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:

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)

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)