The classic Prisoner’s Dilemma is first and foremost a paradox. The classic two-person situation results in neither player being able to avoid a loss, even when each selects his optimal strategy. Many business analysts have generalized the Prisoner’s Dilemma to business competition. While the same dynamics may exist in the hypothetical Dilemma and in many real-world situations, the latter are usually far more complex than the theoretical construct. Most importantly, when the Prisoner’s Dilemma exists in real life, there is almost always a solution.
The Prisoner’s Dilemma is a hypothetical situation wherein each of the two opponents must choose either a cooperative or an uncooperative strategy. If each chooses the cooperative strategy, both will gain (or both will lose relatively little); if one defects while the other cooperates, the defector will gain more than he would have by cooperating, while the cooperating party will lose heavily; if both defect, each will lose moderately. It has been shown that the optimal strategy is for both to defect. The “dilemma,” or paradox is that the best strategy for each results in a worse outcome than if they had cooperated. This situation, where neither party can form a strategy that will improve his result, is called the “Nash equilibrium.”
Of course, this equilibrium is dictated by precise conditions. If, for instance, the reward from mutual cooperation is greater than the gain from defecting (while the other person cooperates), then the Nash equilibrium will have both parties selecting a strategy of continuing cooperation. The scenario also assumes that both players must play. If the best possible strategy still results in a loss, then the rational thing to do, if the choice exists, is to not play at all. The fact that participants almost always engage in markets voluntarily undermines the usefulness of the Prisoner’s Dilemma as a model; in the Dilemma, the prisoners are forced to play.
Yet another problem with the Prisoner’s Dilemma as a strategy model is that by itself, it is not an iterative strategy. That is to say, it is a one-shot. But that is not the way real life works. In most business as well as diplomatic and even personal relations, the standard default setting is “trust but verify.” In other words, start with a cooperative strategy but be ready to punish defectors. Nowak and Sigmund noted that the first strategy shown to be successful in an iterative game of Prisoner’s Dilemma is tit-for-tat; do what your opponent did last time: “Thus in a single round it is always best to defect, but cooperation may be rewarded in an iterated (or spatial) Prisoner’s Dilemma” (Nowak & Sigmund 56). They went on to explain, however, that a superior strategy existed, namely, that of “win/stay, lose/shift,” wherein a given player does best to stick with a given stance until he loses, at which time he should shift (Nowak & Sigmund 57). It is interesting to examine these strategies in a “real-world” scenario.
Let us hypothesize that two gas stations are located on opposite sides of a busy intersection. Each is as easy to get to like the other, and each offers similar amenities such as a snack store, clean restrooms, etc. Therefore neither has a competitive advantage over the other aside from whatever cachet may be attached to the respective brands of gasoline they sell. When this situation is seen in real life, very often the two stations’ prices are exactly the same. This is the result more often than not of a cooperative effort, wherein each station’s proprietor wishes to avoid the Prisoner’s Dilemma in iterated form. For example, each station sells regular unleaded for $3.50/gallon. A cooperative strategy would have them maintaining their prices at equal levels. Should their costs go up or down, they should raise or lower prices in tandem. The owner who either doesn’t raise his price enough or lowers it too far in an effort to undercut his competition is the defector. At this point, the cooperator has no choice but to match his competitor’s price cut the way Target does with competitors and price-matching. Thus, defection produces an initial gain (before the cooperator can react), but in the second iteration, the gain is wiped out and both players lose, now splitting sales as before but with lower profit margins for each. This retaliatory move, in the tit-for-tat strategy, punishes the player who lowers his prices, with the idea that the initial cooperator will revert to cooperation until the other player defects again. This produces a stable situation (mutual cooperation), assuming both players are rational.
Let us examine the two gas stations in light of the win/stay lose/shift strategy. Here, if one station lowers its prices but the other does not, the former station will stay with its strategy of price-cutting until the other side reacts. If one station loses, either by setting its prices so low that it no longer makes sufficient profit or by leaving its prices so high that it loses business to its cost-cutting competitor, it will change its pricing strategy. Thus, the iteration is more important than the game itself. The reason why the Prisoner’s Dilemma in its unvarnished form is a paradox is that there is no prior iteration. A crucial, one might say the only, piece of information needed to make the right choice in the history of one’s opponent. If, for instance, the opponent is a habitual cooperator, then one should cooperate if the reward is greater than that gained from defecting (in the scenario where the opponent cooperates) and defect if the reward is greater from defecting. If one’s opponent is a habitual defector, then one should use the exact opposite of the above strategy. It is rare in real life that two selfish, competing entities do not know each other’s history.
