# Game Theory for Humans with Hearts

The following is a slightly revised excerpt of Section 1.2 from my paper on Empirical Evidence Against Utility Theory – Game theorists rule out Humans with hearts by assumption. The excerpt provides some empirical evidence (not needed by anyone except economists) that human actually do have hearts, and this actually affects their behavior! surprise, surprise!

The “Goeree-Holt Humans with Hearts” (GHHwH) Game: Conventional game theory operates under the assumption that both players (A-player labelled Aleena, and B-player labelled Babar) are heartless human beings. They have no emotions; rather, they are disembodied brains floating in vats. For more explanation and discussion, see Homo Economics: Cold, Calculating, and Callous. Below we discuss a game described in Goeree, Jacob K. and Charles A. Holt (2001). “Ten Little Treasures of Game Theory and Ten Intuitive Contradictions,” American Economic Review, vol. 91(5): 1402-1422. They do not provide a name for this game, so we will call it the GH Humans with Hearts game; it is a convenient way to prove the human beings do not behave like homo economicus. Furthermore, this assertion is not a surprise to anyone except economists, who are trained to think like economists. This means deep training in learning to model human behaviour as heartless, which blinds them to the complex realities of human behaviour.

At the initial node, Aleena has the choice to PLAY or to OPT-OUT. If she opts out she receives AOP < \$10, and Babar received BOP – Aleena and Babar’s Opt-Out Payoff.  If Aleena chooses to PLAY, then Babar has a choice between High, which gives him \$5 and Aleena \$10, or Low which gives him some payoff  BLO < \$5, while Aleena gets ALO.

Game-theoretic analysis of this game is simple and straightforward. We work by backwards induction. Given that BLO < \$5, Babar will always play High. So Aleena can count on receiving \$10, which she gets in this case. This is higher than her opt-out payoff of AOP (by assumption), so she will choose to play.

The standard game theoretic analysis of this game provides us with the following insights:

1. The value of ALO does not matter, since Babar will always play High.
2. The value of BLO does not matter, as long as it is strictly less than \$5.
3. If Aleena chooses PLAY, she can count on receiving \$10
4. The value of AOP does not matter, as long as AOP<\$10

All four of these insights, which come from game theory for humans without hearts,  are wrong. Furthermore, ordinary untrained subjects who play this game behave in ways which show deeper understanding of human behavior.  Thus game theory systematically handicaps the understanding of actual observed behavior in this game.

Experimental evidence provided in Goeree and Holt (2010) reveals the following patterns of behavior:

1. When the difference between \$5 and \$BLO is small, Aleena cannot rely on Babar choosing High. Suppose BLO = \$4.75, which is only a bit smaller than \$5. In one experiment, 15% of the B-players choose Low, which gives them a quarter less than the optimal move High.
2. As a consequence of possible “mistakes” by Babar, Aleena will compare ALO to AOP, to decide between Opt-Out and Play. If her optout payoff is \$7, while BLO is \$0, then Aleena makes a large loss when Babar does not make the right choice of High. In this situation, experimental evidence shows that A-players often opt-out.
3. As the difference between \$5 and BOP increases, the chances of B-player playing High increase. In experiments, A-Player anticipates this and chooses to PLAY more often. None of these phenomena is predicted by game theory, showing the theory is blind to aspects of the game which untrained observers are aware off.
4. A high value of BOP can create resentment in B-player . For example if BOP=\$10, then PLAY move by player Aleena reduces the maximum payoff of B-player to \$5. This could easily motivate B-player to take revenge for being deprived of \$10. Babar can do this playing Low, accepting a lower payoff for himself, and punishing Aleena by giving her \$0=ALO. Anticipating this, A-player takes the secure option of Opt-Out very often in this situation. Again this behavior shows greater wisdom than game theory.

Many questions about the theory of rational behavior are creating by these empirical observations on human behavior. Among the simplest of this is the question:  “Why does it happen that, 15% of the time, B-players choose the LOW outcome of \$4.75 over the HIGH outcome of \$5.00?”

There are many possible explanations, from satisficing to computational costs to near-indifference or fuzzy sets. One plausible explanation comes from the concept of Just Noticeable Difference (JND) – If two outcomes are sufficient close, then they are treated as “about the same” by mental decision-making heuristics.

An immediate consequence is that we cannot count on “maximization” of utility. Near-Maximization leads to a host of difficult problems for economic theories. Mankiw (1985) shows that small menu costs – changing prices at a restaurant requires reprinting the menu – can lead to large business cycles.  Similarly, Akerlof and Yellen (1985) show that “near rationality” — or approximate maximization – can have large effects on markets. More than 800 later publications which cite these papers show that approximate instead of exact maximization could be responsible for a wide range of phenomenon, such as sticky wages, the Phillips curve, non-neutrality of money, efficiency wages, and many others. If objective functions to be maximized are nearly flat in a neighbourhood of a unique global maximum, then approximate maxima can range over a very wide set, leaving the approximate equilibria very indeterminate. Virtually no one would seriously argue that people always exactly maximize utilities, but it is widely believed that approximate maximization would lead to approximately the same results as exact maximization. The literature cited above shows that this is not true; bounds on computational ability have serious consequences for economic theory

Some unexplored variants of the GH Humans with Hearts Game are listed below.

