Group 4: Game Theory and Adam Smith

In his book, Game Theory Evolving, Herbert Gintis illustrates the importance of game theory, believing it helps us “ understand the stunning interplay of cooperation and conflict that accounts for the strengths (and weaknesses) of the market economy and our strengths (and weaknesses) as a species” (xxii). By developing mathematical models, game theory predicts outcomes of human interactions. Adam Smith’s theories of human behavior, described in his Theory of Moral Sentiments, can be confirmed with game theoretic models, which justify sympathy as a dominate human trait and explain how altruism can serve one’s self interest.

Utlitiy functions

Adam Smith uses TMS to elaborate on the altruistic behavior inherent in human nature. He begins by stating, “How selfish soever man may be supposed, there are evidently some principles in his nature, which interest him in the fortune of others, and render their happiness necessary to him, though he derives nothing from it except the pleasure of seeing it”(I.I.1). Game theorists have adopted this; In his book, Nuts and Bolts for the Social Sciences, Jon Elster states, “Sometimes we take account of other people’s success and well-being and are willing to sacrifice some of our own for their sake” (52). In their article, “Modeling Strong Reciprocity,” Armin Falk and Urs Fischbacher use this concept to construct a utility function that includes not only an individual’s monetary payoffs, but the other players’ payoffs as well:

U_i =π_i+ ρ_iφσ

So, player i’s utility is a combination of the material payoff (π_i )and the satisfaction he receives from the other players’ payoffs (ρ_iφσ).

where ρ_i = reciprocity parameter: measures the strength of player i’s reciprocal preferences.

φ = kindness term: measures the kindness player i experiences form another player j’s actions.

If φ is positive, the action of j is considered kind. If it is negative, player i can increase his utility by rejecting the offer and reducing player j’s payoff.

σ = reciprocation term: player j’s payoff

The Samartian’s Dilemma

Herbert Ginitis uses utility function models to show how altruistic behavior among family members improves saving habits; “James Buchanan (1975) has made the insightful point that even if people are perfectly capable of managing their retirement savings, if we are altruistic towards others, we will force people to save more than they otherwise would” (33-34). Ginitis’s model is very similar to Falk’s and Fischbacher’s, except Ginitis chooses family members as players. It is clear that Smith believed the strongest forms of altruism are between family members:

After himself, the members of his own family, those who usually live in the same house with him, his parents, his children, his brothers and sisters, are naturally the objects of his warmest affections. They are naturally and usually the persons upon whose happiness or misery his conduct must have the greatest influence. He is more habituated to sympathize with them. He knows better how every thing is likely to affect them, and his sympathy with them is more precise and determinate, than it can be with the greater part of other people.(VI.II.5)

  Daughter
  income z > 0 
  Save amount s for her schooling next year
  receiving interest rate r > 0 
  Receive a transfer t from her father in 2nd period.   
  v(s,t)=v1 (z-s)+δv2 (s(1+r)+t)
  where δ > 0 

  Father
  income y > 0 
  u(y)
  But has degree α > 0 of altruistic feeling 
  maximizes U = u(y-t) + αv(s,t)

Ultimatum Game

Intentions play a crucial role in game theoretic explanations of human nature. Falk and Fischbacher use the Ultimatum Game to show the importance of intentions. For Games are set up, each giving the proposer the option of choosing an (8/2) offer in the first round. Each game allows the proposer varying alternative offers. Falk and Fischbacher studied the rejection rate of the (8/2) offer and found it to be inversely related to the perceived fairness of the proposer.

In TMS Adam Smith highlights how individuals derive notions of fairness by viewing their desire to be no more important than someone else’s:

When he views himself in the light in which he is conscious that others will view him, he sees that to them he is but one of the multitude in no respect better than any other in it. If he would act so as that the impartial spectator may enter into the principles of his conduct, which is what of all things he has the greatest desire to do, he must, upon this, as upon all other occasions, humble the arrogance of his self-love, and bring it down to something which other men can go along with. They will indulge it so far as to allow him to be more anxious about, and to pursue with more earnest assiduity, his own happiness than that of any other person. Thus far, whenever they place themselves in his situation, they will readily go along with him. In the race for wealth, and honours, and preferments, he may run as hard as he can, and strain every nerve and every muscle, in order to outstrip all his competitors. But if he should justle, or throw down any of them, the indulgence of the spectators is entirely at an end. It is a violation of fair play, which they cannot admit of. This man is to them, in every respect, as good as he: they do not enter into that self-love by which he prefers himself so much to this other, and cannot go along with the motive from which he hurt him. They readily, therefore, sympathize with the natural resentment of the injured, and the offender becomes the object of their hatred and indignation.

