International Workshop on Logic, Rationality and Interaction

Logic, Rationality, and Interaction pp 411-415 | Cite as

Reflective Oracles: A Foundation for Game Theory in Artificial Intelligence

  • Benja Fallenstein
  • Jessica Taylor
  • Paul F. Christiano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9394)

Abstract

Game theory treats players as special: A description of a game contains a full, explicit enumeration of all players. This isn’t a realistic assumption for autonomous intelligent agents. In this paper, we propose a framework in which agents and their environments are both modelled as probablistic oracle machines with access to a “reflective” oracle, which is able to answer questions about the outputs of other machines with access to the same oracle. These oracles avoid diagonalization problems by answering some queries randomly. Agents make decisions by asking the oracle questions about their environment, which they model as an arbitrary oracle machines. Since agents are themselves oracle machines, the environment can contain other agents as non-distinguished subprocesses, removing the special treatment of players in the classical theory. We show that agents interacting in this way play Nash equilibria.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Binmore, K.: Modeling rational players: Part I. Economics and Philosophy 3(02), 179–214 (1987)CrossRefGoogle Scholar
  2. 2.
    Fallenstein, B., Soares, N., Taylor, J.: Reflective variants of Solomonoff induction and AIXI. In: Bieger, J., Goertzel, B., Potapov, A. (eds.) AGI 2015. LNCS, vol. 9205, pp. 60–69. Springer, Heidelberg (2015)CrossRefGoogle Scholar
  3. 3.
    Fallenstein, B., Taylor, J., Christiano, P.: Reflective oracles: A foundation for classical game theory. Tech. rep., Machine Intelligence Research Institute (2015), http://intelligence.org/files/ReflectiveOracles.pdf
  4. 4.
    Hutter, M.: Universal Artificial Intelligence. Texts in Theoretical Computer Science. Springer (2005)Google Scholar
  5. 5.
    Kreps, D.M.: A Course in Microeconomic Theory. Princeton University Press (1990)Google Scholar
  6. 6.
    Rogers, H.: Theory of Recursive Functions and Effective Computability. McGraw-Hill (1967)Google Scholar
  7. 7.
    Solomonoff, R.J.: A formal theory of inductive inference. Part I 7(1), 1–22 (1964)Google Scholar
  8. 8.
    Weirich, P.: Causal decision theory. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (2012)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Benja Fallenstein
    • 1
  • Jessica Taylor
    • 1
  • Paul F. Christiano
    • 2
  1. 1.Machine Intelligence Research InstituteBerkeleyUSA
  2. 2.UC BerkeleyBerkeleyUSA

Personalised recommendations