12,881 research outputs found
Dynamic Sender-Receiver Games
We consider a dynamic version of sender-receiver games, where the sequence of
states follows an irreducible Markov chain observed by the sender. Under mild
assumptions, we provide a simple characterization of the limit set of
equilibrium payoffs, as players become very patient. Under these assumptions,
the limit set depends on the Markov chain only through its invariant measure.
The (limit) equilibrium payoffs are the feasible payoffs that satisfy an
individual rationality condition for the receiver, and an incentive
compatibility condition for the sender
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
Learning and Type Compatibility in Signaling Games
Which equilibria will arise in signaling games depends on how the receiver
interprets deviations from the path of play. We develop a micro-foundation for
these off-path beliefs, and an associated equilibrium refinement, in a model
where equilibrium arises through non-equilibrium learning by populations of
patient and long-lived senders and receivers. In our model, young senders are
uncertain about the prevailing distribution of play, so they rationally send
out-of-equilibrium signals as experiments to learn about the behavior of the
population of receivers. Differences in the payoff functions of the types of
senders generate different incentives for these experiments. Using the Gittins
index (Gittins, 1979), we characterize which sender types use each signal more
often, leading to a constraint on the receiver's off-path beliefs based on
"type compatibility" and hence a learning-based equilibrium selection
Reinforcement learning in signaling game
We consider a signaling game originally introduced by Skyrms, which models
how two interacting players learn to signal each other and thus create a common
language. The first rigorous analysis was done by Argiento, Pemantle, Skyrms
and Volkov (2009) with 2 states, 2 signals and 2 acts. We study the case of M_1
states, M_2 signals and M_1 acts for general M_1, M_2. We prove that the
expected payoff increases in average and thus converges a.s., and that a limit
bipartite graph emerges, such that no signal-state correspondence is associated
to both a synonym and an informational bottleneck. Finally, we show that any
graph correspondence with the above property is a limit configuration with
positive probability.Comment: 6 figure
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