“Without having a broad set of facts on which to theorize, there is a certain danger of spending too much time on models that are mathematically elegant, yet have little connection to actual behavior. At present our empirical knowledge is inadequate and it is an interesting question why game theorists have not turned more frequently to psychologists for information about the learning and information processing processes used by humans.” (van Damme, 1995)
As researchers consider the future of judgment and decision-making sciences, a debate emerges as to which tools and branches will be most essential to understanding human behaviors. Which models will be most predictive? As Eric van Damme indicates in the previous quote however, mathematically elegant models only go so far in explaining the decision-making patterns of human behavior. Does cultural, societal, or environmental context matter? I believe that behavioral game theory is the most essential approach to judgment and decision-making sciences for the next generation of researchers. Behavioral game theory models a wide variety of interactions. Yet, the strength of behavioral game theory lies in its ability to grow in an incremental manner, slowly increasing the complexity of such games. In this paper, I will describe the strengths and possible critiques of behavioral game theory, and outline the reasons why further research in behavioral game theory would be fruitful for the area of judgment and decision making sciences.
Game theory studies what happens when two people, or more generally, two entities, interact. There are countless instances of such interactions everyday, for example, a person trying to bargain at a flea market, a football player deciding who to pass the ball to, or people bidding on an artwork at an auction. In all of these circumstances, a person, group of people, or entity must anticipate what others will do while at the same time trying to decipher what others will infer from their own actions. These situations can be referred to as games, and the people or entities playing it are mere players. More generally, we could say that a game consists of strategies that each players utilizes. The game also has precise rules. These rules dictate the order in which players will choose strategies, the information that is available when they choose, and how desirable each of the possible outcomes might be (C. F. Camerer, 2003).
Game theory is a relatively new field of study, defined by Jhon von Neumann and Oskar Morgenstern, paternal figures for the field, who introduced many of game theory’s features back in 1944 (C. F. Camerer, 2003). Since then, several great thinkers and scientists have contributed to the field. Among them is John Nash, who proposed a solution to the problem of how rational players would play, now referred to as “Nash equilibrium”. Nash equilibrium is the idea that when playing a game, players will adjust their strategies until no player can benefit from changing (C. F. Camerer, 2003). In other words, it would be the moment when all players are choosing the strategies that are the best responses to the other players’ strategies.
Not only does game theory have the capacity to describe a variety of different worldly interactions through games, but it has practical applications as well. Because of its unique approach, it can give standard definitions to words that have a long history of being interpreted differently, depending on the branch of social science in which a word is referenced. Take “trust”, for example, which is studied by psychologists, sociologists, philosophers, and economists alike. But what is trust? “Because of its game approach, game theory can give a more standard definition to be used in all areas of social sciences. Would you lend money to somebody who doesn’t have to pay you back, but might feel morally obliged to do so? If you would, you trust her. If she pays you back, she is trustworthy.” (C. F. Camerer, 2003).
Game theory is the umbrella term that describes what happens when two entities interact. For the purposes of this paper, I will also discuss and compare analytical game theory and behavioral game theory, in order to highlight the significance and potential of behavioral game theory to deepen our understanding of decision-making processes. It is therefore necessary to begin by briefly defining analytical game theory. Analytical game theory is “a mathematical derivation of what different players with different cognitive capacities are likely to do in games” (C. F. Camerer, 2003). That is to say, analytical game theory is the manner in which non-emotional, rational, and analytical beings should play. This does not fully capture how human beings interact in reality! Consider a person bargaining at a flea market over the price of a couch as a real life example of a game. The experimental recreations of such a game prove the analytical game theory behind it to be half right and half wrong. Wrong about the opening prices sellers state, but right about the rate at which sellers drop the prices over time (C. F. Camerer, 2003). Behavioral game theory came to exist as an attempt to give better predictions or explanations to such phenomena. Behavioral game theory “expands upon analytical game theory by adding emotion, mistakes, limited foresight, doubts about how smart others are, and learning to it” (C. F. Camerer, 2003).
A further strength of behavioral game theory is its capability to model so many different phenomena as a simplified game. Consider, for example, the continental divide game. The continental divide game alludes with its name to a geographical continental divide. If you are in the continental divide in Alaska and pour some water exactly on it, some water will flow towards the Arctic Ocean while the rest will flow towards the Pacific Ocean. More generally, continental divide games show how two things that started right next to each other might end very far away from each other (C. F. Camerer, 2003). In other words, it attempts to model some sort of butterfly effect. A famous theory portraying such effect is the broken glass theory. The broken glass theory explains how something as small as a broken window can have enormous consequences in a neighborhood. It explains in an anecdotal manner how a broken window can lead neighbors to feel less obligated to mow their lawn, put a fresh coat of paint on their house, or even to replace broken windows (C. F. Camerer, 2003). This effect can spiral further into urban decay that is associated with more criminal behavior and violence. Alternatively, if the window had been fixed immediately it would not have produced this butterfly effect of social decay. In other words, this theory explains how disorder can breed more disorder. This seemingly simple solution to a large-scale problem is what makes this theory so appealing.
