Game Theory Deck: Can 'Rational Decisions' Keep You Out of Jail?

Two prisoners are being interrogated. The matrix below displays the outcomes of their strategies.

Which one should they choose?

In game theory, rational players will always choose a “dominant strategy”—the best thing to do for oneself no matter what the other prisoner does—if there is one.

This reasoning suggests that both prisoners in the example above will confess. This is also a Nash equilibrium: each prisoner’s strategy yields the highest possible payoff given the other prisoner’s strategy.

In the prisoners’ dilemma, if both prisoners confess and thereby arrive at a Nash equilibrium, both are worse off than if they kept quiet.

Sending both prisoners to jail for ten years is not a satisfactory outcome.

Strategic thinking,

however,

is not the only

valid form of rationality.

Other concepts can be invoked to allow an individual to make rational decisions.

Bounded rationality is one of them.

Both prisoners could also assume that their decisions will mirror each other and thus decide to keep quiet, spending only one year in jail.

Given their options, this is the best possible outcome.

For example, Kantian optimisation posits that players modify their strategy assuming that their opponent will do the same.

Such reasoning leads to both prisoners choosing to “keep quiet". Each prisoner thus spends a single year in jail: the collectively rational solution to the game.

Jean Dreze’s article, “The Real Insights of Game Theory” discusses the nature of strategic reasoning and argues that in strategic situations, self-interested behaviour need not be well defined, or let alone compelling.

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