The axiom of real Blackwell determinacy

نویسندگان

  • Daisuke Ikegami
  • David de Kloet
  • Benedikt Löwe
چکیده

The theory of infinite games with slightly imperfect information has been focusing on games with finitely and countably many moves. In this paper, we shift the discussion to games with uncountably many possible moves, introducing the axiom of real Blackwell determinacy Bl-ADR (as an analogue of the axiom of real determinacy ADR). We prove that the consistency strength of Bl-ADR is strictly greater than that of AD.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Simulation Technique and Its Applications to Infinitary Combinatorics under the Axiom of Blackwell Determinacy

The Axiom of Blackwell Determinacy is a set-theoretic axiom motivated by games used in statistics. It is known that the Axiom of Determinacy implies the Axiom of Blackwell Determinacy. Tony Martin has conjectured that the two axioms are equivalent. We develop the “simulation technique” which allows us to simulate boundedness proofs under the assumption of Blackwell Determinacy and deduce strong...

متن کامل

A parametrised choice principle and Martin's conjecture on Blackwell determinacy

Tony Martin proved in [Mar98] that the Axiom of Determinacy AD implies the Axiom of Blackwell Determinacy Bl-AD, and conjectured that the converse holds as well: Conjecture 1 The Axiom of Blackwell Determinacy Bl-AD implies the Axiom of Determinacy AD. Although Martin, Neeman and Vervoort in their [MarNeeVer03] have made considerable progress on Martin’s Conjecture 1, the full conjecture remain...

متن کامل

A Note on Pure Variations of Axioms of Blackwell Determinacy

In this note, we look at weaker versions of the Axiom of Blackwell Determinacy introduced in [Lö02b] and [Lö03]. We use these results to get a new lower bound for the consistency strength of the Axiom of pure Blackwell Determinacy pBl-AD. We shall investigate Blackwell games against opponents with arbitrary mixed strategies Bl-Det(Γ), against opponents with usual pure strategies pBl-Det(Γ), and...

متن کامل

A pr 1 99 6 Blackwell Games 1 Blackwell Games

Blackwell games are infinite games of imperfect information. The two players simultaneously make their moves and are then informed of each other’s moves. Payoff is determined by a Borel measurable function f on the set of possible resulting sequences of moves. A standard result in Game Theory is that finite games of this type are determined. Blackwell proved that infinite games are determined, ...

متن کامل

Blackwell Games

Blackwell games are infinite games of imperfect information. The two players simultaneously make their moves and are then informed of each other’s moves. Payoff is determined by a Borel measurable function f on the set of possible resulting sequences of moves. A standard result in Game Theory is that finite games of this type are determined. Blackwell proved that infinite games are determined, ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Arch. Math. Log.

دوره 51  شماره 

صفحات  -

تاریخ انتشار 2012