Academic journal article Economic Inquiry

Leadership by Example in the Weak-Link Game

Academic journal article Economic Inquiry

Leadership by Example in the Weak-Link Game

Article excerpt


The weak-link game was first introduced by Hirshleifer (1983) as a stylized way to capture the private provision of many public goods. As an illustration, Hirshleifer tells the story of Anarchia, a low lying island protected from flooding through a network of interconnected dikes. The crux of the story is that each citizen makes a private decision about how strong a dike to build on their land, yet the island will be flooded if the weakest dike breaks. Most relevant, therefore, is not the average or total contributions to the public good but the minimum contribution. The same could be said for the production of any good, public or private, where output is determined by the weakest component of production. Consequently, the weak-link game is of much applied interest in understanding the performance of groups, organizations and nations (e.g., Brandts and Cooper 2006b; Knez and Camerer 1994). For example, it can help explain the high wage and productivity differentials between rich and poor countries (Kremer 1993).

Hirshleifer argued that production will be efficient in a weak-link game. The basic reasoning is that a person cannot free-ride in the game and so there is an incentive to contribute an efficient amount to the public good. This hypothesis was confirmed in two-player games (e.g., Harrison and Hirshleifer 1989), and also fares well in three-player games (e.g., Knez and Camerer 1994; Weber, Camerer, and Knez 2004). It soon became clear, however, that in games with more than three players things are different (Isaac, Schmidtz, and Walker 1989; Van Huyck, Battalio, and Beil 1990). What we typically observe is considerable coordination failure with contributions rapidly falling to the minimum level (Camerer 2003). (1) The common explanation for this is that to contribute an efficient amount requires trust in others, because the low contribution of one player will make any high contribution redundant and costly for that contributor, and in games with more than three players any trust quickly disappears (Yamagishi and Sato 1986).

How can such coordination failure be avoided? Various solutions have been considered in the literature (Devetag and Ortmann 2007). For instance, coordination failure is less following a temporary increase in the gains of coordinating (Brandts and Cooper 2006b), if there is pre-play communication (Blume and Ortmann 2007; Brandts and Cooper 2007; Chaudhuri, Schotter, and Sopher 2009), and if players opt in to play the game (Cachon and Camerer 1996). Generally speaking, however, these solutions may not always be practical. For example, pre-play communication may be unwieldy in large groups, and many of the solutions rely on the full distribution of contributions being known rather than just the minimum (a point taken up by Brandts and Cooper 2006a). (2)

The basic objective of this paper was to ask whether leadership reduces coordination failure in the weak-link game. Leadership evolved to solve coordination problems between individuals and is common in all social species (Van Vugt 2006; Van Vugt, Hogan, and Kaiser 2008). Our main hypothesis, therefore, is that leadership can help individuals coordinate in the weak-link game. By leadership we shall mean that one player can lead by publicly choosing a contribution before all other players. Our focus is thus on leadership by example. (3) Various experimental studies have already demonstrated the positive effect of this kind of leadership on cooperative behavior in public good and public bad games (Guth et al. 2007; Pogrebna et al. 2008; Van der Heijden and Moxnes 2003). (4) It remains to be seen whether it also works in the weak-link game.

Some evidence on the effectiveness of leadership by example in the weak-link game is provided by Weber, Camerer, and Knez (2004) and Li (2007). They analyze a three-player weak-link game in which choices are made sequentially according to some exogenous order. …

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