Deterministic Calibration and Nash Equilibrium
نویسندگان
چکیده
We provide a natural learning process in which the joint frequency of (time-averaged) empirical play converges into the set of convex combinations of Nash equilibria. Furthermore, the actual distribution of players’ actions is close to some (approximate) Nash equilibria on most rounds (on all but a vanishing fraction of the rounds). In this process, all players rationally choose their actions using a public prediction made by a deterministic, weakly calibrated algorithm. For this to be possible, we show that such a deterministic (weakly) calibrated learning algorithm exists. © 2007 Elsevier Inc. All rights reserved.
منابع مشابه
Non-Determinism and Nash Equilibria for Sequential Game over Partial Order
In sequential games of traditional game theory, backward induction guarantees existence of Nash equilibrium by yielding a sub-game perfect equilibrium. But if payoffs range over a partially ordered set instead of the reals, then the backward induction predicate does no longer imply the Nash equilibrium predicate. Non-determinism is a solution: a suitable non-deterministic backward induction fun...
متن کاملSmooth Calibration, Leaky Forecasts, Finite Recall, and Nash Dynamics
We propose to smooth out the calibration score, which measures how good a forecaster is, by combining nearby forecasts. While regular calibration can be guaranteed only by randomized forecasting procedures, we show that smooth calibration can be guaranteed by deterministic procedures. As a consequence, it does not matter if the forecasts are leaked, i.e., made known in advance: smooth calibrati...
متن کاملLearning to Play Nash in Deterministic Uncoupled Dynamics
This paper is concerned with the following problem. In a bounded rational game where players cannot be as super-rational as in Kalai and Leher (1993), are there simple adaptive heuristics or rules that can be used in order to secure convergence to Nash equilibria, or convergence only to a larger set designated by correlated equilibria? Are there games with uncoupled deterministic dynamics in di...
متن کاملAlgorithms for computing Nash equilibria in deterministic LQ games
In this paper we review a number of algorithms to compute Nash equilibria in deterministic linear quadratic differential games. We will review the open-loop and feedback information case. In both cases we address both the finite and the infinite-planning horizon.
متن کاملExistence and Efficiency of Nash Equilibria under Deterministic Voting
This paper considers an economy with a public good where a decision must be made both about the level of the public good and the taxation imposed on each citizen (multi-dimensional policy space). In this context, we derive two results: i) we show that a Nash equilibrium exists under deterministic voting, ii) we show that political competition is a necessary but not sufficient condition for the ...
متن کامل