(II.II.11)

The Ultimatum Game illustrates how perceptions of fairness vary with the intentions of the proposer. The (8/2) offer is perceived as less fair in game (a) than in game (b), since “the proposer could have proposed the egalitarian offer;” in game (c) “the proposer has no choice at all so that the proposer’s behavior cannot be judged in terms of fairness,” and in game (d) the (8/2) offer could even be seen as fair (Falk and Fischbacher 198). The results highlight how the intentions of the proposer determine the responder’s actions, regardless of the payoff received.

Adam Smith shows how agents sympathize more with the motives of others than the outcomes of their actions. He states,

It is to be observed, however, that, how beneficial soever on the one hand, or how hurtful soever on the other, the actions or intentions of the person who acts may have been to the person who is, if I may say so, acted upon, yet if in the one case there appears to have been no propriety in the motives of the agent, if we cannot enter into the affections which influenced his conduct, we have little sympathy with the gratitude of the person who receives the benefit: or if, in the other case, there appears to have been no impropriety in the motives of the agent, if, on the contrary, the affections which influenced his conduct are such as we must necessarily enter into, we can have no sort of sympathy with the resentment of the person who suffers. Little gratitude seems due in the one case, and all sort of resentment seems unjust in the other. The one action seems to merit little reward, the other to deserve no punishment. (II.I 15)

According to Falk and Fischbacher, there are two motives for punishment in the Ultimatum Game—retaliation, where the respondent punishes the proposer “in order to reciprocate an unkind act” and “lower the (unkind) opponent’s payoff” and inequity aversion, where “the aim of the reciprocation subject is to reduce distributional inequality” (202).

Public Goods Game

To test which approach best described common human behavior, Falk and Fischbacher use a one-shot public goods game, which allows players to punish uncooperative behavior. In the first stage of this game, 3 players simultaneously decide on their contribution to the public good (0-20 points). payoffs = 20 - own provision + 0.6 * sum of all provisions In the second stage of the game, the players are allowed to sanction other members; however, for each point a player chooses to deduct from the other players, he or she faces a cost of one point. When selfish preferences are assumed, each member chooses to keep all of his or her income in the initial stage, and the total group income = 60. Under this assumption no sanction will take place in the second stage, since no player will be willing to bear the cost. Notice that the social surplus is maximized when each player invests all of his of her income in the first stage. The total group income would then be 60 * 1.8 = 108. Realizing this, players will choose to punish those who do not contribute an acceptable amount of their income to the public good. Since the cost of punishment eliminates any inequity reduction motives, punishment must result from retaliation. Falk and Fischbacher note that “46.8% of the cooperators punish even if they are facing two defectors” (204). Since most of the sanctions were imposed by cooperators on the defectors, the retaliation motive it further supported, concluding retaliation drives retribution. This corresponds with Adam Smith’s view of retaliation as a strong motive for punishment; Resentment seems to have been given us by nature for defence, and for defence only. It is the safeguard of justice and the security of innocence. It prompts us to beat off the mischief which is attempted to be done to us, and to retaliate that which is already done; that the offender may be made to repent of his injustice, and that others, through fear of the like punishment, may be terrified from being guilty of the like offence.(II.II. 4)

The Smith Game

In their article, “A game-theoretic re-evaluation of Adam Smith’s Theory of Moral Sentiments and Wealth of Nations,” Andreas Ortmann and Stephen Meardon note that “for a well-defined class of passions, no commitment device of third-party enforcement is necessary to ensure that people will meet the standards of propriety, or abide by the general rules of morality” (47). By incorporating foresight with their actions, individuals can view the long-run consequences of their actions and chose to practice self restraint; “for the future to influence action in the present, it must somehow be anticipated in the present through a medium of consciousness” (Elster 51). Adam Smith describes foresight as necessary to preserve individual’s well-being. He states,

As he grows up, he soon learns that some care and foresight are necessary for providing the means of gratifying those natural appetites, of procuring pleasure and avoiding pain, of procuring the agreeable and avoiding the disagreeable temperature of heat and cold.In the proper direction of this care and foresight consists the art of preserving and increasing what is called his external fortune. (IV.I. 3)

Ortmann and Meardon construct the Smith Game to examine how individuals use foresight to control their passion driven actions. They model “acquisition of self command” as a “struggle between two ‘selves’ with different preferences,” using players from Smith’s TMS (44). According to Smith, even an irrational person inflamed with passion is capable of realizing the impropriety of his intended actions, by evaluating their negative effects on his future state of mind;

