Optimal team composition for tool‐based problem solving

• DOI: http://doi.org/10.1111/jems.12295
• Author: Jonathan Bendor,Scott E. Page
• Date: 01 November 2019
• Published date: 01 November 2019

Received: 31 March 2017

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Revised: 18 June 2018

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Accepted: 3 October 2018

DOI: 10.1111/jems.12295

ORIGINAL ARTICLE

Optimal team composition for tool‐based problem solving

Jonathan Bendor

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Scott E. Page

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Department of Political Economy,

Stanford University Graduate School of

Business, Stanford, California

2

Center for the Study of Complex Systems,

Departments of Political Science and

Economics, University of Michigan, Ann

Arbor, Michigan, Santa Fe Institute

Correspondence

Jonathan Bendor, Department of Political

Economy, Stanford University Graduate

School of Business, Stanford, CA 94305.

Email:jonathan.bendor@stanford.edu

Funding information

Army Office of Research, Grant/Award

Number: W911NF1010379

Abstract

In this paper, we construct a framework for modeling teams of agents who apply

techniques or procedures (tools) to solve problems. In our framework, tools differ

in their likelihood of solving the problem at hand; agents,who may be of different

types, vary in their skill at using tools. We establish baseline hiring rules when a

manager can dictate tool choiceand then derive results for strategic tool choice by

team members. We highlight three main findings: First, that cognitively diverse

teams are more likely to solve problems in both settings. Second, that teams

consisting of types that master diverse tools have an indirect strategic advantage

because tool diversity facilitates coordination. Third, that strategic tool choice

creates counterintuitive optimal hiring practices. For example, optimal teams may

exclude the highest ability types and can include dominated types. In addition,

optimal groups need not increase setwise. Our framework extends to cover

teamwork on decomposable problems, to cases where individuals apply multiple

tools, and to teams facing a flow or set of problems.

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INTRODUCTION

Over the past 35 years the number of people used as cognitive, nonroutine workers has doubled to 60 million. The job

classifications for this category of workers include managing, designing, performing basic research, investing, strategic

consulting, engineering, and providing legal advice and medical care.

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The tasks carried out by cognitive, nonroutine

workers consist in large part of solving problems. Biomedical researchers isolate molecules. Financial analysts build

portfolios. Consultants develop reorganization plans. Engineers design batteries. Equally relevant to our analysis, most

problem solving is now done in teams. Therefore, the study of problem solving is also the study of teams and teamwork.

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In this paper, we construct a framework for studying team performance on problem solving. Specifically, we analyze the

proability of success at problem solving given team composition and derive optimal hiring rules. Our framework assumes

problem solvers who possess skill of varying degrees at applying tools. Better problem solvers know more tools and are more

adept at applying them. Given that problem solving is done primarily in teams, our framework focuses on teamwork. We

assume that a team either succeeds or fails depending upon whether any member of the group finds a solution. We do not

constrain the definition of a problem, so the binary nature of outcomes—success or failure—does not greatly limit the scope

of our framework. Any task that requires constraint satisfaction (with or without an optimization criterion), such as reducing

the rate of defects in a manufacturing process by a certain percentage or designing an internal combustion engine that

exceeds environmental standards while maintaining a torque profile, is admissible.

The difficulty of developing an optimal hiring policy stems from a lack of separability. Ability corresponds to the

probability of solving the problem, which in turn implies a facility with potentially successful tools. Ability fails as a proxy for

aperson’s added value to a group because the group may already contain people who possess the high‐ability person’s tools.

As a rule, the best team of problem solvers need not consist of the most able individuals (Hong & Page, 2004; Page, 2008;

Marcolino, Jiang, & Tambe, 2013). In fact, for some classes of problems no measure applied to individuals determines

J Econ Manage Strat. 2019;28:734–764.wileyonlinelibrary.com/journal/jems734

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© 2018 Wiley Periodicals, Inc.

optimal team composition (Kleinberg & Raghu, 2018). The best person to add to a group will be the one most likely to apply

a tool that is both novel and effective. Therefore, optimal hiring depends on the group composition (Prat, 2002).

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If firms had

little choice in whom to hire, this optimal hiring problem would not be relevant. That is decidedly not the typical case.

