BUIR Repository :: Browsing by Subject "Game theory"

Browsing by Subject "Game theory"

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Open Access
An Application of Expected Utility Modeling and Game Theory in IR: Assessment of International Bargaining on Iran’s Nuclear Program
(Dış Politika ve Barış Araştırmaları Merkezi, İhsan Doğramacı Barış Vakfı, 2019) Özdamar, Özgür
This article provides an introduction to the theoretical underpinnings of expected utility and game theory approaches in IR studies. It goes on to explore their application to a specific research subject, international bargaining on Iran’s nuclear program. In this application, the article presents forecasts about Iran’s nuclear program using a game theoretic, bounded rationality model called the expected utility model (Bueno de Mesquita 2002). Three analyses were made in December 2005, September 2006 and March 2007. All three forecasts appear to be in line with real-life developments regarding the issue. The results show that Iran has been losing international support since the analyses started, and the last forecast suggests a pro-US position supported by all major international actors. Also, all three analyses suggest that Russian and Chinese support is vital to curb the Iranian nuclear program.
Open Access
Camera-based virtual environment interaction on mobile devices
(Springer, 2006-11) Çapin, Tolga; Haro, A.; Setlur, V.; Wilkinson, S.
Mobile virtual environments, with real-time 3D and 2D graphics, are now possible on smart phone and other camera-enabled devices. Using computer vision, the camera sensor can be treated as an input modality in applications by analyzing the incoming live video. We present our tracking algorithm and several mobile virtual environment and gaming prototypes including: a 3D first person shooter, a 2D puzzle game and a simple action game. Camera-based interaction provides a user experience that is not possible through traditional means, and maximizes the use of the limited display size. © Springer-Verlag Berlin Heidelberg 2006.
Open Access
Centralized and decentralized management of groundwater with multiple users
(Elsevier, 2011) Saleh, Y.; Gürler, Ü.; Berk, E.
In this work, we investigate two groundwater inventory management schemes with multiple users in a dynamic game-theoretic structure: (i) under the centralized management scheme, users are allowed to pump water from a common aquifer with the supervision of a social planner, and (ii) under the decentralized management scheme, each user is allowed to pump water from a common aquifer making usage decisions individually in a non-cooperative fashion. This work is motivated by the work of Saak and Peterson [14], which considers a model with two identical users sharing a common aquifer over a two-period planning horizon. In our work, the model and results of Saak and Peterson [14] are generalized in several directions. We first build on and extend their work to the case of n non-identical users distributed over a common aquifer region. Furthermore, we consider two different geometric configurations overlying the aquifer, namely, the strip and the ring configurations. In each configuration, general analytical results of the optimal groundwater usage are obtained and numerical examples are discussed for both centralized and decentralized problems.
Open Access
Common knowledge and state-dependent equilibria
(Springer, Berlin, Heidelberg, 2012) Dalkıran, Nuh Aygun; Hoffman, M.; Paturi, R.; Ricketts, D.; Vattani, A.
Many puzzling social behaviors, such as avoiding eye contact, using innuendos, and insignificant events that trigger revolutions, seem to relate to common knowledge and coordination, but the exact relationship has yet to be formalized. Herein, we present such a formalization. We state necessary and sufficient conditions for what we call state-dependent equilibria - equilibria where players play different strategies in different states of the world. In particular, if everybody behaves a certain way (e.g. does not revolt) in the usual state of the world, then in order for players to be able to behave a different way (e.g. revolt) in another state of the world, it is both necessary and sufficient for it to be common p-believed that it is not the usual state of the world, where common p-belief is a relaxation of common knowledge introduced by Monderer and Samet [16]. Our framework applies to many player r-coordination games - a generalization of coordination games that we introduce - and common (r,p)-beliefs - a generalization of common p-beliefs that we introduce. We then apply these theorems to two particular signaling structures to obtain novel results. © 2012 Springer-Verlag.
Open Access
Consensus as a Nash equilibrium of a dynamic game
(IEEE, 2016) Niazi, Muhammad Umar B.; Özgüler, Arif Bülent; Yıldız, Aykut
Consensus formation in a social network is modeled by a dynamic game of a prescribed duration played by members of the network. Each member independently minimizes a cost function that represents his/her motive. An integral cost function penalizes a member's differences of opinion from the others as well as from his/her own initial opinion, weighted by influence and stubbornness parameters. Each member uses its rate of change of opinion as a control input. This defines a dynamic non-cooperative game that turns out to have a unique Nash equilibrium. Analytic explicit expressions are derived for the opinion trajectory of each member for two representative cases obtained by suitable assumptions on the graph topology of the network. These trajectories are then examined under different assumptions on the relative sizes of the influence and stubbornness parameters that appear in the cost functions.
