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New Approaches to Modeling Strategic Interactions

Paper Session

Saturday, Jan. 6, 2018 8:00 AM - 10:00 AM

Marriott Philadelphia Downtown, Meeting Room 413
Hosted By: Econometric Society
  • Chair: George J. Mailath, University of Pennsylvania

Learning Dynamics Based on Social Comparisond

Juan Block
,
University of Cambridge
Drew Fudenberg
,
Massachusetts Institute of Technology
David K. Levine
,
European University Institute and Washington University-St. Louis

Abstract

We study models of learning in games where agents with limited memory use social information
to decide when and how to change their play. When agents only observe the aggregate
distribution of payoffs and only recall information from the last period, we show that aggregate
play comes close to Nash equilibrium behavior for (generic) games, and that pure equilibria are
generally more stable than mixed equilibria. When agents observe not only the payoff distribution
of other agents but also the actions that led to those payoffs, and can remember this for
some time, the length of memory plays a key role. When agents’ memory is short, aggregate
play may not come close to Nash equilibrium, but it does so if the game satisfies a acyclicity
condition. When agents have sufficiently long memory their behavior comes close to Nash equilibrium
for generic games. However, unlike in the model where social information is solely about
how well other agents are doing, mixed equilibria can be favored over pure ones

Collusion Constrained Equilibrium

Rohan Dutta
,
McGill University
David K. Levine
,
European University Institute and Washington University-St. Louis
Salvatore Modica
,
University of Palermo

Abstract

We study collusion within groups in non-cooperative games. The primitives are the
preferences of the players, their assignment to non-overlapping groups and the goals of the
groups. Our notion of collusion is that a group coordinates the play of its members among
different incentive compatible plans to best achieve its goals. Unfortunately, equilibria that
meet this requirement need not exist. We instead introduce the weaker notion of collusion
constrained equilibrium. This allows groups to put positive probability on suboptimal alternatives
in certain razor’s edge cases where the set of incentive compatible plans changes
discontinuously. These collusion constrained equilibria exist and are a subset of the correlated
equilibria of the underlying game. We examine four perturbations of the underlying
game. In each case we show that equilibria in which groups choose the best alternative exist
and that limits of these equilibria lead to collusion constrained equilibria. We also show
that for a sufficiently broad class of perturbations every collusion constrained equilibrium
arises as such a limit. We give an application to a voter participation game showing how
collusion constraints may be socially costly.

Multi-dimensional Reasoning in Games: Framework, Equilibrium and Applications

Ayala Arad
,
Tel Aviv University
Ariel Rubinstein
,
Tel Aviv University and New York University

Abstract

We develop a framework for analyzing multi-dimensional reasoning in strategic interactions,
motivated by the following experimental findings: (a) in games with a large and complex space of
strategies, players tend to think in terms of strategy characteristics rather than the strategies themselves, and (b) in choosing between strategies with a number of characteristics, players consider one characteristic at a time. The solution concept captures Nash-like stability of a choice of features of strategies rather than of strategies. The concept is applied to a number of economic interactions, where stable modes of behavior are identified.

The Implementation Duality

Larry Samuelson
,
Yale University

Abstract

Conjugate duality relationships are pervasive in matching and implementation problems and provide much of the structure essential for characterizing stable matches and implementable allocations in models with quasilinear (or transferable) utility. In the absence of quasilinearity, a more abstract duality relationship, known as a Galois connection, takes the role of (generalized) conjugate duality. While much weaker, this duality relationship still induces substantial structure. We show that this structure can be used to extend existing results for, and gain new insights into, adverse-selection principal-agent problems and two-sided matching problems without quasilinearity.
Discussant(s)
Johannes Horner
,
Yale University
David Rahman
,
University of Minnesota
Muhamet Yildiz
,
Massachusetts Institute of Technology
Bruno Strulovici
,
Northwestern University
JEL Classifications
  • C7 - Game Theory and Bargaining Theory