The target article's core argument (sect. 2.1.4) reiterates the basic economic principle that an individual's bargaining power is improved by outside options. Baumard et al. rely on their previous bargaining model (André & Baumard Reference André and Baumard2011a) in which simulated agents played a modified Ultimatum Game. When responders rejected an offer, they did not get zero, as usual, but instead interacted with a new partner. Further, they had a 50% chance of being the proposer in the new interaction. Offers depended on the costs of switching partners and approached 50% as the costs approached zero. The authors concluded that this finding explains the evolution of fairness. The most straightforward prediction of this model is that people's offers (and fairness judgments) will be sensitive to the costs of switching but the authors did not offer evidence about this prediction.
The importance of outside options is well known from previous research in economics, game theory, biology, political science, and social psychology. This research includes classic economic models of monopoly, duopoly, oligopoly, and competition (Holt Reference Holt2007); market experiments (Smith Reference Smith1962; Reference Smith1982); and multi-player bargaining models and experiments (Mesterton-Gibbons et al. Reference Mesterton-Gibbons, Gavrilets, Gravner and Akcay2011; Murnighan Reference Murnighan1978; Von Neumann & Morgenstern Reference Von Neumann and Morgenstern1944). Particularly relevant to the authors' model, previous experiments showed that proposer competition increases offers in ultimatum games, but also, importantly, responder competition decreases offers (Fischbacher et al. Reference Fischbacher, Fong and Fehr2009).
Baumard et al. further argue that outside options are necessary for even splits: “Quite generally, in the absence of outside options, there is no particular reason why an interaction should be governed by fairness considerations” (sect. 2.1.4, para. 2). Contradicting this claim, Nash showed for a two-player game (no outside option) that “the solution has each bargainer getting the same money profit” (Nash Reference Nash1950, p. 162). Schelling (Reference Schelling1960) showed how conspicuous division points, including (but not limited to) equality, can be stable solutions. Also, offers of half (and even more) can be promoted by additional bargaining stages (Goeree & Holt Reference Goeree and Holt2000) and reputation (Nowak et al. Reference Nowak, Page and Sigmund2000).
Does market competition explain fairness? It might help to examine a classic model of outside options. Consider the following scenario. Annie, Betty, and Cathy (A, B, and C) find a cave full of treasure. It takes exactly two people to carry a treasure chest. Annie is stronger than Betty, and Cathy is the weakest. Together, Annie and Betty can carry $8 million (M) of treasure, Annie and Cathy can carry $6M, and Betty and Cathy can carry only $4M. Any two individuals can agree to any possible division of cash, but the third individual receives $0. Which pairs might work together to carry treasure, and how might each pair divide the cash?
Von Neumann and Morgenstern (Reference Von Neumann and Morgenstern1944, p. 227) found that the division of surplus depends on outside options – the surplus each individual could generate with the third player. They showed that all pairings are equally likely, including the least productive pair (so much for the invisible hand). Each pair has a unique stable division: Annie $5M and Betty $3M, Annie $5M and Cathy $1M, and Betty $3M and Cathy $1M. More generally, for pairs AB, AC, and BC with group payoffs x, y, and z, respectively, each individual's payoffs are A = (x + y – z)/2, B = (x – y + z)/2, and C = (–x + y + z)/2, for both groups each person could join. This implies that if Betty were stronger, then Cathy would get a better deal from Annie. For example, if AB generated $10M, AC generated $6M (same as before), and BC generated $6M, then Annie and Cathy would split more evenly: $4M and $2M rather than $5M and $1M. Also, the Annie-Betty split would now be equal: $5M and $5M.
Outside options influence bargaining but it is not clear that they explain people's fairness judgments. Was Annie's original 5:1 division with Cathy “fair”? Is it “fair” that Cathy's split with Annie depends not only on their respective talents, but also on Betty's talents?
Humans do not seem to equate fairness with market price. For example, people think it is unfair to raise the price of snow shovels when demand increases after a snow storm (Kahneman et al. Reference Kahneman, Knetsch and Thaler1986b). People were outraged when hotels increased prices after the 9/11 attacks (New York State Attorney General, 2001). The idea that prices – divisions of surplus – depend on supply and demand is notoriously difficult for people to accept. That's why humans experience the diamond–water paradox, confusion about why luxuries can be priced higher than necessities (Smith Reference Smith and Methuen1776/1904). People represent goods as having intrinsic prices, and they expect current prices to match previous prices – precedents. This fits with Schelling's (1960) focal point model of bargaining because precedents can increase the conspicuousness of division points, independent of supply and demand.
The target article's model seems to predict that humans will perceive free-market capitalism as maximally fair. Instead, popular culture includes anti-globalization, the “99 percent,” opposition to organ markets, and complaints about the earnings of CEOs, actors, and athletes – despite their rare talents. This might be because partner competition can increase wealth disparities. Consider a simple market with three buyers who value a good X at $9, $6, and $3, respectively, and three sellers whose costs for producing X are $7, $4, and $1, respectively. It is possible for the higher-value buyers to trade with higher-cost sellers, generating $2 surplus per buyer-seller pair to yield $1 per player. But, the competitive equilibrium price is $5, yielding the unequal payoffs of $4, $1, and $0, symmetrically to buyers and sellers, in order of descending values and ascending costs (with a greater total surplus of $10). Competitive markets can exacerbate inequality and people often perceive this as unfair.
Market competition is a critical feature of human social life and much remains to be learned about the underlying cognitive systems. However, the target article seems to be overextending its bargaining model by applying it to fairness, impartiality, cooperation, mutualism, and morality. Future work should develop more specific models of strategic behavior to provide closer fits with the nuanced structure of human social computations.