Open Access
Contracting under uncertain capacity
(Inderscience publishers, 2010) Jemai, Z.; Erkip, N. K.; Dallery, Y.
In this paper, we develop a two-stage supply-chain in which a supplier with uncertain capacity sells to a retailer facing a Newsvendor problem. We analyze the centralized system where both partners take their decisions to optimize the expected system profit and the decentralized system where they make decisions individually. We show that, in a framework of Stackelberg equilibrium, the decentralized model is less efficient than the centralized model and we propose a buy-back contract that coordinates the system.
Open Access
Coordination of staffing and pricing decisions in a service firm
(John Wiley & Sons, 2008) Serel, D. A.; Erel, E.
Customer demand is sensitive to the price paid for the service in many service environments. Using queueing theory framework, we develop profit maximization models for jointly determining the price and the staffing level in a service company. The models include constraints on the average waiting time and the blocking probability. We show convexity of the single-variable subproblem under certain plausible assumptions on the demand and staffing cost functions. Using numerical examples, we investigate the sensitivity of the price and the staffing level to changes in the marginal service cost and the user-specified constraint on the congestion measure.
Open Access
Design and analysis of mechanisms for decentralized joint replenishment
(Elsevier B.V., 2017) Güler, K.; Körpeoğlu, E.; Şen, A.
We consider jointly replenishing multiple firms that operate under an EOQ like environment in a decentralized, non-cooperative setting. Each firm's demand rate and inventory holding cost rate are private information. We are interested in finding a mechanism that would determine the joint replenishment frequency and allocate the joint ordering costs to these firms based on their reported stand-alone replenishment frequencies (if they were to order independently). We first provide an impossibility result showing that there is no direct mechanism that simultaneously achieves efficiency, incentive compatibility, individual rationality and budget-balance. We then propose a general, two-parameter mechanism in which one parameter is used to determine the joint replenishment frequency, another is used to allocate the order costs based on firms’ reports. We show that efficiency cannot be achieved in this two-parameter mechanism unless the parameter governing the cost allocation is zero. When the two parameters are same (a single parameter mechanism), we find the equilibrium share levels and corresponding total cost. We finally investigate the effect of this parameter on equilibrium behavior. We show that properly adjusting this parameter leads to mechanisms that are better than other mechanisms suggested earlier in the literature in terms of fairness and efficiency. © 2016 Elsevier B.V.
Open Access
Dynamic signaling games with quadratic criteria under Nash and Stackelberg equilibria
(Elsevier, 2020-01) Sarıtaş, Serkan; Yüksel, Serdar; Gezici, Sinan
This paper considers dynamic (multi-stage) signaling games involving an encoder and a decoder who have subjective models on the cost functions. We consider both Nash (simultaneous-move) and Stackelberg (leader–follower) equilibria of dynamic signaling games under quadratic criteria. For the multi-stage scalar cheap talk, we show that the final stage equilibrium is always quantized and under further conditions the equilibria for all time stages must be quantized. In contrast, the Stackelberg equilibria are always fully revealing. In the multi-stage signaling game where the transmission of a Gauss–Markov source over a memoryless Gaussian channel is considered, affine policies constitute an invariant subspace under best response maps for Nash equilibria; whereas the Stackelberg equilibria always admit linear policies for scalar sources but such policies may be non-linear for multi-dimensional sources. We obtain an explicit recursion for optimal linear encoding policies for multi-dimensional sources, and derive conditions under which Stackelberg equilibria are informative.
