GAMENET, the European Network for Game Theory is a COST Action funded project (CA 16228) which aims to be the European network for game theoretic research.
With the rapid advancement of technological innovations, modern societies rely more and more on the proper functioning of complex networks. Since the state and the dynamics of these networks are determined by independent decision makers, a solid understanding, control and optimization of such networked systems constitutes a major challenge for modern societies. GAMENET is the European Network where scientists jointly develop game-theoretic solutions to these complex social problems.
The weekly game theory seminar of Bar-Ilan University will take place in Zoom in this coming year (every Tuesday 10:30-13:00 (CET)).
Please email firstname.lastname@example.org to join the seminar’s mailing list, and get the the Zoom link for each talk.
In even stages 0,2,4,… Player 1 selects a bit (0 or 1), and in odd stages 1,3,5,… Player 2 selects a bit (0 or 1). This way the two players select (the binary representation of) a number in the unit interval x. Player 1 wins if x is in some given target set A, and Player 2 wins otherwise. Does necessarily one of the players have a winning strategy, namely, a strategy that guarantees that that player wins, regardless of the choices of the other players? The game we just described is an infinite-horizon extensive-form game. The determinacy of this game, namely, the existence of a winning strategy to one of the players, is an extension of the famous Zermelo’s Theorem to this setup, and was fully answered in 1975 by Donald Martin.
Borel games are two-player alternating-move games where the action sets of each player after each history may be an arbitrary set, and the winning set is a Borel set of plays. The determinacy of Borel games is a momentous result. It has numerous applications in set theory, topology, logic, computer science, and, of course, in game theory. In 1998 Martin extended his determinacy result to two-player zero-sum simultaneous-move games with both players have finite action sets. The two results were then unified and extended by Eran Shmaya in 2011, who studied alternating-move games with eventual perfect monitoring.
In this workshop we intend to go over some of the determinacy results and their applications. Our approach is didactic, and our ambition is to guide the participants through the details of the results and the proofs. We also present very recent papers with applications of Borel games to game theory and analysis.