Behavioral Game Theory: Not Just a Theory and More Than a Game
“Don’t play the odds, play the man.”
- Harvey Specter (Suits)
In economics classes, we are usually introduced to game theory as a way to explain oligopolies, as the decisions of one firm are influenced by the decisions of other firms. However, game theory can be used to explain a lot more: aspects of human nature, business decisions, and largely the world around us. For game theory to do all that though, we need to incorporate human emotions and actions into our games, so we can truly play both the odds and the man.
The Classic Prisoner’s Dilemma
Most people who’ve taken an economics class have heard about the famous “prisoner’s dilemma”. To recap the rules, let’s begin by reading an excerpt by Clark Donley, professor of Philosophy at Georgetown, who summarizes the premise of the game.
(A paraphrased version):
“John (Prisoner A) and Ben (Prisoner B) have been arrested for robbing a bank and are placed in separate isolation cells. Both care much more about their personal freedom than about the welfare of their accomplice. A clever prosecutor makes the following offer to each: “You may choose to confess or remain silent. If you confess and your accomplice remains silent I will drop all charges against you and use your testimony to ensure that your accomplice does serious time. Likewise, if your accomplice confesses while you remain silent, they will go free while you do the time. If you both confess I get two convictions, but I’ll see to it that you both get early parole. If you both remain silent, I’ll have to settle for token sentences on firearms possession charges. The choice is yours”.
In chart format, the prisoners’ options look like this (Prisoner A’s entries are in the left hand column, and Prisoner B’s entries are in the right hand column):
In other words, if they both confess they both get 5 years in prison; if they both stay silent they each get 1 year. If one player confesses and the other stays silent, the one who confessed gets off free while the other does 10 years.
To break this down, let’s first look at Prisoner A’s options. If he thinks his accomplice will confess, he should also confess to get 5 years in jail instead of the 10 years if he stayed silent. If he thinks his accomplice will stay silent, he should also confess, as getting off free would be better than spending 1 year in jail if he also stayed silent.
Prisoner B’s options are essentially the same thing: he would also be better off confessing no matter what Prisoner A does. Acting in their own self-interest, both parties’ dominant strategies — the strategy that he or she should choose regardless of the other player’s actions — is to confess. If both prisoners confess, the game ends in Nash equilibrium — the position where both players’ strategies are optimized when taking the other’s decision into account — with both players spending 5 years in prison. As both prisoners act in their own self-interest, they actually move away from the most optimal outcome for both parties where both stay silent to avoid 4 extra years in prison, demonstrating the trade-off between optimization and self-interest in some game theory scenarios.
Behavioral Game Theory
In the “prisoner’s dilemma”, the prisoners acted in their own self-interest despite the opportunity for both prisoners to get away with less jail time, not choosing the most optimal outcome for the game. This was likely because of a couple factors: both prisoners acted rationally to get the best outcome for themselves, and both prisoners had the common knowledge of the game’s structure.
However, in real-world scenarios, we can’t assume that every player acts rationally every time and has perfect, common knowledge of the scenario. Real-world scenarios play out differently because we must acknowledge and take into account human irrationality and emotion. Hence, games which internalize and acknowledge these factors are termed behavioral game theory.
There are three key factors (beyond rational thought) that influence decision-making in behavioral game theory:
- Social Preferences: considering the effect of human factors like fairness, selfishness, and reciprocity into the scenario
- Bounded Rationality: the idea that individuals (due to “cognitive limitations”) will likely choose a more satisfactory option rather than a more rational one
- Framing Effects: the way that options are presented influence an individual’s decision-making
Of these three factors, the most important and impactful is likely social preferences, especially fairness. As humans, we have a natural tendency to wish to better ourselves but not at the complete expense of the other person. We like to make ourselves better off while avoiding extreme inequality in the outcome of a game. This is a concept we call inequality aversion — where inequality is an unfavorable outcome, so we include fairness into our games.
Accounting for Inequality Aversion
Created by Ernst Fehr and Klaus Schmidt, the Fehr-Schmidt model can be used to show the impact of inequality aversion on utility and decision-making, demonstrating that inequity and unfairness affect the Nash equilibrium and dominant strategies.