Open Access
Essays in collective decision making
(2014-10) Derya, Ayşe Mutlu
Four different problems in collective decision making are studied, all of which are either formulated directly in a game-theoretical context or are concerned with neighboring research areas. The rst two problems fall into the realm of cooperative game theory. In the first one, a decomposition of transferable utility games is introduced. Based on that decomposition, the structure of the set of all transferable utility games is analyzed. Using the decomposition and the notion of minimal balanced collections, a set of necessary and sufficient conditions for a transferable utility game to have a singleton core is given. Then, core selective allocation rules that, when confronted with a change in total cost, not only distribute the initial cost in the same manner as before, but also treat the remainder in a consistent way are studied. Core selective rules which own a particular kind of additivity that turns out to be relevant in this context are also characterized. In the second problem, different notions of merge proofness for allocation rules pertaining to transferable utility games are introduced. Relations between these merge proofness notions are studied, and some impossibility as well as possibility results for allocation rules are established, which are also extended to allocation correspondences. The third problem deals with networks. A characterization of the Myerson value with two axioms is provided. The first axiom considers a situation where there is a change in the value function at a network g along with all networks containing g. At such a situation, the axiom requires that this change is to be divided equally between all the players in g who are not isolated. The second axiom requires that if the value function assigns zero to each network, then each player gets zero payo at each network. Modifying the rst axiom, along a characterization of the Myerson value, a characterization of the position value is also provided. Finally, the fourth problem is concerned with social choice theory which deals with collective decision making in a society. A characterization of the Borda rule for a given set of alternatives with a variable number of voters is studied on the domain of weak preferences, where indi erences between alternatives are allowed at agents' preferences. A new property, which we refer to as degree equality, is introduced. A social choice rule satis es degree equality if and only if, for any two pro les of two nite sets of voters, equality between the sums of the degrees of every alternative under these two pro les implies that the same alternatives get chosen at both of them. The Borda rule is characterized by the conjunction of faithfulness, reinforcement, and degree equality on the domain of weak preferences.
Open Access
Essays on non-cooperative inventory games
(2012) Körpeoğlu, Evren
In this thesis we study different non–cooperative inventory games. In particular, we focus on joint replenishment games and newsvendor duopoly under asymmetric information. Chapter 1 contains introduction and motivation behind the research. Chapter 2 is a preliminary chapter which introduce basic concepts used in the thesis such as Nash equilibrium, Bayesian Nash equilibrium and mechanism design. In Chapter 3, we study a non-cooperative game for joint replenishment of multiple firms that operate under an EOQ–like setting. Each firm decides whether to replenish independently or to participate in joint replenishment, and how much to contribute to joint ordering costs in case of participation. Joint replenishment cycle time is set by an intermediary as the lowest cycle time that can be financed with the private contributions of participating firms. We consider two variants of the participation-contribution game: in the single–stage variant, participation and contribution decisions are made simultaneously, and, in the two-stage variant, participating firms become common knowledge at the contribution stage. We characterize the behavior and outcomes under undominated Nash equilibria for the one-stage game and subgame-perfect equilibrium for the two-stage game. In Chapter 4, we extend the private contributions game to an asymmetric information counterpart. We assume each firm only knows the probability distribution of the other firms’ adjusted demand rates (demand rate multiplied by inventory holding cost rate). We show the existence of a pure strategy Bayesian Nash equilibrium for the asymmetric information game and provide its characterization. Finally, we conduct some numerical study to examine the impact of information asymmetry on expected and interim values of total contributions, cycle times and total costs. quantities for all firm types except the type that has the highest possible unit cost, who orders the same quantity as he would as a monopolist newsboy. Consequently, competition leads to higher total inventory in the industry. A firm’s equilibrium order quantity increases with a stochastic increase in the total industry demand or with an increase in his initial allocation of the total industry demand. Finally, we provide full characterization of the equilibrium, corresponding payoffs and comparative statics for a parametric special case with uniform demand and linear market shares.
Open Access
Evolutionary explanations of Syrian—Turkish water conflict
(Springer, Dordrecht, 2008) Güner, Serdar Ş.; Wiegandt, E.
The issues of water and territory dominate relations between Syria and Turkey, upstream and downstream riparians in the Euphrates and Tigris basin. This chapter propose an evolutionary game to explore eventual trajectories of riparian relations. Turkish hawks are defined as those Turkish foreign policies that support no water concessions. Turkish doves can instead support the flow of an increased amount of water to Syria on the basis of an international agreement. Syrian hawks are those Syrian foreign policies that do not recognize Turkish sovereignty over Hatay—also known as the Sandjak of Alexandretta. Syrian doves can in turn accept that the territory belongs now to Turkey. It is found that evolutionary stability does not depend upon the values territory and water represent for the fitness of Syrian and Turkish foreign policies. No evolutionary stability is possible unless doves are cooperative towards hawks. If doves are cooperative towards hawks, the unique evolutionarily stable outcome implies their extinction. Riparian relations will ultimately evolve into mutual intransigence.
Open Access
Foraging swarms as Nash equilibria of dynamic games
(IEEE, 2014) Özgüler, A. B.; Yildiz, A.
