Home » Game Theory

Category: Game Theory

Games & Strategy

Game Theory, as described on Wikipedia, is:

the study of mathematical models of conflict and cooperation between intelligent rational decision-makers.

A classic example is the Prisoner’s Dilemma:

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:

  • If A and B each betray the other, each of them serves two years in prison
  • If A betrays B but B remains silent, A will be set free and B will serve three years in prison (and vice versa)
  • If A and B both remain silent, both of them will only serve one year in prison (on the lesser charge).

Prisoner's Dilemma

Pirates & Coins

The Game:

There are 5 rational pirates (in strict order of seniority A, B, C, D and E) who found 100 gold coins. They must decide how to distribute them.

The pirate world’s rules of distribution say that the most senior pirate first proposes a plan of distribution. The pirates, including the proposer, then vote on whether to accept this distribution. If the majority accepts the plan, the coins are dispersed and the game ends. In case of a tie vote, the proposer has the casting vote. If the majority rejects the plan, the proposer is thrown overboard from the pirate ship and dies, and the next most senior pirate makes a new proposal to begin the system again. The process repeats until a plan is accepted or if there is one pirate left.

Pirates base their decisions on four factors:

  1. First of all, each pirate wants to survive.
  2. Second, given survival, each pirate wants to maximize the number of gold coins he receives.
  3. Third, each pirate would prefer to throw another overboard, if all other results would otherwise be equal.
  4. And finally, the pirates do not trust each other, and will neither make nor honor any promises between pirates apart from a proposed distribution plan that gives a whole number of gold coins to each pirate.

Five Pirates, One Hundred Coins


Extension:  Keep everything above the same, except change it to 500 pirates rather than 5.   Can the same strategy be applied?