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Predicting Outcomes in Games: New Directions

Paper Session

Saturday, Jan. 6, 2018 2:30 PM - 4:30 PM

Marriott Philadelphia Downtown, Meeting Room 406
Hosted By: Econometric Society
  • Chair: Andrew Postlewaite, University of Pennsylvania

Equilibrium Selection in Auctions and High Stakes Games

Paul Milgrom
,
Stanford University

Abstract

We introduce the test-set equilibrium refinement of Nash equilibrium and apply it
to three well-known auction games, comparing our findings to similar ones previously
obtained by ad hoc equilibrium selections. We also introduce a theory of high stakes
versions of games, in which strategies are first proposed and then subjected to a potentially
costly review-and-revise process. For finite games, when the cost of revising strategies
is small, a Nash equilibrium is a test-set equilibrium if and only if those strategies are
chosen for play in a quasi*-perfect equilibrium of the corresponding high stakes version.

Perfect Conditional ε-Equilibria of Multi-Stage Games with Infinite Sets of Signals and Actions

Philip J. Reny
,
University of Chicago
Roger B. Myerson
,
University of Chicago

Abstract

We extend Kreps and Wilson's concept of sequential equilibrium to games where the sets of actions that players can choose and the sets of signals that players may observe are infinite. A strategy profile is a conditional ε-equilibrium if, for any player and for any of his positive probability signal events outside a uniformly unlikely set, the player's conditional expected utility would be within ε of the best that the player could achieve by deviating. Perfect conditional ε-equilibria are defined by testing conditional ε-rationality also under nets of small perturbations of the players' strategies and of nature's probability function that can make any finite collection of signals have positive probability. Every perfect conditional ε-equilibrium strategy profile is a subgame perfect ε-equilibrium and admits a finitely consistent conditional belief system that makes it sequentially ε-rational. Nature's perturbations can produce equilibria that seem unintuitive and so we consider two ways to limit the effects of those perturbations, using topologies on nature's states and on players' actions.

Applying `Theory of Mind': Theory and Experiments

Erik O. Kimbrough
,
Chapman University
Nikolaus Robalino
,
Rochester Institute of Technology
Arthur J. Robson
,
Simon Fraser University

Abstract

This paper investigates our capacity to attribute preferences to
others. This ability is intrinsic to game theory, and is a central component of
“Theory of Mind”, perhaps the capstone of social cognition. In particular, this
component of theory of mind allows individuals to learn more rapidly in strategic
environments with an element of novelty. We show here that the capacity to
attribute preferences yields a clear advantage over less sophisticated approaches
to strategic interaction (such as reinforcement learning) because it allows agents
to extrapolate to novel circumstances information about counterparts’ preferences
that was learned previously. We report experiments investigating this capacity in
simple extensive form games. We find significant learning of others’ preferences,
providing evidence for the presence and effectiveness of this aspect of theory of
mind. Moreover, scores on standard measures of autism-spectrum tendencies are
modest but significant determinants of individual speeds of learning, so our notion
of theory of mind is related to the notion as it is understood in psychology.

An Algorithm for Stochastic Games With Perfect Monitoring

Dilip Abreu
,
Princeton University
Benjamin Brooks
,
University of Chicago
Yuliy Sannikov
,
Stanford University

Abstract

We study the subgame perfect equilibria of two player stochastic games with perfect
monitoring and geometric discounting. A novel algorithm is developed for calculating
the discounted payos that can be attained in equilibrium. This algorithm generates a
sequence of tuples of payos vectors, one payo for each state, that move around the
equilibrium payo sets in a clockwise manner. The trajectory of these \pivot" payos
asymptotically traces the boundary of the equilibrium payo correspondence. We also
provide an implementation of our algorithm, and preliminary simulations indicate that
it is more ecient than existing methods. The theoretical results that underlie the
algorithm also yield a bound on the number of extremal equilibrium payoffs.
Discussant(s)
Bart Lipman
,
Boston University
Paulo Barelli
,
University of Rochester
J. Aislinn Bohren
,
University of Pennsylvania
Takuo Sugaya
,
Stanford University
JEL Classifications
  • C72 - Noncooperative Games