1 Introduction
Coordination problems arise in many organizations. There are often complementarities between members’ choices, and these complementarities can lead to multiple stable outcomes. Organizations may be successful in coordinating on a good outcome, or they may become trapped in an inefficient situation even though better outcomes are also potentially stable.
Few coordination problems are as stark as those arising in the
minimum effort game (also called
weakest-link game), analyzed first in Huyck et al. (
1990). In this game, a player’s payoff depends, in addition to the player’s own choice, on the minimum choice in the group.
1 This game is a coordination game with multiple Pareto-ranked equilibria: any situation where all players make the same effort is a Nash equilibrium, but equilibria with a higher effort level have greater payoffs for all players.
Huyck et al. (
1990) find that failure to coordinate on the efficient outcome in the minimum effort game is common in the laboratory. They point out that this coordination failure is due to the effects of strategic uncertainty: players do not choose the efficient action because they cannot be sure that all others will choose it.
2 These findings have been confirmed by later studies (see Camerer
2003 Chapter 7; Devetag and Ortmann
2007, for an overview). A typical pattern of behavior found in minimum effort game experiments is that initially many subjects choose high levels of effort, but after several rounds the majority choose a low effort.
3
Coordination failure in a minimum effort game could be
prevented if the game is modified from the beginning, possibly avoiding the decline of effort choices to a low level. For example, Blume and Ortmann (
2007) find that pre-play communication significantly increases efficiency relative to the baseline treatment with no communication.
4 Cartwright et al. (
2013) let one of the players “lead-by-example” by choosing effort before the other players. This arrangement increases effort in some groups, although not many groups reached the maximum possible effort. Sahin et al. (
2015) compare the effects of communication and leading-by-example and find that both modifications lead to an increased group effort in the minimum effort game, and the magnitude of the increase is similar in both cases.
5
Although the above studies found that coordination failure can be prevented in the minimum effort game by introducing various extensions, how robust is this result? Does it depend on the particular parametrization of the minimum effort game? And what if a group has already played the game and converged to low effort? Can modifying the game restore coordination on a higher effort after a history of being trapped in an inefficient equilibrium? After all, most organizations have existed for a period of time and a mechanism that works with zero-experience groups might not work with groups that already have a history. For example, a device that is successful in a new company might not work in restructuring an old one.
In this paper, we look at a more challenging minimum effort game parametrization, introduced by Brandts and Cooper (
2006) in the context of their “turnaround game”. For this environment, which typically leads to coordination failure in the absence of further modifications, we focus on two leadership mechanisms similar to the ones discussed above. One mechanism involves
cheap-talk (CT) one-way pre-play communication, where one of the group members acts as a leader by suggesting an effort level; after observing the suggestion, all players choose an effort level simultaneously. The second mechanism entails a
first-mover (FM) leader that leads by example. One player chooses an effort level prior to his followers, who observe this choice and then choose their own effort simultaneously. We subject these mechanisms to a stringent test by looking at their ability to
restore higher effort after a history of coordination failure, and we compare the results of this test with their ability to
prevent coordination failure in groups without history.
Both CT and FM mechanisms are expected to help players to coordinate on a more efficient equilibrium since in both cases the leader’s suggestion or choice may act as a focal point. In addition, in the leading-by-example case, observing the leader’s effort reduces the strategic uncertainty faced by the followers. On the other hand, commiting to a choice is more risky for the leader than making a non-binding suggestion. Which mechanism is more successful overall is not clear a priori. A novel aspect of our experiment is to elicit responses of followers to all possible suggestions or choices by the leader using the strategy method. This allows us to analyze followers’ behavior more systematically by classifying their strategies into types. In this way we can measure how their responsiveness to the leader’s choice in the two mechanisms changes over time. In addition, we are able to conduct a counterfactual analysis of the consequences of alternative choices by the leaders.
Our interest is whether in our tough environment, the leadership mechanisms can prevent or overcome coordination failure (without changing the payoff structure of the game).
