Smaldino's reconsideration of the importance of group traits that involve differentiation of roles is useful and important. However, it could be enriched by a more complete understanding of game theory and also by a revisit to some of the ideas of the classical political economists. This comment will take the two points in reverse order.
We find a parallel in Adam Smith's Wealth of Nations (Smith Reference Smith1994), in which he discusses the division of labor and illustrates it with the famous example of the pin factory, among others. According to Smith, in the first sentence of Chapter One, “The greatest improvement in the productive powers of labour, and the greater part of the skill, dexterity, and judgment with which it is any where directed, or applied, seem to have been the effects of the division of labour.”
In his Principles of Political Economy, John Stuart Mill (Reference Mill1987) returned to Smith's discussion of the division of labor. Mill clearly thought of the division of labor as a (if not the) fundamental cause of improving standards of living. Mill used the term “complex co-operation” to designate what Smith had called “division of labor,” and he distinguished it from “simple cooperation,” which seems to correspond to what Smaldino (sect. 2.2, para. 2), following Wimsatt (Reference Wimsatt, Schaffner and Cohen1974), calls “aggregate” group properties (or group actions). Mill stresses that complex cooperation (“collaboration” for Smaldino) offers further increases in labor productivity beyond that available through simple cooperation.
In McCain (Reference McCain2014, Ch. 2) the theory of production shared by Smith and Mill is called a “complex combination of labor” theory, that is, one that holds that labor productivity is primarily determined by the complex combination of labor, rather than by the combination of simple labor with great quantities of other resources. Another example of a complex combination of labor theory of productivity is found in the writings of the Elder Austrian School, (esp. Menger Reference Menger, Dingwall and Hoselitz1871/1976), which stresses the complexity of production in terms of the tools used. These two strains of complex combination of labor theory were synthesized by Ely (Reference Ely1901) but largely lost sight of in the twentieth century.
Complex cooperation in the writings of Mill seems to correspond more closely to what Smaldino calls collaboration than to what he calls cooperation. No doubt this terminological novelty is worthwhile: the word “cooperation” has a great deal of baggage. It is not so much ambiguous as polyguous.
Nevertheless, Smaldino's understanding of game theory and its relation to cooperation or collaboration seems incomplete. Smaldino stresses some rather simple game examples, but these by no means exhaust the resources of noncooperative game theory. Here is an example, only slightly more complex, that seems to capture both complex cooperation as understood by Mill and collaboration as understood by Smaldino (esp. sect. 2, para. 1; sect. 4.1, para. 1).
The Smith–Mill game shown in Table 1 is adapted from McCain (Reference McCain2014), Chapter 3. Essentially the game in McCain's Chapter 3 expands the “Stag Hunt” game to allow for division of labor. The game at Table 1 modifies it further to allow for different aptitudes along the lines of Mill's discussion of complex division of labor and Smaldino's kayak maker and seal hunter example (sect. 4.1, para. 3). The players are Worker 1 and Worker 2. The strategies are to work alone or work collaboratively taking Task 1 or Task 2. Assume Worker 1 has a “knack” for Task 1 and Worker 2 for Task 2. To realize the benefits of collaboration, it is necessary that each worker take one of the two tasks.
Table 1.
A Smith-Mill Game
This game has three distinct Nash equilibria that are ranked in Paretian terms. As such, it mixes elements of a coordination game (e.g., the Stag Hunt) and an anticoordination game (Tardos & Vazirani Reference Tardos, Vazirani, Nisan, Roughgarden, Tardos and Vazirani2007). One possible solution is a hierarchy, whereby one of the two is designated as “leader” and the other as “follower.” The “leader” directs the strategies of both. In this case, it does not matter which player is designated as “leader,” because it is in the interest of both to choose Task 1, Task 2. (This is further discussed in McCain Reference McCain2014, Ch. 7, sect. c).
It seems that the Nash equilibrium in the rightmost column in the second row from the bottom is the collaborative outcome of this game as Smaldino understands it. It is also the unique cooperative solution. For noncooperative games in standard form (such as Table 1), there seems to be no very general way of identifying a cooperative solution. In this case, however, we can rely on Aumann's (Reference Aumann1959) criterion as the distinct cooperative solution to the game. The collaborative solution in the rightmost column is the only strong Nash equilibrium in the game. It will also correspond to each of the several criteria for solutions of cooperative games.
Responding to social-dilemma examples along the lines of public goods, Smaldino writes, “Yet, the group-level behavior is defined not simply in terms of individuals donating or withholding contributions, but in terms of each individual doing his own part in a coordinated and organized manner. These hunters are doing more than cooperating: they are collaborating” (sect. 4.1, para. 1). Nevertheless, they are enacting the cooperative solution, not to a simplified game, but to the game they are playing.
