How Large Looms the Ghost of the Past? State Dependence versus Heterogeneity in Coordination Games

[Author Affiliation]Omar Al-Ubaydli, , , , omar@omar.ec[Acknowledgment]I wish to thank Jason Aimone, Steffen Andersen, Jonathan Baron, Glenn Harrison, Garett Jones, Min Sok Lee, Ragan Petrie, Laura Razzolini, Nat Wilcox, and two anonymous referees for helpful comments. I wish to thank the anonymous donors to the economics department at George Mason University for funding this research.1. IntroductionIn coordination games, can people "get stuck" in bad equilibria? Coordination games have been used as a metaphor for a wide variety of social interactions, such as the establishment of a new institution, the implementation of a new technology that has network externalities, or even the overthrow of a dictatorial regime.1 An understanding of the effect of bad precedents is critical to policies that try to lift groups out of inefficient equilibria. The persistence of poor institutions has been blamed for the inferior economic performance of many countries and the often complementary difficulty in transiting to democracy.2In this article, I demonstrate the way in which use of naturally occurring data to estimate the effect of bad precedents can lead to large biases. I do this by comparing estimates from naturally occurring data to estimates from data where I randomly induce a bad precedent. The bias arises because the inefficient equilibrium is associated with the safest strategy. People who naturally arrive at the inefficient equilibrium are more likely to remain there not only due to a precedent effect but also due to their systematic aversion to the riskiness of the efficient equilibrium.Variations of the stag hunt have been used to study the issue of precedent. Figure 1 is the N -player stag hunt (also referred to as the average opinion game). Its key features are: (i) There are two Pareto-rankable pure strategy Nash equilibria, (1, 1) and (0, 0), and (ii) the choice corresponding to the inefficient equilibrium is the safest (it has the highest guaranteed payoff).3Figure 1The N -player stag hunt. The number in each cell is your payoff. Payoffs are symmetric. (Figure omitted. See article image.)Suppose that this game is repeated and players are informed about the median at the end of every period. A precedent effect occurs when a median in period t - 1 causally increases the likelihood of that same median occurring in period t .As part of their pioneering work on coordination games, Van Huyck, Battalio, and Beil (1991) used a version of the N -player stag hunt with more strategies (see Figure A1 in the Appendix).4Every time the game was played, they found that the median in the first period was perpetuated for the remaining periods--statistically seemingly the most acute possible precedent effect. Similar results were reported by Cachon and Camerer (1996) and Blume and Ortmann (2007). Van Huyck, Battalio, and Beil (1991) concluded that "subjects select an equilibrium that is determined by the historical accident of the initial median" (p. 898).Precedent effects are a plausible explanation for the perpetuation of inefficient equilibria. Schelling's (1960) focal point theory, and its formalization by Bacharach and Bernasconi (1997), argues that in multiple equilibrium games, players search for salient equilibria (focal points). In repeated play, the preceding median can be quite salient, especially when it is one of the few pieces of information delivered to players after each round.Returning to Van Huyck, Battalio, and Beil's (1991) data, was the initial median actually a historical accident? Perhaps not. Serial correlation can be explained by state dependence, such as the precedent effect, but it can also be the result of heterogeneity in unobservable explanatory variables that persists over time (Heckman 1991). Whatever generated the first-round median of 0 may also directly increase the likelihood of a subsequent median being 0. …