In behavioral game theory, when creating a game, the number of players and iterations as well as the system of punishment and rewards for cooperation or defection can be determined. The visibility of the players towards the outside observers can also be defined, which in turn would affect their reputation. The validity of research documenting the nature of altruistic behavior, for example, rests on the careful design of such games to be able to isolate specific conditions and behaviors (Benenson, Pascoe, & Radmore, 2007). If such isolation is not achieved successfully, the amount of influences a person might have when making a decision might fall beyond measure. On the other hand, because of the isolation of factors and behaviors in these games, it could be argued that they lack ecological validity and therefore provide imperfect predictors. Nevertheless, if a single experiment is taken into account along with the field evidence of naturally occurring altruistic behavior (Barraza & Zak, 2009; Fehr & Fischbacher, 2003; Joyce Berg, Dickhaut, & McCabe, 1995), it could provide its much needed ecological validation as well as shedding a light into what parameters influence this behavior. Once these parameters are known, we can modify or mimic them in experiments to simulate a more natural interaction (Benenson et al., 2007).
One might wonder how reliable are the generalization of these games? How well can a game played by college students portray more complex circumstances such as companies creating corporate strategies or diplomats negotiating foreign policy? Nevertheless any doubts about the generalizability of such games is an indication of the need for more complex games, not a dismissal of the experimental method per se (C. F. Camerer, 2003). I believe that if the isolation of conditions and behaviors is done appropriately, and results are carefully documented, researchers can slowly make conditions more complex. This way we can approach and recreate more natural and complex circumstances in an incremental manner without losing the insight that each step is there to offer. (C. F. Camerer, 2003). An example of such small increments on previous knowledge can be found in Andersson, Galizzi, et al.’s paper “Persuasion in experimental ultimatum game”. In the paper they expand on the known behavior in the ultimatum game by adding possible conversation between the participants (Andersson et al., 2010). When thinking about this approach, a clear downside comes to my mind. As games evolve to simulate more complex scenarios, it becomes harder and harder to to decipher what influence did each variable have and how the interaction of those variables affects the whole scenario. Furthermore true causality of the influence of each variable and their interactions would become harder and harder to prove.
As I stated before, behavioral game theory looks to expand upon analytical game theory. By expanding on it, it introduces variables and observations. Such variables and observations need to be analyzed and studied very carefully before being introduced in order not to draw erroneous or misguided conclusions. An example of very careful careful planing can be found in the paper “Children’s Altruistic Behavior in the Dictator Game” (Benenson et al., 2007). The experiment of such paper consisted in letting kids choose their ten favorite stickers out of a bunch of thirty. From those ten, the kids would be asked to put the stickers they were willing to donate into an envelope. The researchers explained to them that the donated stickers would go to kids who were not fortunate enough to participate in the experiment. The careful planning of the experiment is demonstrated with the stickers. First, the reason the experimenters decided to use stickers is because they are valued by children. Second, the stickers were from a foreign country (the study was ran in the United Kingdom), therefore ensuring that no kid would have obtained an identical one before. Third, even though children from lower socioeconomic status (SES) are likely to value stickers more, this would be unlikely since the experimenters made sure that in both schools (low and high SES) teachers use stickers to reward superior performance. Lastly, the size of classes in both schools were the same, therefore ensuring that the stickers would not represent a scarce resource at either school. This shows that experiments need to be planned with luxury of detail in order to prevent the development of misguided conclusions. While this is a weakness of game theory, it illuminates an important point for the future of judgment and decision-making sciences and the way scientists conduct their research.
Behavioral game theory not only can build upon game theory by adding variables and different observations to analytical game theory, but I believe it can expand our perspectives. I am a preference utilitarian and a mathematician. As a mathematician I used to hold a very analytical and rational approach towards games. As a preference utilitarian I believed that humans are self-interested. As Camerer would say, I was smitten by the elegance of analytical game theory. That drove me to believe that if a person in an experiment acted as game theory would have predicted, then that person understood the game. If the person acted in any other way, then he/she did not understand the game.
An example of how I reached this conclusion can be found in the results of an ultimatum game. In an ultimatum game, two players, a proposer and a responder bargain over a certain amount, say 10 dollars. The proposer has to offer an amount x to the responder. This amount has to be between 0 and 10. If the responder accepts, he/she gets x while the proposer gets 10 – x. If the responder rejects the offer, no one gets anything (C. F. Camerer, 2003). With my old ideologies and beliefs, I used to think that any person playing as a responder should accept the quantity x no matter how much it was. This was because I believed that as a self-interested rational person, anyone would take x over 0 which is the consequence of not accepting. Analytical game theory supported this belief I had. I found myself believing that anyone who would not take x did not understand the game properly. It was not until I learned about behavioral game theory that I changed my perspective. Behavioral game theory experiments proved that responders are willing to take costly actions to show their disgust with outcomes that seem unfair (Andersson et al., 2010). In other words they were willing to get nothing if they could take the proposers down with them and cause them to earn nothing as well. In general, these experiments showed that responders think that about less than half is unfair and are more willing to reject the offer to punish the proposer (Andersson et al., 2010). These results differed from what analytical game theory proposed and therefore attracted the attention of behavioral game theory (C. Camerer & Thaler, 1995). This act of being willing to punish the other at a great cost to oneself is called negative reciprocity (C. F. Camerer, 2003) and it can actually be found in many forms in real life. An obvious example, might be a bitter divorce, when both parties incur high sums to prevent an ex-partner from receiving more than what they deem as “fair.”
