On the origin of convention: evidence from symmetric bargaining games

On The Origin of Convention:
Evidence From Symmetric Bargaining Games

John Van Huyck, Raymond Battalio, Sondip Mathur, Andreas Ortmann,
and Patsy Van Huyck.

[ Download | Introduction | References | Footnotes | John's Web ]

Abstract: We use a dynamical systems approach to model the origin of bargaining conventions and report the results of a symmetric bargaining game experiment. Our experiment also provides evidence on the psychological salience of symmetry and efficiency. The observed behavior in the experiment was systematic, replicable, and roughly consistent with the dynamical systems approach. For instance, we do observe unequal-division conventions emerging in communities of symmetrically endowed subjects.

Key Words: convention, symmetry, bargaining, dynamical systems, adaptive learning, human behavior.

JEL classification: c720, c780, c920, d830.

Introduction

A satisfactory theory of games would not only identify the outcomes that are equilibrium points, but also explain the origin of mutually consistent behavior. When there is a unique equilibrium and the strategic interdependence is not too complicated, one possibility is that people simply deduce the equilibrium from their understanding of the game. However, deductive analysis based on the abstraction assumptions of individual rationality and mutual consistency often fails to determine a unique equilibrium. For example, economists have long known that an analysis of simultaneous bargaining results in multiple equilibria. When equilibrium analysis generates multiple equilibria it fails to prescribe rational behavior in the game or predict the outcome of the game, because it fails to determine which, if any, equilibrium will be selected. Consequently, a theory of equilibrium selection would appear to be an essential complement to the theory of equilibrium points. [1]

It is possible to construct a deductive equilibrium selection theory by introducing abstraction assumptions that go beyond individual rationality and mutual consistency: assumptions like symmetry and efficiency. These additional assumptions imply equal-division in symmetric bargaining games. The coincidence of this result with conventional notions of fairness might be taken as supporting a deductive approach. However, if the deductive approach is to provide an accurate theory of observable games, the selection principles of symmetry and efficiency must formalize characteristics that are universally perceived to be psychologically salient. [2]

An alternative approach to the equilibrium selection problem investigates how experience with related games influences people's beliefs about each other's behavior in the current game. Experience with related games leads them to believe that a specific equilibrium outcome is the conventional outcome and they conform to the convention because doing so is in their interest. A convention is a regularity in behavior that is customary, expected, and self-enforcing, see Lewis (1969) or Young (1993).

We model the origin of convention using a dynamical systems approach. We assume that people learning from experience behave adaptively. It is well known that adaptive behavior may eventually allow communities of people interacting repeatedly to coordinate on an equilibrium outcome, see Milgrom and Roberts (1991) or Friedman (1991) for examples and references. This inductive selection theory makes predictions that can be very different from predictions made by a deductive selection theory. For instance, it is possible for adaptive behavior to lead communities of symmetrically endowed people to coordinate on an unequal-division convention, which violates symmetry.

In this paper, we use the experimental method to study the origin of convention in symmetric bargaining games. Our experiment also provides evidence on the psychological salience of symmetry and efficiency. The observed behavior in the experiment was systematic, replicable, and roughly consistent with the dynamical systems approach. For instance, we do observe unequal-division conventions emerging in communities of symmetrically endowed subjects.

Primary Data Set

Data set available here.

Data set description available here.

Surface mail request (comments, suggestions, references, etc.): john.vanhuyck@tamu.edu

References

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Footnotes

[1] A conventional selection theory is that an arbiter makes a common knowledge equilibrium assignment to the players. Van Huyck, Gillette, and Battalio (1992) examine an arbiter's ability to determine the outcome of two-person coordination games. Their subjects did not find the individual rationality and mutual consistency of an equilibrium assignment to be sufficient reason for implementing the arbiter's assignment when doing so conflicts with payoff-dominance or symmetry.

[2] Harsanyi and Selten (1988) demonstrate that it is possible to construct a deductive equilibrium selection theory for a general class of games. However, Selten views the Harsanyi/Selten solution concept as an exercise in the logic of strategic rationality, rather than as a foundation for a science of strategic behavior. Schelling [1960,(1980)] argues against the psychological salience of symmetry. Roth and Schoumaker's (1983) experiment on reputation provides evidence against equal-division in an asymmetric game, see also Binmore, et al. (1992). Bardhan (1984) reports crop shares for paddy leases varying from 3:1 to 1:3 in the surveyed villages of West Bengal, India, with only two-thirds of the villages using equal-division. Share cropping is not a symmetric game and Bardhan devotes substantial effort to measuring the costs falling on the tenant and the owner.