1. Building on the idea of the JND, we can assess the attitude of the B-player towards the A-Player. Keeping the B-player payoff at 5 for HIGH and 4.75 for LOW, we can vary the A-Player Payoff and see the effects. For example, suppose ALO is set to \$20, double of the \$10 that A-player gets when B-player plays HIGH. It is our guess that most human beings would voluntary forego the extra 0.25 cents they would get by playing HIGH, in order to provide a benefit of an additional \$10 to the A-player, regardless of whether or not they know who A is. This possibility cannot be contemplated by game-theorists or economists, committed to a model of infinite greed for human behaviour.
2. A negative value of BOP can create gratitude in player A. Suppose that AOP is \$15 and BOP is -\$10. Aleena should play Opt-Out to get the payoff which is higher than \$10 that she will get when Babar plays High. Suppose that ALO is \$20, and while BLO is \$3. When Babar gets the move, he might return the favour by deliberately making the Low move, choosing \$3 instead of \$5, in order to reward Aleena with the higher payoff of \$20.
3. Many possibilities for altruism and reciprocity along the lines above can be investigated. Would A-player forego Opt-Out in order to provide greater benefits to B? Would B return the favor by choosing the lower payoff, to provide a greater benefit to A? Again, conventional game theory, and economists, are completely blind to these possibilities, which do not arise in their models of heartless humans.

What is the harm of reducing the complexity of human motives to the simple one of greed? We have just seen that understanding human behavior in a very simple game requires taking into account resentment, gratitude, revenge, carelessness and reciprocity. Contrary to the reductionist economic views, a vast number of market transactions are based on motives other than greed. The widely recognized phenomenon of conspicuous consumption creates an externality and hence market failure which should be regulated – however economists fail to acknowledge the phenomenon because it requires motivations other than greed. An additional problem is that highlighting a single motive both legitimizes and encourages it: witness the “Greed is Good” maxim of Wall street.

End of slightly revised Excerpt of Section 1.2 from my paper on Empirical Evidence Against Utility Theory

Addendum 1 (Caring for Others): Developing the idea of reciprocity and altruism, I wonder what would happen if player B had an option to sacrifice his gains, in order to create greater gains for A. For example, if HIGH gives B \$5 while LOW give B \$0=BLO. But, A gets something big, like \$100. My guess is that most B-player human beings with hearts would choose to play LOW, sacrificing \$5 in order to provide \$100 to the other player. A higher order question is – how would player A play in this situation? Suppose that when B-player plays HIGH, A-player gets \$0 instead of \$10. Then A-players would OPT-OUT and take \$7, because they know that a “rational” B-player will go for the HIGH payoff, preferring \$5 to \$0, and so the A-player will end up with \$0 if A-player chooses to PLAY. However, if I was the A-player, and the game was being played in a traditional society with norms of cooperation and generosity, I would be able to COUNT on B-player to sacrifice her \$5 in order to allow me to gain \$100. In a market society with rampant individualism, where children grow up in broken families and see everyone acting selfishly, and no examples of selfless sacrifice, I would not be so sure, but I may still be willing to take a chance on the B-player. If the game was being playing in a community of professional economists, then I would certainly opt-out, because, being brainwashed by their own theories, professional economists would almost certainly choose to take their \$5 and ignore the option to sacrifice this small amount in order to allow me to win \$100.

ADDENDUM 2 (Social Versus Market Frames): A very interesting finding of experimenters (see Dan Ariely – Predictably Irrational) is the people behave very differently in SOCIAL situations and in MARKET situations. For example, many people would be very happy to DONATE blood for a good cause, but would not agree to do so for money.  Economists have a REALLY difficult time understanding this — Nobel Laureates argued that adding a money payoff would only strengthen the motivation to donate blood, but experiments show otherwise. Economists also have difficulty understanding FRAMING effects — how the game is described MATTERS – people do not see through to the final payoffs, as game theory predicts they should. According to economists the framing – the words used to describe the game – should be irrelevant. The “rational” homo economicus sees through the empty words and only concerns himself with the payoffs. HOWEVER, human beings with hearts DO NOT behave like this. When playing this ARTIFICIAL game, HOW we described the game is EXTREMELY important. They will translate this decision into EITHER a social frame OR a market frame – and then they will behave very differently. So one important factor to consider in setting up an experimental game is whether the description of the game evokes a social context or a market context.

ADDENDUM 3 (Neutral Description of Games): Standard protocol for experimental game theory holds that we should try to describe the game in neutral language, which does not evoke any emotions. If subjects are used to decision making in adversarial market-contexts (my gain is your loss) and also in social contexts (with cooperation, generosity, and win-win outcomes) then neutral language leaves them clueless. As a result, they will ARBITRARILY translate the game into one of the two frames (my guess). This will introduce a random variation in outcomes. It might be better to explicitly specify one of the two frames, so as to eliminate this source of variation. This would be contrary to standard methodological practice.

ADDENDUM 4 (Poisoning the Well): This game illustrates the argument of Julie Nelson that Economic Theory damages Moral Imagination. A game-theorist B-player may feel happy to give up his measly five bucks in order to give a gift of \$100 to the A-player, but training in game-theory tells him that this is  irrational behavior, and so he over-rides his natural impulses towards generously in order to behave like the greedy homo economicus.