Abstract
Motivated by recent path-breaking contributions in the theory of repeated games in continuous time, this paper presents a family of discrete-time games which provides a consistent discrete-time approximation of the continuous-time limit game. Using probabilistic arguments, we prove that continuous-time games can be defined as the limit of a sequence of discrete-time games. Our convergence analysis reveals various intricacies of continuous-time games. First, we demonstrate the importance of correlated strategies in continuous-time. Second, we attach a precise meaning to the statement that a sequence of discrete-time games can be used to approximate a continuous-time game.
Highlights
In this paper we study a class of repeated games with imperfect public monitoring which has been introduced in a continuous-time framework in the important contribution of Sannikov (2007)
We feel that an honest study of the foundations of continuous-time game theory is important from a theoretical as well as from an applied perspective
While we are not able to say much about the general connection between the sets of sequential equilibrium payoffs of the discrete-time and continuous-time games,3 we rigorously prove the weak convergence of the game dynamics and the total expected payoffs of the players to corresponding objects of the limit continuous-time game with imperfect public monitoring as introduced in Sannikov (2007)
Summary
In this paper we study a class of repeated games with imperfect public monitoring which has been introduced in a continuous-time framework in the important contribution of Sannikov (2007). As has been convincingly shown in that paper and its followers, continuous-time games are in certain ways analytically more tractable than their discretetime counterparts. There are still open methodological questions how the continuous-time game model fits into the perceived game-theoretic literature. We feel that an honest study of the foundations of continuous-time game theory is important from a theoretical as well as from an applied perspective. From a theoretical point of view, we are the first who present a rigorous convergence analysis for the aforementioned class of continuous-time games. A continuous-time framework of the strategic interaction can be regarded as an idealized model, which can be analyzed with the help of powerful analytic tools
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