We can never survey our own sentiments and motives, we can never form any judgment concerning them; unless we remove ourselves, as it were, from our own natural station, and endeavour to view them as at a certain distance from us. […] We endeavour to examine our own conduct as we imagine any other fair and impartial spectator would examine it. […] I divide myself, as it were, into two persons; […] There are two different occasions upon which we examine our own conduct, and endeavour to view it in the light in which the impartial spectator would view it: first, when we are about to act; and secondly, after we have acted. […]When we are about to act, the eagerness of passion will seldom allow us to consider what we are doing, with the candour of an indifferent person.[…] We cannot even for that moment divest ourselves entirely of the heat and keenness with which our peculiar situation inspires us, nor consider what we are about to do with the complete impartiality of an equitable judge. […] When the action is over, indeed, and the passions which prompted it have subsided, we can enter more coolly into the sentiments of the indifferent spectator. […] The man of to-day is no longer agitated by the same passions which distracted the man of yesterday. (III.I. 2-6 & 89-91)

The players are the Man Yesterday, the person inflamed by passion, and the Man Today, the same person after his passion has diminished. Ortmann and Meardon note that the Man Today can be seen as a real person existing after the action has taken place or as an imaginary construct in the Man Yesterday’s mind. The payoffs are feeling of praise worthiness and blame worthiness. Ortmann and Meardon draw on an important implication of Smith’s TMS; the beneficent man is seldom a genuine altruist, since self-interested people act benevolently to generate feelings of praiseworthiness and avoid feelings of blame worthiness. They state, “By choosing his action, a player chooses the set of emotions he may possible feel as a result of the action”(45).

The Man Yesterday can either act properly or improperly. (The standards of propriety are assumed to be predetermined and known.) The Man Today can either perform a routine evaluation and evaluate the Man Yesterday’s actions casually, or he can perform a real evaluation and evaluate carefully. A real evaluation is costly because of the time and effort it requires and the blame that must result from an improper action if evaluated carefully; however, suppose the Man Yesterday acts improperly, then the Man Today would prefer to make a real evaluation in order to prevent the Man Yesterday from repeating the offense. The Man Today feels praiseworthy for enduring a painful self-evaluation to promote self command in the future.

In a one-shot game, both players will chose to defect. The Man Yesterday maximizes his payoffs by acting improperly. Knowing this, the Man Today will feel inclined to make a real evaluation. An equilibrium is reached, since neither player has incentive to change his or her action (Elster 102). The outcome of the game changes, however, if the game is played continuously. Ortmann and Meardon use the trigger strategy to explain the outcome of a repeated game. The trigger strategy states that the Man Today will continue to make real evaluation once the Man Yesterday has chosen to act improperly. The players then become concerned not with the payoffs of the current round, but the sum of all payoffs from future rounds.

It is then in both players’ best interest to cooperate. Thus, a new Nash equilibrium emerges, one that is Pareto optimal.

Ortmann and Meardon form a convincing model of self –command acquisition using Adam Smith’s TMS; however, they fail to prove that the outcomes of the Smith Game are based on the players’ rational decisions. They state, “Even though his payoffs are in the realm of emotions, his decisions are rational in the sense of payoff maximizing”(45), but Smith doubted the ability of individuals to form an unbiased opinion regarding their own conduct. He states,

Rather than see our own behaviour under so disagreeable an aspect, we too often, foolishly and weakly, endeavour to exasperate anew those unjust passions which had formerly misled us; we endeavour by artifice to awaken our old hatreds, and irritate afresh our almost forgotten resentments: we even exert ourselves for this miserable purpose, and thus persevere in injustice, merely because we once were unjust, and because we are ashamed and afraid to see that we were so. […] So partial are the views of mankind with regard to the propriety of their own conduct, both at the time of action and after it; and so difficult is it for them to view it in the light in which any indifferent spectator would consider it. (III.I. 91-92)

When becoming the Man Today, the Man Yesterday must enter into the mind of an impartial by-stander, but Smith finds a complete transition improbable. Under this assumption, the payoffs in Ortmann and Meardon’s Smith Game should be changed. Because the results of the Man Today’s evaluations will be biased, he might not believe his improper actions warrant punishment, so he will not incur the negative cost of blame-worthiness. Since technically both of the players are the same person, the total payoff he receives by acting improperly will be equal to the payoff he would receive by acting properly. A definite final outcome is uncertain. The Man Yesterday’s actions vary with his preferred timing of payment. If the higher immediate payoff is preferred, the Man Yesterday will chose to act improperly (Elster 46-47).