Smaldino's reconsideration of the importance of group traits that involve differentiation of roles is useful and important. However, it could be enriched by a more complete understanding of game theory and also by a revisit to some of the ideas of the classical political economists. This comment will take the two points in reverse order.
We find a parallel in Adam Smith's Wealth of Nations (Smith Reference Smith1994), in which he discusses the division of labor and illustrates it with the famous example of the pin factory, among others. According to Smith, in the first sentence of Chapter One, “The greatest improvement in the productive powers of labour, and the greater part of the skill, dexterity, and judgment with which it is any where directed, or applied, seem to have been the effects of the division of labour.”
In his Principles of Political Economy, John Stuart Mill (Reference Mill1987) returned to Smith's discussion of the division of labor. Mill clearly thought of the division of labor as a (if not the) fundamental cause of improving standards of living. Mill used the term “complex co-operation” to designate what Smith had called “division of labor,” and he distinguished it from “simple cooperation,” which seems to correspond to what Smaldino (sect. 2.2, para. 2), following Wimsatt (Reference Wimsatt, Schaffner and Cohen1974), calls “aggregate” group properties (or group actions). Mill stresses that complex cooperation (“collaboration” for Smaldino) offers further increases in labor productivity beyond that available through simple cooperation.
In McCain (Reference McCain2014, Ch. 2) the theory of production shared by Smith and Mill is called a “complex combination of labor” theory, that is, one that holds that labor productivity is primarily determined by the complex combination of labor, rather than by the combination of simple labor with great quantities of other resources. Another example of a complex combination of labor theory of productivity is found in the writings of the Elder Austrian School, (esp. Menger Reference Menger, Dingwall and Hoselitz1871/1976), which stresses the complexity of production in terms of the tools used. These two strains of complex combination of labor theory were synthesized by Ely (Reference Ely1901) but largely lost sight of in the twentieth century.
Complex cooperation in the writings of Mill seems to correspond more closely to what Smaldino calls collaboration than to what he calls cooperation. No doubt this terminological novelty is worthwhile: the word “cooperation” has a great deal of baggage. It is not so much ambiguous as polyguous.
Nevertheless, Smaldino's understanding of game theory and its relation to cooperation or collaboration seems incomplete. Smaldino stresses some rather simple game examples, but these by no means exhaust the resources of noncooperative game theory. Here is an example, only slightly more complex, that seems to capture both complex cooperation as understood by Mill and collaboration as understood by Smaldino (esp. sect. 2, para. 1; sect. 4.1, para. 1).
The Smith–Mill game shown in Table 1 is adapted from McCain (Reference McCain2014), Chapter 3. Essentially the game in McCain's Chapter 3 expands the “Stag Hunt” game to allow for division of labor. The game at Table 1 modifies it further to allow for different aptitudes along the lines of Mill's discussion of complex division of labor and Smaldino's kayak maker and seal hunter example (sect. 4.1, para. 3). The players are Worker 1 and Worker 2. The strategies are to work alone or work collaboratively taking Task 1 or Task 2. Assume Worker 1 has a “knack” for Task 1 and Worker 2 for Task 2. To realize the benefits of collaboration, it is necessary that each worker take one of the two tasks.
A Smith-Mill Game
This game has three distinct Nash equilibria that are ranked in Paretian terms. As such, it mixes elements of a coordination game (e.g., the Stag Hunt) and an anticoordination game (Tardos & Vazirani Reference Tardos, Vazirani, Nisan, Roughgarden, Tardos and Vazirani2007). One possible solution is a hierarchy, whereby one of the two is designated as “leader” and the other as “follower.” The “leader” directs the strategies of both. In this case, it does not matter which player is designated as “leader,” because it is in the interest of both to choose Task 1, Task 2. (This is further discussed in McCain Reference McCain2014, Ch. 7, sect. c).
It seems that the Nash equilibrium in the rightmost column in the second row from the bottom is the collaborative outcome of this game as Smaldino understands it. It is also the unique cooperative solution. For noncooperative games in standard form (such as Table 1), there seems to be no very general way of identifying a cooperative solution. In this case, however, we can rely on Aumann's (Reference Aumann1959) criterion as the distinct cooperative solution to the game. The collaborative solution in the rightmost column is the only strong Nash equilibrium in the game. It will also correspond to each of the several criteria for solutions of cooperative games.
Responding to social-dilemma examples along the lines of public goods, Smaldino writes, “Yet, the group-level behavior is defined not simply in terms of individuals donating or withholding contributions, but in terms of each individual doing his own part in a coordinated and organized manner. These hunters are doing more than cooperating: they are collaborating” (sect. 4.1, para. 1). Nevertheless, they are enacting the cooperative solution, not to a simplified game, but to the game they are playing.