The question of whether foraging swarms can form as a result of a noncooperative game played by individuals is shown here to have an affirmative answer. A dynamic game played by N agents in 1-D motion is introduced and models, for instance, a foraging ant colony. Each agent controls its velocity to minimize its total work done in a finite time interval. The game is shown to have a unique Nash equilibrium under two different foraging location specifications, and both equilibria display many features of a foraging swarm behavior observed in biological swarms. Explicit expressions are derived for pairwise distances between individuals of the swarm, swarm size, and swarm center location during foraging.
Open Access
Game theoretic modeling of driver and vehicle interactions for verification and validation of autonomous vehicle control systems
(Institute of Electrical and Electronics Engineers, 2018) Li, N.; Oyler, D.W.; Zhang M.; Yildız, Yıldıray; Kolmanovsky, I.; Girard, A. R.
Autonomous driving has been the subject of increased interest in recent years both in industry and in academia. Serious efforts are being pursued to address legal, technical, and logistical problems and make autonomous cars a viable option for everyday transportation. One significant challenge is the time and effort required for the verification and validation of the decision and control algorithms employed in these vehicles to ensure a safe and comfortable driving experience. Hundreds of thousands of miles of driving tests are required to achieve a well calibrated control system that is capable of operating an autonomous vehicle in an uncertain traffic environment where interactions among multiple drivers and vehicles occur simultaneously. Traffic simulators where these interactions can be modeled and represented with reasonable fidelity can help to decrease the time and effort necessary for the development of the autonomous driving control algorithms by providing a venue where acceptable initial control calibrations can be achieved quickly and safely before actual road tests. In this paper, we present a game theoretic traffic model that can be used to: 1) test and compare various autonomous vehicle decision and control systems and 2) calibrate the parameters of an existing control system. We demonstrate two example case studies, where, in the first case, we test and quantitatively compare two autonomous vehicle control systems in terms of their safety and performance, and, in the second case, we optimize the parameters of an autonomous vehicle control system, utilizing the proposed traffic model and simulation environment. IEEE
Open Access
A game theoretical framework for the evaluation of unmanned aircraft systems airspace integration concepts
(2017-07) Musavi, Neginsadat
Predicting the outcomes of integrating Unmanned Aerial Systems (UAS) into the National Aerospace (NAS) is a complex problem which is required to be addressed by simulation studies before allowing the routine access of UAS into the NAS. This thesis focuses on providing 2D and 3D simulation frameworks using a game theoretical methodology to evaluate integration concepts in scenarios where manned and unmanned air vehicles co-exist. The fundamental gap in the literature is that the models of interaction between manned and unmanned vehicles are insu cient: a) they assume that pilot behavior is known a priori and b) they disregard decision making processes. The contribution of this work is to propose a modeling framework, in which, human pilot reactions are modeled using reinforcement learning and a game theoretical concept called level-k reasoning to ll this gap. The level-k reasoning concept is based on the assumption that humans have various levels of decision making. Reinforcement learning is a mathematical learning method that is rooted in human learning. In this work, a classical and an approximate reinforcement learning (Neural Fitted Q Iteration) methods are used to model time-extended decisions of pilots with 2D and 3D maneuvers. An analysis of UAS integration is conducted using example scenarios in the presence of manned aircraft and fully autonomous UAS equipped with sense and avoid algorithms.
Open Access
A game theoretical modeling and simulation framework for the integration of unmanned aircraft systems in to the national airspace
(AIAA, 2016) Musavi, Negin; Tekelioğlu, K. B.; Yıldız, Yıldıray; Güneş, Kerem; Onural, Deniz
The focus of this paper is to present a game theoretical modeling and simulation frame- work for the integration of Unmanned Aircraft Systems (UAS) into the National Airspace system (NAS). The problem of predicting the outcome of complex scenarios, where UAS and manned air vehicles co-exist, is the research problem of this work. The fundamental gap in the literature in terms of developing models for UAS integration into NAS is that the models of interaction between manned and unmanned vehicles are insufficient. These models are insufficient because a) they assume that human behavior is known a priori and b) they disregard human reaction and decision making process. The contribution of this paper is proposing a realistic modeling and simulation framework that will fill this gap in the literature. The foundations of the proposed modeling method is formed by game theory, which analyzes strategic decision making between intelligent agents, bounded rationality concept, which is based on the fact that humans cannot always make perfect decisions, and reinforcement learning, which is shown to be effective in human behavior in psychology literature. These concepts are used to develop a simulator which can be used to obtain the outcomes of scenarios consisting of UAS, manned vehicles, automation and their interactions. An analysis of the UAS integration is done with a specifically designed scenario for this paper. In the scenario, a UAS equipped with sense and avoid algorithm, moves along a predefined trajectory in a crowded airspace. Then the effect of various system parameters on the safety and performance of the overall system is investigated.
