74 research outputs found
On values of repeated games with signals
We study the existence of different notions of value in two-person zero-sum
repeated games where the state evolves and players receive signals. We provide
some examples showing that the limsup value (and the uniform value) may not
exist in general. Then we show the existence of the value for any Borel payoff
function if the players observe a public signal including the actions played.
We also prove two other positive results without assumptions on the signaling
structure: the existence of the value in any game and the existence of
the uniform value in recursive games with nonnegative payoffs.Comment: Published at http://dx.doi.org/10.1214/14-AAP1095 in the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Advances in Zero-Sum Dynamic Games
International audienceThe survey presents recent results in the theory of two-person zero-sum repeated games and their connections with differential and continuous-time games. The emphasis is made on the following(1) A general model allows to deal simultaneously with stochastic and informational aspects.(2) All evaluations of the stage payoffs can be covered in the same framework (and not only the usual Cesàro and Abel means).(3) The model in discrete time can be seen and analyzed as a discretization of a continuous time game. Moreover, tools and ideas from repeated games are very fruitful for continuous time games and vice versa.(4) Numerous important conjectures have been answered (some in the negative).(5) New tools and original models have been proposed. As a consequence, the field (discrete versus continuous time, stochastic versus incomplete information models) has a much more unified structure, and research is extremely active
Stochastic Games: Existence of the Minmax
The existence of the value for stochastic games with finitely many states and actions, as well as for a class of stochastic games with infinitely many states and actions, is proved in [2]. Here we use essentially the same tools to derive the existence of the minmax and maxmin for n-player stochasti
Constant payoff in zero-sum stochastic games
In a zero-sum stochastic game, at each stage, two adversary players take
decisions and receive a stage payoff determined by them and by a random
variable representing the state of nature. The total payoff is the discounted
sum of the stage payoffs. Assume that the players are very patient and use
optimal strategies. We then prove that, at any point in the game, players get
essentially the same expected payoff: the payoff is constant. This solves a
conjecture by Sorin, Venel and Vigeral (2010). The proof relies on the
semi-algebraic approach for discounted stochastic games introduced by Bewley
and Kohlberg (1976), on the theory of Markov chains with rare transitions,
initiated by Friedlin and Wentzell (1984), and on some variational inequalities
for value functions inspired by the recent work of Davini, Fathi, Iturriaga and
Zavidovique (2016
Playing off-line games with bounded rationality
We study a two-person zero-sum game where players simultaneously choose sequences of actions, and the overall payo is the average of a one-shot payo over the joint sequence. We consider the maxmin value of the game played in
pure strategies by boundedly rational players and model bounded rationality by introducing complexity limitations. First we dene the complexity of a sequence by its smallest period (a non-periodic sequence being of innite complexity) and study the maxmin of the game where player 1 is restricted to strategies with complexity at most n and player 2 is restricted to strategies with complexity at
most m. We study the asymptotics of this value and a complete characterization in the matching pennies case. We extend the analysis of matching pennies to strategies with bounded recall.We study a two-person zero-sum game where players simultaneously choose sequences of actions, and the overall payo is the average of a one-shot payo over the joint sequence. We consider the maxmin value of the game played in
pure strategies by boundedly rational players and model bounded rationality by introducing complexity limitations. First we dene the complexity of a sequence by its smallest period (a non-periodic sequence being of innite complexity) and study the maxmin of the game where player 1 is restricted to strategies with complexity at most n and player 2 is restricted to strategies with complexity at
most m. We study the asymptotics of this value and a complete characterization in the matching pennies case. We extend the analysis of matching pennies to strategies with bounded recall.Refereed Working Papers / of international relevanc
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