Browsing by Subject "Games"
Now showing 1 - 7 of 7
Results Per Page
Sort Options
Item Open Access Binary signaling under subjective priors and costs as a game(Institute of Electrical and Electronics Engineers Inc., 2019) Sarıtaş, S.; Gezici, Sinan; Yüksel, S.; Teel, A. R.; Egerstedt, M.Many decentralized and networked control problems involve decision makers which have either misaligned criteria or subjective priors. In the context of such a setup, in this paper we consider binary signaling problems in which the decision makers (the transmitter and the receiver) have subjective priors and/or misaligned objective functions. Depending on the commitment nature of the transmitter to his policies, we formulate the binary signaling problem as a Bayesian game under either Nash or Stackelberg equilibrium concepts and establish equilibrium solutions and their properties. In addition, the effects of subjective priors and costs on Nash and Stackelberg equilibria are analyzed. It is shown that there can be informative or non-informative equilibria in the binary signaling game under the Stackelberg assumption, but there always exists an equilibrium. However, apart from the informative and non-informative equilibria cases, under certain conditions, there does not exist a Nash equilibrium when the receiver is restricted to use deterministic policies. For the corresponding team setup, however, an equilibrium typically always exists and is always informative. Furthermore, we investigate the effects of small perturbations in priors and costs on equilibrium values around the team setup (with identical costs and priors), and show that the Stackelberg equilibrium behavior is not robust to small perturbations whereas the Nash equilibrium is.Item Open Access A game theoretical model of traffic with multiple interacting drivers for use in autonomous vehicle development(IEEE, 2016) Oyler, D. W.; Yıldız, Yıldıray; Girard, A. R.; Li, N. I.; Kolmanovsky, İ. V.This paper describes a game theoretical model of traffic where multiple drivers interact with each other. The model is developed using hierarchical reasoning, a game theoretical model of human behavior, and reinforcement learning. It is assumed that the drivers can observe only a partial state of the traffic they are in and therefore although the environment satisfies the Markov property, it appears as non-Markovian to the drivers. Hence, each driver implicitly has to find a policy, i.e. a mapping from observations to actions, for a Partially Observable Markov Decision Process. In this paper, a computationally tractable solution to this problem is provided by employing hierarchical reasoning together with a suitable reinforcement learning algorithm. Simulation results are reported, which demonstrate that the resulting driver models provide reasonable behavior for the given traffic scenarios.Item Open Access Hierarchical reasoning game theory based approach for evaluation and testing of autonomous vehicle control systems(IEEE, 2016) Li, N.; Oyler, D.; Zhang, M.; Yıldız, Yıldıray; Girard, A.; Kolmanovsky, İ.A hierarchical game theoretic decision making framework is exploited to model driver decisions and interactions in traffic. In this paper, we apply this framework to develop a simulator to evaluate various existing autonomous driving algorithms. Specifically, two algorithms, based on Stackelberg policies and decision trees, are quantitatively compared in a traffic scenario where all the human-driven vehicles are modeled using the presented game theoretic approach.Item Open Access Nash equilibria for exchangeable team against team games and their mean field limit(IEEE, 2023-07-03) Sanjari, S.; Saldı, Naci; Yüksel, S.We study stochastic mean-field games among finite number of teams each with large finite as well as infinite numbers of decision makers (DMs). We establish the existence of a Nash equilibrium (NE) and show that a NE exhibits exchangeability in the finite DM regime and symmetry in the infinite one. We establish the existence of a randomized NE that is exchangeable (not necessarily symmetric) among DMs within each team for a general class of exchangeable stochastic games. As the number of DMs within each team drives to infinity that is for the mean-field games among teams), using a de Finetti representation theorem, we establish the existence of a randomized NE that is symmetric (i.e., identical) among DMs within each team and also independently randomized. Finally, we establish that a NE for a class of mean-field games among teams (which is symmetric) constitutes an approximate NE for the corresponding pre-limit game among teams with mean-field interaction and large but finite number of DMs.Item Open Access On the number of bins in equilibria for signaling games(IEEE, 2019-07) Sarıtaş, Serkan; Yüksel, Serdar; Gezici, SinanWe investigate the equilibrium behavior for the decentralized quadratic cheap talk problem in which an encoder and a decoder, viewed as two decision makers, have misaligned objective functions. In prior work, we have shown that the number of bins under any equilibrium has to be at most countable, generalizing a classical result due to Crawford and Sobel who considered sources with density supported on [0, 1]. In this paper, we refine this result in the context of exponential and Gaussian sources. For exponential sources, a relation between the upper bound on the number of bins and the misalignment in the objective functions is derived, the equilibrium costs are compared, and it is shown that there also exist equilibria with infinitely many bins under certain parametric assumptions. For Gaussian sources, it is shown that there exist equilibria with infinitely many bins.Item Open Access The performance comparison of different training strategies for reinforcement learning on DeepRTS(IEEE, 2022-08-29) Şahin, Safa Onur; Yücesoy, VeyselIn this paper, we train reinforcement learning agents on the game of DeepRTS under different training strategies, which are i) training against rule based agents, ii) self-training and iii) training by adversarial attack to another agent. We perform certain modifications on the DeepRTS game and the reinforcement learning framework to make it closer to real life decision making problems. For this purpose, we allow agents take macro actions based on human heuristics, where these actions may last multiple time steps and the durations for these actions may differ from each other. In addition, the agents simultaneously take actions for each available unit at a time step. We train the reinforcement learning based agents under three different training strategies and we provide a detailed performance analysis of these agents against several reference agents.Item Open Access Quadratic signaling with prior mismatch at an encoder and decoder: equilibria, continuity, and robustness properties(Institute of Electrical and Electronics Engineers, 2022-01-11) Kazikli, E.; Sartas, S.; Gezici, SinanWe consider communications through a Gaussian noise channel between an encoder and a decoder which have subjective probabilistic models on the source distribution. Although they consider the same cost function, the induced expected costs are misaligned due to their prior mismatch, which requires a game theoretic approach. We consider two approaches: a Nash setup, with no prior commitment, and a Stackelberg solution concept, where the encoder is committed to a given announced policy apriori. We show that the Stackelberg equilibrium cost of the encoder is upper semi continuous, under the Wasserstein metric, as encoder's prior approaches the decoder's prior, and it is also lower semi continuous with Gaussian priors. For the Stackelberg setup, the optimality of affine policies for Gaussian signaling no longer holds under prior mismatch, and thus team-theoretic optimality of linear/affine policies are not robust to perturbations. We provide conditions under which there exist informative Nash and Stackelberg equilibria with affine policies. Finally, we show existence of fully informative Nash and Stackelberg equilibria for the cheap talk problem under an absolute continuity condition.