Open Access
Game-theoretic modeling of traffic in unsignalized intersection network for autonomous vehicle control verification and validation
(IEEE, 2020) Tian, R.; Li, N.; Kolmanovsky, I.; Yıldız, Yıldıray; Girard, A. R.
For a foreseeable future, autonomous vehicles (AVs) will operate in traffic together with human-driven vehicles. Their planning and control systems need extensive testing, including early-stage testing in simulations where the interactions among autonomous/human-driven vehicles are represented. Motivated by the need for such simulation tools, we propose a game-theoretic approach to modeling vehicle interactions, in particular, for urban traffic environments with unsignalized intersections. We develop traffic models with heterogeneous (in terms of their driving styles) and interactive vehicles based on our proposed approach, and use them for virtual testing, evaluation, and calibration of AV control systems. For illustration, we consider two AV control approaches, analyze their characteristics and performance based on the simulation results with our developed traffic models, and optimize the parameters of one of them.
Open Access
Guessing subject to distortion
(Institute of Electrical and Electronics Engineers, 1998-05) Arikan, E.; Merhav, N.
We investigate the problem of guessing a random vector X within distortion level D. Our aim is to characterize the best attainable performance in the sense of minimizing, in some probabilistic sense, the number of required guesses G(X) until the error falls below D. The underlying motivation is that G(X) is the number of candidate codewords to be examined by a rate-distortion block encoder until a satisfactory codeword is found. In particular, for memoryless sources, we provide a single-letter characterization of the least achievable exponential growth rate of the ρth moment of G(X) as the dimension of the random vector X grows without bound. In this context, we propose an asymptotically optimal guessing scheme that is universal both with respect to the information source and the value of ρ. We then study some properties of the exponent function E(D, ρ) along with its relation to the source-coding exponents. Finally, we provide extensions of our main results to the Gaussian case, guessing with side information, and sources with memory.
Open Access
Heterogeneity and strategic sophistication in multi-agent reinforcement learning
(2024-08) Arslantaş, Yüksel
Decision-making powered by artificial intelligence (AI) is becoming increasingly prevalent in socio-technical systems such as finance, smart transportation, security, and robotics. Therefore, there is a critical need for developing the theoretical foundation of how multiple AI decision-makers interact with each other and with humans in order to ensure their reliable use in these systems. Since multiple AI decision-makers make decisions autonomously without central coordination, heterogeneity of their algorithms is inevitable. We establish a theoretical framework for the impact of heterogeneity on multi-agent sequential decision-making under uncertainty. First, we examine the potential heterogeneity of independent learning algorithms assuming that opponents play according to some stationary strategy. To this end, we present a broad family of algorithms that encompass widely-studied dynamics such as fictitious play and Q-learning. While existing convergence results only consider homogeneous cases, where each agent uses the same algorithm; we show that they can still converge to equilibrium if they follow any two different members of this algorithm family. This strengthens the predictive power of game-theoretic equilibrium analysis for heterogeneous systems. We then analyze how a strategically sophisticated agent can manipulate independent learning algorithms, revealing the vulnerability of such independent reinforcement learning algorithms. Finally, we demonstrate the practical implications of our findings by implementing our results in stochastic security games, highlighting its potential for real-life applications, and explore the impact of strategic AI in human-AI interactions in cyberphysical systems.
Embargo
Integrating efforts for product development and market penetration
(Elsevier BV, 2023-07-16) Demirci, Ece Zeliha; Erkip, Nesim
In this paper, we build a decision model to explore an innovative firm’s budget allocation problem, which needs to be solved for each successive generation of a product. The firm introduces the product to the market through a distributor while aiming to maximize the market potential. This goal can be achieved by investing in R&D and increasing availability using subsidies registered to the distributor. We analyze the problem using a game theoretical model and provide a guideline for the funding strategy. We show that the optimal budget allocation decision is characterized by two budget thresholds and a threshold on the cost efficiency of R&D. We identify and analyze the effects of two significant parameters, total available budget and efficiency level of R&D, on the optimal solution. In addition, we assess the model’s applicability by examining the expected excess budget requirement and the distributor’s expected profit. We provide valuable managerial insights on when and how to prioritize the two components of the budget.