On the Role of Non-equilibrium Focal Points as Coordination Devices

Abstract

Considering a pure coordination game with a large number of equivalent equilibria, we argue, first, that a focal point that is itself not a Nash equilibrium and is Pareto dominated by all Nash equilibria, may attract the players' choices. Second, we argue that such a non-equilibrium focal point may act as an equilibrium selection device that the players use to coordinate on a closely related small subset of Nash equilibria. We present theoretical as well as experimental support for these two new roles of focal points as coordination devices.

Many social interactions can be modeled as a coordination game. The players have a common interest, but as there are multiple equilibria, the desired outcomes are only achieved if they mutually adjust their actions in the right way and go for the same equilibrium.

Peyton Young (1993) distinguishes three broad equilibrium selection theories: First, some equilibria may be a priori more reasonable than others (see, e.g., John Harsanyi and Reinhard Selten, 1988). Second, it might be that "agents focus their attention on one equilibrium because it is more prominent or conspicuous than the others" (Peyton Young, 1993, p. 58). Third, expectations may converge on one equilibrium through precedent (see, e.g., Vincent Crawford and Hans Haller, 1990).

Our paper will be most closely related to the second of these theories, but it will differ from all three of them. In our game there will be no equilibrium more reasonable or conspicuous than others, and in the (experimental) setup that we will consider, precedence can be of little help since we will consider a sequence of oneshot games with very limited information feedback.

Thomas Schelling (1960) recognized that in everyday life individuals who are confronted with coordination problems frequently seem to do much better than they would by choosing randomly among the equilibria, and that focal points may play an important role in this by providing a point of convergence for individual expectations.¹ As Thomas Schelling (1960) put it: "Most situations - perhaps every situation for people who are practiced at this kind of game - provide some clue for coordinating behavior, some focal point for each person’s expectation of what the other expects him to expect to be expected to do. Finding the key, or rather finding a key - any key that is mutually recognized as the key becomes the key - may depend on imagination more than on logic; it may depend on analogy, precedent, accidental arrangement, symmetry, aesthetic or geometric configuration, casuistic reasoning, and who the parties are and what they know about each other" (p. 57).

We will consider the role of focal points as a coordination device, but our starting point will be a simple two-player matrix game with common interest and a multiplicity of equivalent and efficient Nash equilibria (NE), none of which stands out. We introduce a salient payoff by reducing one of the equilibrium payoffs, thus eliminating the equilibrium property of the corresponding strategy profile. The question, then, is whether this alteration of the incentive structure (creating a single different payoff) may help individuals to coordinate, even if this payoff is not an equilibrium and it is Pareto dominated by the equilibrium payoffs.

The main contribution of our paper, then, is that we present two new ways in which such a non-equilibrium focal point may help to solve coordination problems. First, we will explain that such a non-equilibrium focal point may be an attractor in itself for the players. Second, we will explain that such a focal point may act as an equilibrium selection device enhancing coordination by becoming a stepping stone from which players jump to a closely related small subset of NE that in themselves are not salient. We will present theoretical as well as experimental support for these two new roles of focal points. The experimental evidence presented will also show that the effect of the focality depends, in a clear way, on the level of the focal payoff, and that the effect of the focal point becomes substantially stronger as the players have time to reconsider and adjust their actions.

Download full text paper via ziddu