated decentralization. In decentralized digital platforms stakeholders inclusively interact, promoting cooperation and sustainability. To the extent that network properties can be mathematically measured, governance issues may be quantified and traced with recursive patterns of expected occurrences.

Towards More Realistic Modeling of Linguistic Color Categorization

Abstract The ways in which languages have come to divide the visible spectrum with their color terminology, in both their variety and the apparent universal tendencies, are still largely unexplained. Building on recent work in modeling color perception and categorization, as well as the theory of signaling games, we incrementally construct a color categorization model which combines perceptual characteristics of individual agents, game-theoretic signaling interaction of these agents, and the probability of observing particular colors as an environmental constraint. We also propose a method of transparent evaluation against the data gathered in the World Color Survey. The results show that the model’s predictive power is comparable to the current state of the art. Additionally, we argue that the model we suggest is superior in terms of motivation of the principles involved, and that its explanatory relevance with respect to color categorization in languages is therefore higher. Our results suggest that the universal tendencies of color categorization cannot be explained solely in terms of the shape of the color space induced by our perceptual apparatus. We believe that only by taking the heterogeneity of the phenomenon seriously can we acquire a deeper understanding of why color categorization takes the forms we observe across languages.

Evolution of fixed demographic heterogeneity from a game of stable coexistence

Background: Demographic heterogeneity refers to the observation that – within the same population – trajectories of survival and reproduction differ substantially between individuals. These differences have been found in both natural and captive populations. Models in ecology and evolution that incorporate demographic heterogeneity can improve both our understanding of the evolution of mortality curves and our population management abilities. Current explanations of the origin of demographic heterogeneity mostly revolve around interindividual differences that are either present at birth (fixed heterogeneity) or the result of stochasticity in life history realization (dynamic heterogeneity). Largely neglected remains the possibility that a form of fixed heterogeneity may evolve from interactions between behaviorally distinct individuals through their lifespan. Objective: We suggest one possible way in which heterogeneity in vital rates may evolve. Our approach assumes game theoretic interactions in the population. Methods: We combine population matrix models and game theory. We study a stable coexistence game between two types that are initially demographically homogeneous and analyze the effect of mutations that influence the trajectories of survival and reproduction. Results: The rise and fixation of mutations can make the population demographically heterogeneous, while the game can preserve the coexistence of different types in the population. Conclusions: Frequency-dependent selection can help to explain the evolution of demographic heterogeneity. Contribution: Frequency-dependent selection can maintain already existing demographic heterogeneity in a population without overlapping generations. Here, we show that this form of selection can also be involved in the origin of a form of fixed heterogeneity.

Game Theoretic Interaction and Decision: A Quantum Analysis

An interaction system has a finite set of agents that interact pairwise, depending on the current state of the system. Symmetric decomposition of the matrix of interaction coefficients yields the representation of states by self-adjoint matrices and hence a spectral representation. As a result, cooperation systems, decision systems and quantum systems all become visible as manifestations of special interaction systems. The treatment of the theory is purely mathematical and does not require any special knowledge of physics. It is shown how standard notions in cooperative game theory arise naturally in this context. In particular, states of general interaction systems are seen to arise as linear superpositions of pure quantum states and Fourier transformation to become meaningful. Moreover, quantum games fall into this framework. Finally, a theory of Markov evolution of interaction states is presented that generalizes classical homogeneous Markov chains to the present context.

Distributed control of flexible demand using proportional allocation mechanism in a smart grid: Game theoretic interaction and price of anarchy

Abstract Demand side management leveraging flexibility of electric loads is a promising approach to reduce peak demand and to maintain supply–demand balance in future power grids with large scale renewable penetration. Distributed control is an important tool used for managing the demand side. In this paper, we develop a distributed method for coordinated control of flexible loads. In an intra-day setting, based on the supply schedule of thermal generators and predicted supply of renewable generators, a central control authority sets up price to maximize social welfare. This can be done using proportional allocation mechanism assuming that the consumers are price takers. If the consumers are price anticipators, the corresponding situation is modeled using non-cooperative game theory and existence of Nash equilibrium is established. Selfish behavior of agents in such a game theoretic set-up can reduce the efficiency of the overall system as compared to centralized control. In this paper, we are able to bound the efficiency loss for our game. The lower bound on the price of anarchy (PoA) for our game is found to be 0.75. For a non-cooperative game in a smart grid with flexible loads having different operating constraints and having utility functions that are non-separable with respect to time, this result is a new contribution to the demand response literature.

A quest toward a mathematical theory of the dynamics of swarms

This paper addresses some preliminary steps toward the modeling and qualitative analysis of swarms viewed as living complex systems. The approach is based on the methods of kinetic theory and statistical mechanics, where interactions at the microscopic scale are nonlocal, nonlinearly additive and modeled by theoretical tools of stochastic game theory. Collective learning theory can play an important role in the modeling approach. We present a kinetic equation incorporating the Cucker–Smale flocking force and stochastic game theoretic interactions in collision operators. We also present a sufficient framework leading to the asymptotic velocity alignment and global existence of smooth solutions for the proposed kinetic model with a special kernel. Analytic results on the global existence and flocking dynamics are presented, while the last part of the paper looks ahead to research perspectives.

Coordination of forest management through market and political institutions

Most forests worldwide are influenced or even dominated by political institutions governed by multilateral agreements. Forestry economic theory is yet mainly concentrated on bilateral exchanges within market institutions. This paper shows how the harvest and regeneration of trees as the objectively observable outcome of forest management vary with the institutional framework. Existing coordination theorems of market institutions are derived from a game theoretic interaction model which allows to extend the institutional setting towards political coordination of forest management. The analysis reveals that privately optimal harvest ages are restricted to fully internalized interdependence settings while external effects under collective ownership cannot be internalized via implicit coordination or exchanges of individual property rights. The derivation of an intertemporal model of public forestry goods provides empirically testable hypotheses on the evolution of forests within political institutional settings.

Existence of Equilibria and Complexity of Computation in Optimizing Complex Systems

This paper characterizes the generic properties of interior equilibria in complex systems. The field of complexity has been growing and is concerned with the complexity of computation of complex systems. Complex systems are characterized as systems with a large number of adaptive interdependent parts. These systems demonstrate several properties including: emergence, where the whole does not act as the sum of the parts, and sensitivity to initial conditions. As the number of economic factors increases, the recursion of input-output and modeling error propagates. These two particular symptoms of complex systems make them difficult to model. Solutions to optimization problems of this sort may have different properties depending on the functional assumptions. The generic properties of solutions to these problems can help us have some expectations over the complexity of computation. One example of a complex system is the Game Theoretic Interaction between economic agents. The paper also attempts to shed light on the complexity of computation of such systems.

Optimal choices of fare collection systems for public transportations: Barrier versus barrier-free

The present study focuses on two major types of fare collection systems for public transportations, barrier and barrier-free, and provides a mathematical framework to evaluate optimal choices between them, i.e., which system can be more profitable for a transit agency. In particular, we consider game-theoretic interactions between the transit agency and passengers for the barrier-free system and suppose that frequencies of free rides of passengers as well as inspections of the transit agency are given as a Nash equilibrium. Then the optimal choice of fare collection system is described as a subgame perfection solution in an extensive form game. We also conduct a comparative static analysis and examine how each parameter can affect the choice. As an application, we use the framework to explain various choices of fare collection systems in our society depending on local circumstances or transportation types.