Elster also doubts the ability of individuals to perform self-evaluations; he states, “The cession of an emotional state- be it positive or negative- does not simply bring us back to the earlier emotional plateau. Rather, it tends to generate another emotional state of opposite sign” (64). Elster believes that actions are developed through desires and opportunities and he explains how desires can sometimes alter the opportunities available and limit certain actions. If applied with Ortmann and Meardon’s Smith Game, Ester’s theory highlights the probability of the Man Today eliminating the opportunity of a real evaluation from his set of possible actions. Elster states, “Sometimes the opportunity set is deliberately shaped by a person’s desires. I do not have in mind here the practically important but theoretically trivial desire to expand one’s opportunity set, but the more puzzling cases in which people find it in their interest to reduce the set of options available to them”(17). Only when the Man Yesterday can completely enter into the mind of an impartial spectator, can the common cause of justice prohibit his desires from limiting his actions. Otherwise, the Man Today might be prohibited form performing a real evaluation and an equilibrium could form at the lower left-hand corner.

Adam Smith Problem

sympathy vs. self-interest

Over the years, many contradicting interpretations of Adam Smith’s work have developed. The Wealth of Nations, which claims that individuals act out of self-interest, was a stark contrast from the sympathetic behavior described in TMS; however, games that model the human behavior described in TMS show how self-interested individuals benefit by acting altruistically. Individuals integrate the satisfaction of others into their own utility functions. Unkind acts encourage retaliation, so individuals will choose to cooperate in order to maximize log-run gains.

"minimalist" vs. "activist"

Other disputes arise when deciding Smith’s stance on government intervention; “ [t]hat Adam Smith stands for the themes of laissez-faire, noninterventionism, and minimal government is a dominant theme in economics and elsewhere – including among those critical of the laissez-fair position” (Samuels and Medema 219). As the games modeled after Smith’s TMS have shown, individuals act as reciprocators. In his article, “The Logic of Reciprocity,” Dan Kahan explains the reciprocity theory of human behavior. By comparing the reciprocity theory with the conventional theory of collective action, Kahan highlights how the behavior developed in Smith’s TMS warrants government intervention. Kahan views agents as emotional/ moral reciprocators rather than wealth maximizers; “[m]ost persons think of themselves and want to be understood by others as cooperative and trustworthy and are thus perfectly willing to contribute their fair share to securing collective goods” (341).

Adam Smith shows how individuals value the acquisition of trust over material wealth. He states, "Humanity does not desire to be great, but to be beloved. It is not in being rich that truth and justice would rejoice, but in being trusted and believed, recompenses which those virtues must almost always acquire" (III.I. 107). The conventional theory treats defection as the dominant strategy for every individual, since “the theory predicts a single collective behavioral equilibrium: universal noncooperation;” however, with the reciprocity theory, no dominate individual strategy exist, so multiple equilbria emphasized by tipping points emerge (342). Kahan explains,

If for whatever reason, some individuals conclude that those around them are inclined to contribute, they’ll respond by contributing in kind, prompting still others to contribute, and so forth and so on until a highly cooperative state of affairs takes root. But if some individuals conclude that others are free-riding, then they will respond by free-riding, too, spurring others to do the same, and so forth and so on until a condition of mass cooperation becomes the norm. (342-343)

Using the Smith Game, Ortmann and Meardon describe how these equilibriums can be reached. They note that equilibriums form due to the players’ eductive or evolutive strategies. Eductive strategies require “careful reasoning on the part of the players”, and they must sympathize with each other in order to “ simulate the reasoning process of other players; evolutive strategies describe how an “adjustment takes place as a result of integrated play by myopic players” (Binmore qt. in Ortmann and Meardon 47).

Ortmann and Meardon believe evolutionary strategies are problematic, since players are “not able to determine in advance that a strategy of abiding strictly to the moral standards […] is in the long-run best interest” (48). They argue some players lack the abilities required to perform eductive strategies, such as “the ability to observe and recall behaviors of others, computational ability, and the ability to gauge the ‘payoffs’ that future interactions promise” (48). Since multiple equilibriums can be reached with reciprocal behavior, evolutionary strategies could force a society to become locked into a sub-optimal position, granting strong justification for government intervention, stating,

Adam Smith’s “‘Newtonian’ view of the world-- the notion that all of the universe, even down to the sentiments of man, functions as a great machine powered by the will of the Deity and moving towards a grand design—would seem to suggest players’ strategies should actually be thought of as being formed eductively.” (48)

