533 research outputs found
On the Structure of Equilibrium Strategies in Dynamic Gaussian Signaling Games
This paper analyzes a finite horizon dynamic signaling game motivated by the
well-known strategic information transmission problems in economics. The
mathematical model involves information transmission between two agents, a
sender who observes two Gaussian processes, state and bias, and a receiver who
takes an action based on the received message from the sender. The players
incur quadratic instantaneous costs as functions of the state, bias and action
variables. Our particular focus is on the Stackelberg equilibrium, which
corresponds to information disclosure and Bayesian persuasion problems in
economics. Prior work solved the static game, and showed that the Stackelberg
equilibrium is achieved by pure strategies that are linear functions of the
state and the bias variables. The main focus of this work is on the dynamic
(multi-stage) setting, where we show that the existence of a pure strategy
Stackelberg equilibrium, within the set of linear strategies, depends on the
problem parameters. Surprisingly, for most problem parameters, a pure linear
strategy does not achieve the Stackelberg equilibrium which implies the
existence of a trade-off between exploiting and revealing information, which
was also encountered in several other asymmetric information games.Comment: will appear in IEEE Multi-Conference on Systems and Control 201
Imitative Follower Deception in Stackelberg Games
Information uncertainty is one of the major challenges facing applications of
game theory. In the context of Stackelberg games, various approaches have been
proposed to deal with the leader's incomplete knowledge about the follower's
payoffs, typically by gathering information from the leader's interaction with
the follower. Unfortunately, these approaches rely crucially on the assumption
that the follower will not strategically exploit this information asymmetry,
i.e., the follower behaves truthfully during the interaction according to their
actual payoffs. As we show in this paper, the follower may have strong
incentives to deceitfully imitate the behavior of a different follower type
and, in doing this, benefit significantly from inducing the leader into
choosing a highly suboptimal strategy. This raises a fundamental question: how
to design a leader strategy in the presence of a deceitful follower? To answer
this question, we put forward a basic model of Stackelberg games with
(imitative) follower deception and show that the leader is indeed able to
reduce the loss due to follower deception with carefully designed policies. We
then provide a systematic study of the problem of computing the optimal leader
policy and draw a relatively complete picture of the complexity landscape;
essentially matching positive and negative complexity results are provided for
natural variants of the model. Our intractability results are in sharp contrast
to the situation with no deception, where the leader's optimal strategy can be
computed in polynomial time, and thus illustrate the intrinsic difficulty of
handling follower deception. Through simulations we also examine the benefit of
considering follower deception in randomly generated games
Strategic Communication Between Prospect Theoretic Agents over a Gaussian Test Channel
In this paper, we model a Stackelberg game in a simple Gaussian test channel
where a human transmitter (leader) communicates a source message to a human
receiver (follower). We model human decision making using prospect theory
models proposed for continuous decision spaces. Assuming that the value
function is the squared distortion at both the transmitter and the receiver, we
analyze the effects of the weight functions at both the transmitter and the
receiver on optimal communication strategies, namely encoding at the
transmitter and decoding at the receiver, in the Stackelberg sense. We show
that the optimal strategies for the behavioral agents in the Stackelberg sense
are identical to those designed for unbiased agents. At the same time, we also
show that the prospect-theoretic distortions at both the transmitter and the
receiver are both larger than the expected distortion, thus making behavioral
agents less contended than unbiased agents. Consequently, the presence of
cognitive biases increases the need for transmission power in order to achieve
a given distortion at both transmitter and receiver.Comment: 6 pages, 3 figures, Accepted to MILCOM-2017, Corrections made in the
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