847 research outputs found
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
Computing Bayes Nash Equilibrium Strategies in Auction Games via Simultaneous Online Dual Averaging
Auctions are modeled as Bayesian games with continuous type and action
spaces. Computing equilibria in auction games is computationally hard in
general and no exact solution theory is known. We introduce algorithms
computing distributional strategies on a discretized version of the game via
online convex optimization. One advantage of distributional strategies is that
we do not have to make any assumptions on the shape of the bid function.
Besides, the expected utility of agents is linear in the strategies. It follows
that if our regularized optimization algorithms converge to a pure strategy,
then they converge to an approximate equilibrium of the discretized game with
high precision. Importantly, we show that the equilibrium of the discretized
game approximates an equilibrium in the continuous game. In a wide variety of
auction games, we provide empirical evidence that the method approximates the
analytical (pure) Bayes Nash equilibrium closely. This speed and precision is
remarkable, because in many finite games learning dynamics do not converge or
are even chaotic. In standard models where agents are symmetric, we find
equilibrium in seconds. The method allows for interdependent valuations and
different types of utility functions and provides a foundation for broadly
applicable equilibrium solvers that can push the boundaries of equilibrium
analysis in auction markets and beyond
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