The target article's core argument (sect. 2.1.4) reiterates the basic economic principle that an individual's bargaining power is improved by outside options. Baumard et al. rely on their previous bargaining model (André & Baumard Reference André and Baumard2011a) in which simulated agents played a modified Ultimatum Game. When responders rejected an offer, they did not get zero, as usual, but instead interacted with a new partner. Further, they had a 50% chance of being the proposer in the new interaction. Offers depended on the costs of switching partners and approached 50% as the costs approached zero. The authors concluded that this finding explains the evolution of fairness. The most straightforward prediction of this model is that people's offers (and fairness judgments) will be sensitive to the costs of switching but the authors did not offer evidence about this prediction.
The importance of outside options is well known from previous research in economics, game theory, biology, political science, and social psychology. This research includes classic economic models of monopoly, duopoly, oligopoly, and competition (Holt Reference Holt2007); market experiments (Smith Reference Smith1962; Reference Smith1982); and multi-player bargaining models and experiments (Mesterton-Gibbons et al. Reference Mesterton-Gibbons, Gavrilets, Gravner and Akcay2011; Murnighan Reference Murnighan1978; Von Neumann & Morgenstern Reference Von Neumann and Morgenstern1944). Particularly relevant to the authors' model, previous experiments showed that proposer competition increases offers in ultimatum games, but also, importantly, responder competition decreases offers (Fischbacher et al. Reference Fischbacher, Fong and Fehr2009).
Baumard et al. further argue that outside options are necessary for even splits: “Quite generally, in the absence of outside options, there is no particular reason why an interaction should be governed by fairness considerations” (sect. 2.1.4, para. 2). Contradicting this claim, Nash showed for a two-player game (no outside option) that “the solution has each bargainer getting the same money profit” (Nash Reference Nash1950, p. 162). Schelling (Reference Schelling1960) showed how conspicuous division points, including (but not limited to) equality, can be stable solutions. Also, offers of half (and even more) can be promoted by additional bargaining stages (Goeree & Holt Reference Goeree and Holt2000) and reputation (Nowak et al. Reference Nowak, Page and Sigmund2000).
Does market competition explain fairness? It might help to examine a classic model of outside options. Consider the following scenario. Annie, Betty, and Cathy (A, B, and C) find a cave full of treasure. It takes exactly two people to carry a treasure chest. Annie is stronger than Betty, and Cathy is the weakest. Together, Annie and Betty can carry $8 million (M) of treasure, Annie and Cathy can carry $6M, and Betty and Cathy can carry only $4M. Any two individuals can agree to any possible division of cash, but the third individual receives $0. Which pairs might work together to carry treasure, and how might each pair divide the cash?
Von Neumann and Morgenstern (Reference Von Neumann and Morgenstern1944, p. 227) found that the division of surplus depends on outside options – the surplus each individual could generate with the third player. They showed that all pairings are equally likely, including the least productive pair (so much for the invisible hand). Each pair has a unique stable division: Annie $5M and Betty $3M, Annie $5M and Cathy $1M, and Betty $3M and Cathy $1M. More generally, for pairs AB, AC, and BC with group payoffs x, y, and z, respectively, each individual's payoffs are A = (x + y – z)/2, B = (x – y + z)/2, and C = (–x + y + z)/2, for both groups each person could join. This implies that if Betty were stronger, then Cathy would get a better deal from Annie. For example, if AB generated $10M, AC generated $6M (same as before), and BC generated $6M, then Annie and Cathy would split more evenly: $4M and $2M rather than $5M and $1M. Also, the Annie-Betty split would now be equal: $5M and $5M.
Outside options influence bargaining but it is not clear that they explain people's fairness judgments. Was Annie's original 5:1 division with Cathy “fair”? Is it “fair” that Cathy's split with Annie depends not only on their respective talents, but also on Betty's talents?
Humans do not seem to equate fairness with market price. For example, people think it is unfair to raise the price of snow shovels when demand increases after a snow storm (Kahneman et al. Reference Kahneman, Knetsch and Thaler1986b). People were outraged when hotels increased prices after the 9/11 attacks (New York State Attorney General, 2001). The idea that prices – divisions of surplus – depend on supply and demand is notoriously difficult for people to accept. That's why humans experience the diamond–water paradox, confusion about why luxuries can be priced higher than necessities (Smith Reference Smith and Methuen1776/1904). People represent goods as having intrinsic prices, and they expect current prices to match previous prices – precedents. This fits with Schelling's (1960) focal point model of bargaining because precedents can increase the conspicuousness of division points, independent of supply and demand.
The target article's model seems to predict that humans will perceive free-market capitalism as maximally fair. Instead, popular culture includes anti-globalization, the “99 percent,” opposition to organ markets, and complaints about the earnings of CEOs, actors, and athletes – despite their rare talents. This might be because partner competition can increase wealth disparities. Consider a simple market with three buyers who value a good X at $9, $6, and $3, respectively, and three sellers whose costs for producing X are $7, $4, and $1, respectively. It is possible for the higher-value buyers to trade with higher-cost sellers, generating $2 surplus per buyer-seller pair to yield $1 per player. But, the competitive equilibrium price is $5, yielding the unequal payoffs of $4, $1, and $0, symmetrically to buyers and sellers, in order of descending values and ascending costs (with a greater total surplus of $10). Competitive markets can exacerbate inequality and people often perceive this as unfair.
Market competition is a critical feature of human social life and much remains to be learned about the underlying cognitive systems. However, the target article seems to be overextending its bargaining model by applying it to fairness, impartiality, cooperation, mutualism, and morality. Future work should develop more specific models of strategic behavior to provide closer fits with the nuanced structure of human social computations.