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LINK: ‘Note Verbale‘, Manila Times (Sunday-Career Section) – 12 August 2007 Issue

Two suspects were arrested for a crime. Because the police have insufficient evidence for a conviction, the suspects were detained in separate rooms at the police station and were offered individually the same terms of deal. If one implicates the other, he may go free while the other could receive a life imprisonment.  If both stay silent or do not implicate the other, it is likely that both of them receive moderate sentences for a minor offense.  If both implicate or betray each other, each receives a severe penalty but less than life.

Each suspect therefore must make the choice whether to implicate the other or to remain silent. Neither suspect however knows for sure what option the other suspect will take.  The dilemma is – how should the individual suspects act?

This situation in game theory is known as the ‘Prisoner’s Dilemma’ (also referred to as PD), a type of non-zero-sum game in which two players may each ‘betray’ or ‘cooperate’ with the other player. In this game, the only concern of each player (prisoner) is maximizing his own payoff without any concern for the other player’s payoff.

Ordinarily, it is crucial to predict what the other person will do to arrive at a strategic decision.  But this is not the case obtaining in the situation. If the suspect knew that his co-suspect would stay silent, his best move is to betray and walk freely out of jail. If the suspect knew that the other would betray, the best move is still to betray in order to receive a penalty less than life because to remain silent would mean getting a capital punishment. Betrayal in this game becomes the dominant strategy because no matter what the other player does, the other player will always gain a greater payoff by opting to betray.

The unique equilibrium of the game is the so-called ‘Pareto Optimality’, named after Italian economist Vilfredo Pareto who used the concept in his studies of economic efficiency and income distribution. The outcome of the Prisoner’s Dilemma is Pareto Optimal if there is no other option that would make every player at least as well off and at least one player strictly better off because the outcome cannot be improved without hurting at least one player.

Another solution concept of the game is the ‘Nash Equilibrium’ named after American mathematician and 1994 Nobel Prize awardee for Economics for his game theory, John Forbes Nash Jr. His life inspired the 2001 drama film, A Beautiful Mind. Under his concept, players are in equilibrium if a change in strategies by any one of them would lead that player to gain less than if he remained with his current strategy.

Technically, PD demonstrates that in a non-zero sum game a Nash Equilibrium need not be a Pareto Optimal.

The ‘game theory’ is a branch of applied mathematics and economics that deals with strategic interactions between agents. It is a theory of competition stated in terms of gains and losses among opposing players. The essential feature is to provide a formal modeling approach to social situations where decision makers interact with other agents.  This interdisciplinary research field came into being with the publication of a 1944 book entitled “Theory of Games and Economics” written by American mathematician John von Neumann and Austrian economist Oskar Morgenstern.

The game theory was widely used by RAND Corporation, a US based non-profit global policy think tank, particularly in defining nuclear strategies. The Prisoner’s Dilemma as a game theory was patterned after the model of cooperation and conflict framed by mathematicians Merrill M. Flood and Melvin Dresher while working at RAND in 1950.  Mathematician Albert W. Tucker subsequently gave the name and interpretation.

The Prisoner’s Dilemma is all about strategic thinking, a mental process which many Filipino leaders seriously and obviously lack these days.