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Decision and Game Theory

Research Statement

Decision and Game Theory are the languages spoken in our group, as also reflected in all other research lines (and in particular Evolution and Networks) and in our teaching. This basic interest has also resulted in research focusing on foundational aspects  of game theory, e.g. the formalization of the concept of focal point  (Alós-Ferrer and Kuzmics, 2010), the existence of equilibria when players employ abstract choice rules (Alcantud and Alós-Ferrer, 2007), the discretization of continuum strategy spaces (Alós-Ferrer 2006), or the formal foundations of game-theoretic dynamical systems with random matching (Alós-Ferrer 1999, 2002)

A long-standing research agenda on the foundations of extensive-form games is developed in collaboration with Klaus Ritzberger (Institute for Advanced Studies, Vienna) with the overall title "Trees and Extensive Forms". This research line is concerned with the development of a general framework for extensive form games that is not plagued with finiteness assumptions. Alós-Ferrer and Ritzberger (2005, 2008) present a unified general framework encompassing finite games, repeated games, stochastic games, and even continuous-time decision problems ("differential games") and large (transfinite) games. The main results achieved up to date include a simple characterization (Alós-Ferrer and Ritzberger 2005) of the natural definition of a game tree and a characterization (Alós-Ferrer and Ritzberger 2008) of the set of game trees which give rise to extensive forms such that every strategy combination induces a unique outcome (hence enabling the specification of an associated normal form game). These results are useful to delimit the confines of extensive form analysis in the abstract.

More recently, we have examined the issue of equilibrium existence in large extensive form games (Alós-Ferrer and Ritzberger 2013). This work identifies two conditions which are necessary and sufficient for the existence of subgame perfect equilibria in large games (infinite action spaces, infinite horizon). That is, in addition to providing a powerful existence theorem, we show exactly how far existence results can be generalized. Hence, our result precisely identifies the minimal conditions that need to be added in order to do equilibrium analysis in large games. More precisely, we characterize the topologies (on the plays of a large game tree) such that every well-behaved perfect information game (w.r.t. the topology) defined on that tree has a subgame perfect equilibrium.

Publications

  • Preference Reversals: Time and Again
    Carlos Alós-Ferrer, Ðura-Georg Granic, Johannes Kern, Alexander K. Wagner.
    Journal of Risk and Uncertainty, February 2016, Vol. 52, Issue 1, pp 65-97.
  • Circulant Games
    Ðura-Georg Granić and Johannes Kern.
    Theory and Decision, Volume 80, January 2016, Issue 1, pp. 43-69.
  • Commitment Through Risk
    Dmytro Kylymnyuk and Alexander Wagner.
    Economics Letters, Vol. 116, No. 3, September 2012, pp. 295-297.
  • Trees and Extensive Forms
    Carlos Alós-Ferrer and Klaus Ritzberger.
    Journal of Economic Theory, Vol. 143, No. 1, November 2008, pp. 216-250.

See also: Comment on Trees and Extensive Forms
Carlos Alós-Ferrer, Johannes Kern, and Klaus Ritzberger. 
Journal of Economic Theory

  • Trees and Decisions
    Carlos Alós-Ferrer and Klaus Ritzberger.
    Economic Theory, Vol. 25, No. 4, June 2005, pp. 763-798.

Working Papers