The Prisoner’s Dilemma can also apply to strategies other than pricing. Let us say that two competing regional airlines each serve a route between two cities and that each loses money on that route. Let us also assume that each is at a price point where fares can’t be lowered without increasing the loss from that route. Let us also assume that should one airline abandon the route, the remaining one would realize a profit on that route; in other words, what makes the route unprofitable is that there is too little business to support both airlines. In such situations, knowledge of the other player’s tendencies is crucial. As Kreps, Milgram and Roberts et al. noted,
A common observation in experiments involving finite repetition of the prisoners' dilemma is that players do not always play the single-period dominant strategies (“finking”), but instead achieve some measure of cooperation. Yet finking at each stage is the only Nash equilibrium in the finitely repeated game. We show here how incomplete information about one or both players' options, motivation or behavior can explain the observed cooperation. (Kreps et al. 245)
There would be two basic strategies each airline could employ. One would be an essentially uncooperative strategy: to lower prices on the route with the idea of taking all the business (however unprofitable in the short term) and driving the other airline away from the route altogether. Another would be a cooperative strategy: to withdraw from the route under an agreement that the other will as well, thereby removing a loss generator for both companies. Again, there would be no winning strategy for a single iteration. In a multiple-iteration situation, though, one airline would withdraw from the route only if the other had a history of cooperation with it; if the other’s history tended more toward defection, then the proper strategy would be to stick with the route and cut prices. In general, “price wars” and large price fluctuations happen when there is a history of inter-business competition and rivalry in a given sector, and prices tend to remain relatively stable when a cooperative atmosphere exists.
There is a major problem with the tit-for-tat strategy and its more sophisticated variants, such as the win/stay strategy. One player or the other may act irrationally. This will have a ripple effect through many subsequent iterations of the game and can produce a single-iteration-style outcome (i.e., both players lose). Molander noted in citing Axelrod’s tournament and subsequent analysis that “When played against itself, the tit-for-tat strategy is extremely vulnerable to disturbances. If for some reason, a defective move is made, then it will echo through the game permanently” (Molander 611). A good example of this is in the market for major-league baseball players. The top athletes command annual salaries in excess of $25 million, the result of bidding wars in the last decade that drove the price of premium baseball players from $1 million annually to the present levels. Obviously, had the owners cooperated, prices would have stayed at reasonable levels. The result is that every single major league baseball team has lost money in the last decade, even those that have been highly successful. Clearly, the defective moves made by owners (overbidding for players) have resulted in a multiple-player Prisoner’s Dilemma: everybody loses (except the players!). In other words, any model based on rational behavior by the participants breaks down when one or more participants do not, in fact, act rationally.
That said, one must assume in making business decisions that one’s rivals will act in a self-interested fashion. What can be done, then, to avoid the Prisoner’s Dilemma outcome? Iterated strategies seem to be the best course, but as noted above, their efficacy depends heavily on accurate prediction of an opponent’s behavior, based on that opponent’s history. The most interesting aspect of this is that one’s own behavior cannot be too predictable: both the habitual cooperator and the habitual defector can be exploited. Segal and Sobel noted that the iterated strategy is most effective when one assigns probabilities to the opponent’s possible reactions: “It provides conditions under which a player's preferences over strategies can be represented as a weighted average of the utility from outcomes of the individual and his opponents. The weight one player places on an opponent's utility from outcomes depend on the players’ joint behavior” (Segal & Sobel 197). In other words, even when the opponent/rival has only two strategies available, it would be a mistake to consider them as either/or; the opponent may strongly prefer one or the other, based either on history or the prevailing situation.
One signal concept emerges from this analysis: the player in iterated Prisoner’s Dilemma who is too predictable will be had for lunch. In business terms, this means that only a flexible business entity will survive in a competitive environment. If it is proper (optimal) to react to a rival’s market moves by changing prices, methods, etc. but a business lacks the ability to make the needed changes, it will ultimately lose market share and profitability. Also, inflexibility equals predictability. The business that cannot quickly adapt is a prime target for those that can. This, in fact, is why smaller businesses entering the market often have an advantage over more established competitors: small size gives mobility and flexibility.
Of course, the whole mess can be avoided by simply establishing cooperation and sticking to it. The trouble, of course, is that one cannot control the actions of others, and if one is “too” cooperative, there will always be the danger than another party will be tempted by the short-term gain of defecting. When alliances are broken because of the prospect of short-term gain, however, everybody ultimately loses, including the original defector(s). That this is pretty much a universal truth can be shown in business, world history, and even personal relationships. The Prisoner’s Dilemma is thus not merely a theoretical issue; it is a real-life threat. Business leaders need to study game theory in order to survive and thrive in a competitive environment and avoid real-life Prisoner’s Dilemmas.
Kreps, David M., et al. "Rational cooperation in the finitely repeated prisoners' dilemma." Journal of Economic theory 27.2 (1982): 245-252.
Molander, Per. "The optimal level of generosity in a selfish, uncertain environment." Journal of Conflict Resolution (1985): 611-618.
Nowak, Martin, and Karl Sigmund. "A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game." Nature 364.6432 (1993): 56-58.
Segal, Uzi, and Joel Sobel. "Tit for tat: Foundations of preferences for reciprocity in strategic settings." Journal of Economic Theory 136.1 (2007): 197-216.