Alphabet, the parent company of Google, annually receives upwards of three million applicants. Leading financial services

companies and consulting companies receive over a quarter of a million applicants. People analytics, the use of data and

models to make hiring decisions, has now become a standard tool (Bock, 2015; Conner, 1991; Conner & Prahalad, 1996;

Demsetz, 1988; Powell & Snellman, 2004).

Our analysis consist of two main parts. We first derive benchmark results where the manager can assign tools to

workers. We find that the manager wants worker types who are proficient with distinct tools. Once we have a firm grasp

of the sometimes subtle relations between individual ability, team diversity, and group effectiveness, this decision

theoretic result is not surprising. We next consider the more complex strategic context in which the manager first

chooses workers who then autonomously choose tools. A worker’s payoff depends on some combination of group

success and individual credit. The manager’s optimal rule takes into account that individual credit matters to workers.

This results in what at first appear to be counterintuitive hiring practices but which upon reflection are rational because

they prevent doubling up on tools.

Our approach complements the traditional models of team performance that take membership as fixed and focus on

moral hazard (Holmstrom, 1982) or both moral hazard and adverse selection (McAfee & McMillan, 1991) in which an

individual’s contribution to the team depends on effort and ability. Their focus on shirking may be more appropriate for

production and the provision of services than for problem solving, where success can produce reputational rents. To the

extent that incentive problems matter in problem solving contexts, we believe they can be handled separately from the

competition arising from team composition.

Within the framework, we uncover direct benefits from cognitive diversity: Teams with diverse tools are more likely

to find solutions to problems. In addition, we find that tool diversity becomes more important both when average skill

increases and group size increases because in such situations existing tools are likely to have been applied correctly. We

also find strategic benefits from diverse teams. They have fewer coordination failures owing to lack of overlap in their

toolkits. We also find strategic advantages to hiring less able workers. Knowing fewer tools can reduce the incentive to

choose the wrong tool, for example, selecting one already tried by teammates. These findings echo a variety of strength‐

through‐weakness results in game theory. Last, extending the model to allow for partial solutions amplifies the benefits

of applying more diverse tools. Thus, our stark model is conservative: It stacks the deck toward ability and simple rules

and away from diversity and complex rules.

Our framework takes an agent’s facility with tools as exogenous. Workers can choose which tool to apply given their set

of tools. They cannot choose to become an expert at a new tool. Robust empirical evidence shows that proficiency with a

tool, particularly one that produces economic value, requires specialized training and hundreds if not thousands of hours of

practice (Ericsson, Krampe, & Tesch‐Romer, 1993; Feltovich, Prietula, & Ericsson, 2006). Consequently, groups that have

tool diversity must have team diversity, that is, people trained in different methods.

To provide context for our results, we refer throughout to five hiring regularities that hold for a constant elasticity of

substitution (CES) production function given equal market wages: Higher ability types should be hired earlier (competency

ordering) and in greater number (competency loading); all previoushiresremainintheoptimalgroupasgroupsizeincreases

(monotonicity); a type that does not have the most skill at some task will not be hired (no dominated hires); eventually all

undominated types will be hired (asymptotic diversity). These regularities bear repeating in more colloquial phrasing to

reinforce their normalcy: Hire the most talented first, hire more of the more talented, do not discard talent, do not hire

ineffective workers, and increase worker diversity as the firm grows.

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These regularity properties hold for a variety of

production functions used in decision‐and team‐theoretic models (Marshack & Radner, 1972).

As we will show, optimal hiring for problem‐solving workers can violate each of these regularities. Moreover, the

violations are not knife‐edge cases; they arise under a range of reasonable assumptions. While many of the violations

result from incentive issues created by strategic tool selection, some arise from properties of problem solving. For

example, competency ordering and competency loading can be violated even when the manager can assign tools to

workers. The violations arise when the toolkits of different types of workers overlap, that is, have some tools in

common. Without overlap, optimal hiring would be straightforward.

Theremainderofthepaperhasfiveparts.Webeginwithinformal and formal descriptions of our framework. We next

derive benchmark results for the centralized structure where the manager selects worker types as well as the tools deployed.

We then turn to the decentralized system in which problem solvers strategically choose tools. In the penultimate section, we

consider three natural extensions. We conclude by summarizing our key results and note some implications.

BENDOR AND PAGE

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