Behavioral game theory taught me that humans do not act solely on rationality and self-interest. Furthermore, I learned that there is rationality behind the responder not taking the amount. It is important to note that behavioral game theory did not come into existence to fight analytical game theory. It was brought as a tool to expand our concept of rationality. In other words, thanks to behavioral game theory I was able to drop my naive perspective and adopt a more holistic approach that models with greater accuracy how humans actually behave. Behavioral game theory is the tool, in and of itself, that allows human beings to realize the complexity and number of variables that are in play in any decision-making process. I believe behavioral game theory can expand the perception of scientists while giving them a tool to make sense of how humans actually interact.
Consider the ultimatum game. Behavioral game theory builds upon analytical game theory, proving that there is more for researchers to consider beyond pure rationality. Consider for example, the idea of cultural context. As stated before, when playing the ultimatum game, people will think unfair any quantity that is not close to half and will likely reject it. Nevertheless this does not hold true for “primitive” cultures in the Amazon, Papua New Guinea, Indonesia, and Mongolia (C. F. Camerer, 2003). These cultures behave exactly as analytical game theory predicts anyone should behave in an ultimatum game. To me, this proves that there is a lot more at play when making a decision than just pure rationality or analytical analysis. Other influences can come from culture (Alvin E. Roth, Vesna Prasnikar, Masahiro Okuno-Fujiwara, & Shmuel Zamir, 1991), societal standards or expectations, or even emotions. That is why behavioral game theory is essential. With it, researchers can eventually decipher what variable or combination of variable is what marks this difference.
As the world becomes increasingly complex, it is critical for researchers to use a model that allows for variability and depth. Behavioral game theory expands upon analytical game theory by adding emotion, limited foresight, doubt, and learning to the variables that influence decision making. By doing so, it is able to portray and predict with greater accuracy the actual behavior of humans. Nevertheless, there are two possible breaking points for this type of research. First, researchers need to plan these experiments and game with luxury of detail in order to make sure that they are isolating the variables that they want to observe and nothing else is coming into play. Second, as scenarios become more and more complex, it becomes harder to determine the causality of each variable or their interactions. Taking all into consideration, I believe that with extensive planning of experiments and deep analysis of results, behavioral game theory remains as a tool capable of providing insights to our behavior that no other tool can provide. If done appropriately, behavioral game theory will provide numerous and more effective models and predictions within each experiment, that building upon previous knowledge. Such models will become widely usable, - applicable to both diplomacy to consumer behavior, for example. But most importantly, behavioral game theory can help us understand that rationality is not purely analytical and unemotional, but variable and complex, just like human beings.
References:
- Alvin E. Roth, Vesna Prasnikar, Masahiro Okuno-Fujiwara, & Shmuel Zamir. (1991). Bargaining and Market Behavior in Jerusalem, Ljubljana, Pittsburgh, and Tokyo: An Experimental Study. The American Economic Review, 81(5), 1068–1095.
- Andersson, O., Galizzi, M. M., Hoppe, T., Kranz, S., der Wiel, K. van, & Wengström, E. (2010). Persuasion in experimental ultimatum games. Economics Letters, 108(1), 16–18. https://doi.org/10.1016/j.econlet.2010.03.011
- Barraza, J. A., & Zak, P. J. (2009). Empathy toward Strangers Triggers Oxytocin Release and Subsequent Generosity. Annals of the New York Academy of Sciences, 1167(1), 182–189. https://doi.org/10.1111/j.1749-6632.2009.04504.x
- Benenson, J. F., Pascoe, J., & Radmore, N. (2007). Children’s altruistic behavior in the dictator game. Evolution and Human Behavior, 28(3), 168–175. https://doi.org/10.1016/j.evolhumbehav.2006.10.003
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- Fehr, E., & Fischbacher, U. (2003). The nature of human altruism. Nature, 425(6960), 785–791. https://doi.org/10.1038/nature02043
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- Joyce Berg, Dickhaut, J., & McCabe, K. (1995). Trust, Reciprocity, and Social History. Games and Economic Behavior.
- Kagel, J. H., Kim, C., & Moser, D. (1996). Fairness in Ultimatum Games with Asymmetric Information and Asymmetric Payoffs. Games and Economic Behavior, 13(1), 100–110. https://doi.org/10.1006/game.1996.0026
- Roth, A. E., & Erev, I. (1995). Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term. Games and Economic Behavior, 8(1), 164–212.
- van Damme, E. (1995). Game Theory: The Next Stage, (10), 122–142.
Best,