6 In our experiment, leaders are chosen randomly,
7 and the leader-communicator in our cheap-talk mechanism can only suggest an effort level rather than send a more complicated message.
8 Our implementations of the leadership mechanisms are thus minimal as they do not require extended messages or (potentially costly) elections to determine the leader. By using a challenging environment (especially after a history of coordination failure) and minimal implementations of the mechanisms, we explore the limits of what these mechanisms can achieve.
After having confirmed that coordination failure happens in our tough environment without a mechanism present, we find, contrary to most of the previous studies, that this history of coordination failure is a powerful attractor, and the leadership mechanisms fail to provide a means to overcome it in the long run. The environment is too challenging for the mechanisms to be effective. Nevertheless, shortly after the introduction of the mechanisms, average effort is higher as some subjects do attempt to make use of the mechanisms. Even without a history of coordination failure, both types of leadership have only a limited ability to prevent it in our environment, with only about 30–40% of the groups having their minimum effort above the lowest level.
Given the relatively poor performance of the mechanisms in terms of escaping from and even preventing coordination failure, what are the reasons for this? Is it due to an ineffective leadership or to the reluctance of other players to follow? We find that followers do follow the leader’s suggestion or choice to some extent (more in the first-mover case than in the cheap-talk one, and more without a history of coordination failure) but there is a sizable minority that always chooses the lowest possible effort. We also find that not all leaders dare to choose a high effort (even after having suggested it); hence, both leaders and followers can be blamed for the poor performance to some degree. Using the data from the strategy method, we find that even if leaders had chosen a higher effort, they would not have increased their payoff. The presence in a group of just one player who is not responsive to the leader’s suggestion or choice makes it impossible to avoid coordination failure, as it is then individually rational for the leader and for any of the followers to choose the lowest possible effort.
The remainder of the paper is organized as follows. Section
2 provides a general background on the minimum effort game and a discussion of possible effects of the leadership mechanisms. Section
3 describes the experimental design and hypotheses. The results of the experiment are discussed in Sects.
4 and
5 concludes.
5 Conclusion
We analyzed the effects of two leadership mechanisms (pre-play communication and leading-by-example) in a tough parametrization of the minimum effort game, both with and without history of coordination failure. Unlike most of the literature (e.g., Blume and Ortmann
2007; Cartwright et al.
2013; Sahin et al.
2015, in different environments), we found that in this challenging setting the mechanisms failed to overcome coordination failure and had only limited effectiveness in preventing it. The mechanisms had some effect in the short run as some players attempted to choose a higher effort but in the long run most players fell back to the lowest possible effort. These results therefore delineate the limits of the mechanisms for preventing and overcoming coordination failure. Our mechanisms involve a rather minimal implementation: our leaders are randomly chosen and communication consists of a single number (interpreted as a suggestion of effort); thus it appears necessary to have more complicated mechanisms to enable players to avoid coordination failure in this game.
In both leadership mechanisms, a substantial proportion of followers chose the effort level corresponding to the leader’s suggestion or choice. However, in each treatment, there was a considerable number of followers who, instead of following the leader, always chose zero effort, irrespective of the suggestion or choice of the leader. Since the outcome depends on the minimum effort in the group, the presence of even one such player often led to the group effort falling back to the lowest level in the long run. Given the non-negligible proportion of such players, the expected payoff of both leaders and followers would be maximized by choosing zero effort. Thus the mechanisms’ failure can be attributed to a large extent to non-responsive followers in our environment.
Notwithstanding the non-responsiveness of some players, the data from the strategy method show that followers followed the leader more in the first-mover treatment than in the cheap-talk treatment. Moving first seems to bestow a greater legitimacy on a leader than simply making a suggestion; indeed, even the leaders themselves did not always follow their own suggestion. However, committing to a high effort is risky in our game and the efforts of first-mover leaders were lower than the suggestions of cheap-talk leaders. The signals sent by leaders were different in the two mechanisms, and followers reacted to them differently, but the combination of leaders’ suggestions or choices and followers’ reaction to them led on aggregate to similar results in both mechanisms.