Game Theory is a specific subset of economics that deals with strategic decision-making and seeks to understand decision-making in decision-making animals under the presumption of man being a rational economic agent. In economics, at least classical economic theory, homo economicus is the presuppositional starting anthropology. Homo economicus, derived from Locke, Smith, and Ricardo, is the assertion that man is an economic producer and consumer—this is man’s primary being—and that he is rational, i.e., man seeks his self-interest (but not necessarily at the exclusion of cooperating with others if such cooperation is in one’s self-interest).
Game theory is really an attempt to understand logical decision-making in economic animals. Games range from asymmetric to symmetric, cooperative and non-cooperative. Cooperative games deal with problems of trust. Non-cooperative games involve competition and given the competitive nature of games non-cooperative games are about scarcity, self-interest, and that the best strategy is to stick with one’s original strategy (the Nash equilibrium).
Game theory includes perfect information and imperfect information. Perfect information gives the player the easiest overview of how logic should develop without interference from other players. Imperfect information adds confusion into the problem of scarcity. For instance, in a game with perfect information, and with the assumption of rational decision-making taken, a player can easily “guess” what the strategy of another player will be. However, games of imperfect information are the closest to reality. Why?
The problem with classical economics that game theory sheds light on is the faulty starting anthropology of the rational economic agent. Heterodox economists, like the Austrians (Austrian school) deny the reality of homo economicus; game theorists generally developed to become leading heterodox economic thinkers because of their studies and dilemmas created by game theory problems. This is one of the ironies of game theory. What started as an attempt to show the homo economicus came to generally disprove the reality of homo economicus. Man is a driven economic animal, to be sure, but he is fundamentally irrational—this is the position adopted by heterodox economists. We cannot predict what man will do—especially other men. This is what game-theory tries to ascertain. What does a supposedly rational economic agent do in games of perfect information, imperfect information, scarcity, abundance, cooperation, and non-cooperation?
The “Prisoner’s Dilemma” is one of the quintessential introductory game to all game-theory students. It was one of the first games I learned in my game-theory class as an economics undergraduate. The game is a game of perfect information and cooperation. It goes like this:
Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The offer is: (1) If A and B each betray the other, each of them serves two years in prison, (2) If A betrays B but B remains silent, A will be set free and B will serve three years in prison (and vice versa) (3) If A and B both remain silent, both of them will only serve one year in prison (on the lesser charge).
Given the four possible outcomes on the table, how should you proceed?
The logical cooperative strategy is that both should remain silent and receive a year-one sentence. But is man rational? What is rationality? Is man social or solitary? Suddenly, we find ourselves asking deeper philosophical questions than mere economics. Can I trust the other player to uphold their bargain? Once you ask this question to yourself the game of perfect information suddenly shifts into a game of imperfect information! With the reality of imperfect information involved despite the “perfect information” of strategy and outcomes, the imperfect information rests on the other player. What will they do? If we agree to cooperate, can I trust him or her to keep their word?
Heterodox economists say no. Suddenly, the impetus of self-preservation kicks in. If I stay loyal to the agreement but the other player does not, I will receive a three-year sentence! If I talk, that is, betray the other player, I am guaranteed a lesser penalty than three-years. At worst, I will suffer a two-year penalty. Possibly, I can get out for free. What should you do? The logical uncooperative (self-interested) strategy is to betray because you are guaranteed not to have the harshest sentence given you do not know what the other player will do. Suddenly we have a conflict in logic. The logic of cooperation vs. the logic of self-interest. Both are logical positions to take, but in this conflict of logic, and there are conflicts of logic, how do we proceed?
We now enter the realm of strong and weak strategies. But we’ll examine strong and weak game theory strategies later. If rationality means self-interest, then the rational decision is not to cooperate but to betray the other. If rationality means cooperation, then the rational decision is to both stay silent—but to stay silent entails a guaranteed one-year sentence. Does the allure of possibly going free win out? Or does trust that the other player will uphold the agreement win out and minimize damage? Do you go for no damage or do you minimize damage? What if you think the other will honor cooperation? Logically, you should betray to go free.
The strong strategy, not getting into the detail of why, is that you should always betray. The weak strategy is cooperation. The strong strategy ensures you are not dependent on the other. The weak strategy keeps you tied up with the other or others. But the strong strategy will probably lead to a two-year sentence (though it has the possibility of no sentence). The weak strategy, which involves cooperation, will lead to a one-year sentence. We encounter a paradox. The strong strategy of betraying will likely lead to increased harm.
But why is the strong strategy to betray? If you think the other player will stay silent, you should betray because you will get to go free. If you think the other player will betray, you should betray to avoid the maximum penalty. Based on the choices available to the other player we see that the best strategy for the self is to always betray.
The Prisoner’s Dilemma is the simplest introduction to game theory. It is not a complex game, and many Game Theory games can become exhaustively complex. What the Prisoner’s Dilemma shows, however, is that those who think economics is simple are probably in for a rude awakening when reality strikes. We will explore more game theory, and substance economics, as time goes on. Meanwhile, we pose the question to you: What would your preferred strategy be and why? What game theory ended up inverting is the understanding of humans as rational animals to decision-making animals. We are posed with decisions but what course of action will these decision-making animals take? Should we assume the worst case scenario or best case scenario, how does our thoughts about human nature impact our decision making?