Imitation and the role of information in overcoming coordination failures

Carlos Alós-Ferrer, Simon Weidenholzer
2014 Games and Economic Behavior  
We model the structure of a firm or an organization as a network and consider minimum-effort games played on this network as a metaphor for cooperations failing due to coordination failures. For a family of behavioral rules, including Imitate the Best and the Proportional Imitation Rule, we show that inefficient conventions arise independently of the interaction structure, if information is limited to the interaction neighborhoods. However, in the presence of informational spillovers, a minimal
more » ... condition on the network guarantees that efficient conventions will eventually dominate. An analogous result is established for average opinion games. 1 There are many situations where the performance of a group depends on the effort exerted by its weakest member. For instance, in synchronized swimming or in rowing one poorly performing team member will jeopardize the team's chance of success. Likewise, in an orchestral concert, a single violin out of tune may spoil an entire performance. Whereas in these examples a good coach or a conductor may help the team overcome coordination failures and achieve a high level of group performance, under many circumstances it is impossible to contract the effort levels chosen by the individual team members. Moreover, as Knez and Camerer (1994) argue, the recent trend of flattening hierarchies has led organizations to coordinate different business functions through informal mechanisms rather than formal lines of authorities. For instance, consider a group of computer programmers who jointly write on a computer program, which consists of several subroutines, each written by one programmer. The performance of the subroutine is determined by the effort exerted by the respective programmer and the performance of the joint program is determined by its weakest subroutine. In this sense, a bug in a subroutine causes the entire program to malfunction. This situation gives rise to a minimum effort or weakest link game, as analyzed by e.g. Van Huyck, Battalio and Beil (1990) , henceforth VHBB, where the payoff 1 of an agent depends on the minimum of all effort levels chosen and a cost associated to the agent's actual effort level. Note that under these premises, a given agent will optimally choose an effort level equal to the minimum of all effort levels chosen. This implies that i) each profile where each agent inserts the same effort level corresponds to a Nash equilibrium and ii) that those Nash equilibria where teams manage to coordinate on high effort level are very "fragile" in the sense that one single agent deviating to a lower effort level will prompt other agents to follow. Thus, this element of strategic uncertainty inherent in minimum effort games might eventually cause entire work groups or cooperations to fail. In the present paper we use social networks to model the organizational structure of a firm or industry that is confronted with such a weakest link problem. 2 The social network determines who interacts with whom in the firm. In fact, by modeling social interactions within the firm as a network, we are able to capture any form of interaction between agents in the firm. Note that in general these interaction structures will be rather local, meaning that agents will only interact with a small subset of the population, so that not everybody will interact with everybody else. Figure 1 provides an example of a possible interaction structure in an IT-firm, which consists of a marketing group, a group of programmers, agents working in a financial division, and a board. Note that while there will be interaction within, say, the group of programmers, there will be hardly any interaction between the group of programmers and the work group in the marketing department. At the behavioral level, we follow Herbert Simon's (1947) classic view that an organization is composed of boundedly rational agents. That is, when deciding on the effort to be invested in some task, agents do not use highly sophisticated forms of reasoning but instead rely on simple behavioral rules. 3 Our main focus is on behavioral rules based on imitation, where agents essentially mimic the behavior of other agents who are perceived as successful. Imitation seems to be a well justified behavioral rule in e.g. circumstances where the game itself is not properly understood, agents lack computing capacities, or simply want to economize on decision costs (see Alós-1 Throughout the paper, we will interpret payoffs as observable performance levels rather than, say, privately known wages. Assuming that performance will eventually influence actual monetary payoffs, focusing on the former is a reasonable simplification when studying learning in organizations. 2 In Section I.A we provide several examples of weakest link games appearing in organizational theory and in social interactions in general. See also Knez and Camerer (1994) for several examples of weakest link games appearing in firms. 3 See Sobel (2000) for a survey of learning models in economics.
doi:10.1016/j.geb.2014.05.013 fatcat:m7guo2w2vjebjkjr52hoqya7i4