The Fehr-Schmidt Model looks like this:
- Ui(x) is the utility of player i where x is the payoff of all players in the game
- Xi is the monetary payoff of player i
- Xj is the monetary payoff of player j (as long player i doesn’t receive the same payoff)
- αi is the coefficient for envy (a high αi has extreme distaste when others have higher payoffs than them)
- βi is the coefficient for guilt (a high βi means that the person feels uncomfortable when they have a higher payoff than others)
The Ultimatum Game
There are two players, player one (the proposer) and player two (the responder). The proposer offers a proposal to split $10 dollars with the responder. The responder can either accept or reject the offer. If the offer is accepted, both players get to keep their share in cash, but if the offer is rejected, both players walk away with nothing.
To understand the individual players, let’s outline their envy and guilt coefficients:
- Proposer: αi = 0.4, βi = 0.3
- Responder: αi = 0.7, βi = 0.2
The responder will accept the offer if Ui(x) > 0.
Let’s start off with the $9/$1 split in favor of the proposer:
Ui(1) = 1–0.7 x max (9–1,0) — 0.2 x max (1–9,0)
Ui (1) = -3 utils (Reject)
With the responder’s higher envy coefficient, he strongly dislikes the idea of him getting “cheated” out of his fair share of money, leading him to reject the offer.
Now let’s look at the $5/$5 split:
Ui(5) = 5–0.7 x max (5–5,0) — 0.2 x max (5–5,0)
Ui(5) = 5 utils (Accept)
The responder highly values equality, and this offer is as equal as it gets. It’s a no-brainer to accept the offer.
How about a split of $7/$3 though?
Ui(3) = 3–0.7 x max (7–3,0) — 0.2 x max (3–7,0)
Ui(3) = 1 util (Accept)
Although not fully equal, the responder would still likely accept the $7/$3 split because he is still $2 better off than the $9/$1 split, and the outcome appears more equal. Instead of feeling the need to punish unfairness, the responder sees it as not optimal but somewhat equal and acceptable given the circumstances of the game.
The Ultimatum Game: Analysis
Thinking purely economically and ignoring human intervention, the optimal outcome to the game would be the $9/$1 split that we saw previously. The proposer (player 1) was in control of the money and situation, meaning he would dictate the outcome of the situation and take the $9 for himself. The responder (player 2) should also accept the $1 because he is $1 better off than he would have been had he not participated in the game. From an economics standpoint, this would be the best and most efficient outcome for the game.
However, when situations incorporate human emotions and actions, the outcome of said game shifts dramatically. Instead of thinking purely economically, player 1 must consider offers that player 2 would be likely to accept, even if that means taking less money for himself. Taking into account player 2’s propensity to reject the offer shifts player 1’s dominant strategy. His change in dominant strategy combined with player 2’s inequality aversion shifts the Nash equilibrium away from the economically-efficient outcome towards a more equal distribution of the money.
Applications of Behavioral Game Theory and Inequality Aversion
We can see the profound impact of behavioral game theory, especially in business, entrepreneurship, and negotiation. If a businessman tries to obtain a favorable contract from suppliers, he must understand who the supplier is, what the target price is, what an objectively fair price is, and a way to obtain a favorable deal without totally screwing over the supplier. If an entrepreneur pitches their startup to investors, they must understand who they are pitching to, a fair valuation for the company, a good deal for the investors, and how easy it is to insult their investors with a lowball offer. Negotiation is about playing the man in these scenarios as much as the data, as taking into account human emotions and the decisions of others is imperative in creating a favorable and equitable outcome for any real-world scenario.
We also see specifically inequality aversion’s impact in business, consumer behavior, and public policy. When hiring employees, businesses often set wages considering fairness, taking into account the amount of responsibilities and stress to decide a fair wage. Consumers are far more willing to pay for products that are fairly priced and produced under fair labor conditions, showing inequality aversion’s place in capitalistic economies. Lastly, public policies, especially those which attempt to reduce poverty, income inequality, and inequality of opportunities, are created with inequality aversion in mind, as these interventions aim to make our society more fair and equal for everyone.
Conclusion
When we look closer at our world, we can see how inequality aversion and behavioral game theory are at the core of transactions, laws, and businesses. Inequality aversion and behavioral game theory have such widespread applications because they account for human nature: an unavoidable part of equations that are largely ignored. Accounting for human nature allows us to better simulate real-world scenarios and find more equitable outcomes for everyone.
In a world dominated by data and facts, human nature is still at the core of every decision we make. That’s why Harvey Specter said, “don’t play the odds, play the man”. However, understanding “the man” and the numbers can help us understand the world around us and maybe even ourselves a little better.
Disclaimer: I am not a professional; my articles are strictly for educational purposes.
Thank you for reading my article! You can find more of my content here. If you want to be a writer for my publication, feel free to email me at kalan.karuppana@gmail.com.