This is supported by Smith in TMS; he states, “But every part of nature, when attentively surveyed, equally demonstrates the providential care of its Author, and we may admire the wisdom and goodness of God even in the weakness and folly of man”(II.III. 25). Smith would find it inefficient for a government to attempt to manipulate individuals’ interest. Drawing from Elster’s definition of institutions, Smith’s aversion for the government seems to correspond with his concerns for the vanity of the philosopher. Elster states,

[An institution] seems to act, choose and decide as it were an individual writ large, but it is also created by and made up of individuals.[…] Talk about institutions is just shorthand for talk about individuals who interact with one another and with people outside the institutions. Whatever the outcome of the interaction, it must be explained in terms of the motives and opportunities of these individuals. (147&158)

Since Smith believes individuals can determine their own actions best, government intervention seems unnecessary;

The ancient stoics were of opinion, that as the world was governed by the all-ruling providence of a wise, powerful, and good God, every single event ought to be regarded, as making a necessary part of the plan of the universe, and as tending to promote the general order and happiness of the whole: that the vices and follies of mankind, therefore, made as necessary a part of this plan as their wisdom or their virtue; and by that eternal art which educes good from ill, were made to tend equally to the prosperity and perfection of the great system of nature.(I. II. 24)

However, Ortmann and Meardon note, “Smith seems to have become more pessimistic in the course of his life of the probability of moral standards converging (without the aid of a third party) toward the will of the Deity—suggesting that in his latter years the evolutive approach seemed to him more realistic. Some form of government intervention might therefore be called for to put moral standards on the correct path” (48).

Kahan shows how government intervention, promoting cooperation among individuals takes different directives under the reciprocity theory. He states, “The conventional theory sees incentives as the solution to collective action problems: Because wealth maximizers cannot be counted on to contribute to public goods, they must be prodded to do so with either rewards or punishments that bring their individual interests into alignment with their collective ones. The strong reciprocity theory suggests an alternative policy—the promotion of trust” (343). As Elster suggests, “Selfishness works best, […] when combined with a modicum of honesty. […] I keep my promise to you not because I care about your welfare, but because I care about my reputation as a person of honor” (59).

Kahan shows how incentives can erode trust and cause noncooperation, since they can be seen as a cue that others are not participating, or they can crowd out altruism by denying individuals the opportunity to demonstrate their sacrifice to the public good.

In their article, “Freeing Smith from the ‘Free Market’: On the Misperception of Adam Smith of the Economic Role of Government,” Warren Samuels and Steven Medema believe that the misconceptions of Smith’s position on government intervention result from Smith’s clearly stated opposition to mercantilism, but believe this opposition to mercantilism does not oppose other forms of government . Smith’s contempt for the mercantilist system could have emerged from the political policies that counteracted altruistic behavior. Smith’s point “is not that government is bad, but that government was doing bad things in promulgating mercantilist policy” (225). As the game theory models have shown, humans inherently posses altruistic behavior. Smith could have approved a government system that encourages complete cooperation among individuals to effectively improve society.

Works Cited

Elster, Jon. Nuts and Bolts for the Social Sciences. New York: Cambridge University Press, 1989.

Falk, Armin and Urs Fischbacher. “Modeling Strong Rciprocity.” Moral Sentiments and Material Interests: The Foundations of Cooperation in

Economic Life. Ed Herbert Gintis et al. Cambridge: The MIT Press, 2005.

Gintis, Herbert. Game Theory Evolving: A Problem-Centered Introduction to Maodeling Strategic Behavior. New Jersey: Prinston University

Press, 2000.

Kahan, Dan M. “The Logic of Reciprocity: Trust, Collective Action, and Law." Moral Sentiments and Material Interests: The Foundations of

Cooperation in Economic Life. Ed Herbert Gintis et al. Cambridge: The MIT Press, 2005.

Ortmann, Andreas and Stephen Meardon. “A game-theoretic re-evaluation of Adam Smith’s Theory of Moral Sentiments and Wealth of

Nations.” The Classical Tradition in Economic Thought. 11 (1995): 43-61.

Samuels, Warren J., and Steven G. Medema. “Freeing Smith from the ‘Free Market’: On the Misperseption of Adam Smith of the Economic

Role of Government.” History of Political Economy 37.2 (2005): 219-226.

Smith, Adam. Theory of Moral Sentiments. 6th ed. London: A. Millar, 1790. http://www.econlib.org/Library/Smith/smMS.html