On multi-dimensional and noisy quadratic signaling games and affine equilibria

Sarıtaş, Serkan; Yüksel, Serdar; Gezici, Sinan

doi:10.1109/acc.2015.7172182

Cited by 7 publications

(11 citation statements)

References 20 publications

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“…Similar conclusions about the qualitative structure of Nash equilibria have since been derived in more general models of cheap talk, such as multidimensional sources [12], noisy channels [13], multiple senders [14], and hierarchical communication networks [15].…”

Section: Introductionsupporting

confidence: 68%

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Estimation With Strategic Sensors

Farokhi

Teixeira

Langbort

2017

IEEE Trans. Automat. Contr.

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Abstract-We introduce a model of estimation in the presence of strategic, self-interested sensors. We employ a game-theoretic setup to model the interaction between the sensors and the receiver. The cost function of the receiver is equal to the estimation error variance while the cost function of the sensor contains an extra term which is determined by its private information. We start by the single sensor case in which the receiver has access to a noisy but honest side information in addition to the message transmitted by a strategic sensor. We study both static and dynamic estimation problems. For both these problems, we characterize a family of equilibria in which the sensor and the receiver employ simple strategies. Interestingly, for the dynamic estimation problem, we find an equilibrium for which the strategic sensor uses a memory-less policy. We generalize the static estimation setup to multiple sensors with synchronous communication structure (i.e., all the sensors transmit their messages simultaneously). We prove the maybe surprising fact that, for the constructed equilibrium in affine strategies, the estimation quality degrades as the number of sensors increases. However, if the sensors are herding (i.e., copying each other policies), the quality of the receiver's estimation improves as the number of sensors increases. Finally, we consider the asynchronous communication structure (i.e., the sensors transmit their messages sequentially).

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Section: Introductionsupporting

confidence: 68%

“…Notice that the matrix E, which appears in the cost function of (13), has, at least, one negative eigenvalue. This is because multiplying a matrix from both sides by a symmetric and invertible matrix does not change the sign of its eigenvalues (see Sylvester's law of inertia [20, p. 282]).…”

Section: A Static Estimationmentioning

confidence: 99%

Estimation With Strategic Sensors

Farokhi

Teixeira

Langbort

2017

IEEE Trans. Automat. Contr.

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“…The problem of information extraction is related to the general problem of communication between sender and receiver with misaligned objectives studied in game theory [1,2,3] control theory [4,5,6], economics [7,8]. Our work is also related to the results in [9] where we discussed a case with a single sender and showed that the maximum rate of information extraction is bounded above by the Shannon capacity of a certain graph.…”

Section: Introductionmentioning

confidence: 89%

Optimal Questionnaires for Screening of Strategic Agents

Vora

Kulkarni

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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During the COVID-19 pandemic the health authorities at airports and train stations try to screen and identify the travellers possibly exposed to the virus. However, many individuals avoid getting tested and hence may misreport their travel history. This is a challenge for the health authorities who wish to ascertain the truly susceptible cases in spite of this strategic misreporting. We investigate the problem of questioning travellers to classify them for further testing when the travellers are strategic or are unwilling to reveal their travel histories. We show there are fundamental limits to how many travel histories the health authorities can recover.

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“…Thus, the main goal of this strand of works is to characterize the (Nash) equilibria of the induced game. Most of the existing work has focused on the static setting [16,8,50,3]. The work of [16] shows that when the state of the system (principal's private information) is one-dimensional and both the principals and the agents utilities are quadratic, the principals equilibrium strategy employs quantization.…”

Section: Review Of Related Workmentioning

confidence: 99%

“…The work of [16] shows that when the state of the system (principal's private information) is one-dimensional and both the principals and the agents utilities are quadratic, the principals equilibrium strategy employs quantization. More general models of cheap talk, such as multidimensional sources [8], noisy communication [50] and multiple principals with misaligned objectives [3], have been studied in the literature for static settings. There are a few works that study the dynamic version of the cheap talk communication [34,35].…”

Section: Review Of Related Workmentioning

confidence: 99%

Dynamic Information Design: A Simple Problem on Optimal Sequential Information Disclosure

Farhadi

Teneketzis

2020

SSRN Journal

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We study a dynamic information design problem in a finite-horizon setting consisting of two strategic and long-term optimizing agents, namely a principal (he) and a detector (she). The principal observes the evolution of a Markov chain that has two states, one "good" and one "bad" absorbing state, and has to decide how to sequentially disclose information to the detector. The detector's only information consists of the messages she receives from the principal. The detector's objective is to detect as accurately as possible the time of the jump from the good to the bad state. The principal's objective is to delay the detector as much as possible from detective the jump to the bad state. For this setting, we determine the optimal strategies of the principal and the detector. The detector's optimal strategy is described by time-varying thresholds on her posterior belief of the good state. We prove that it is optimal for the principal to give no information to the detector before a time threshold, run a mixed strategy to confuse the detector at the threshold time, and reveal the true state afterwards. We present an algorithm that determines both the optimal time threshold and the optimal mixed strategy that could be employed by the principal. We show, through numerical experiments, that this optimal sequential mechanism significantly outperforms any other information disclosure strategy presented in literature.or subsidies) so as to align their strategic objectives (e.g. maximization of a strategic agent's utility) with his own objective (e.g. maximization of social welfare). In this situation, the system's information structure (who knows what and when) is fixed, and the coordinator's goal is to design a mechanism that incentivizes the strategic agents to reveal their information truthfully [48].2. Information Design. In this approach, the coordinator (e.g. a central control center in a metropolitan area) knows perfectly the evolution of the system's state (e.g. the evolution of traffic in the transportation network), but the decision making (e.g. route selection) is done by the strategic agents (e.g. drivers) who have incomplete/imperfect knowledge of the state (e.g. drivers only know the traffic in their immediate vicinity). To incentivize strategic agents to take actions that are desirable for the coordinator, he can provide, sequentially over time, information about the system's state to them (e.g. provide traffic updates to selfish drivers). The goal of information provision/disclosure is the alignment of each agent's objective (e.g. minimization of the average time to reach the destination) with the coordinator's objective (e.g. minimization of the traffic in the roads). In this situation, the game-form/mechanism is fixed but the system's information structure is not fixed. It has to be designed by the coordinator through the sequential disclosure/provision of information to the strategic agents so as to serve his goal [17,59].This paper addresses an information design problem. Information design problems are ...

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On multi-dimensional and noisy quadratic signaling games and affine equilibria

Cited by 7 publications

References 20 publications

Estimation With Strategic Sensors

Estimation With Strategic Sensors

Optimal Questionnaires for Screening of Strategic Agents

Dynamic Information Design: A Simple Problem on Optimal Sequential Information Disclosure

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