====== Iterated Prisoner's Dilemma ======
[[https://en.wikipedia.org/wiki/Prisoner%27s_dilemma|Prisoner's dilemma]] (PD) and its iterated variant (IPD) is a well-known problem in game theory. The goal of this project is to create and compare optimization algorithms that find a good player for a particular IPD problem instance.

An IPD problem instance is given by 
  * the payoff matrix and
  * the number of iterations.

===== Payoff Matrix (PM) =====
The payoff matrix must be set up such that the game is fair for both players. For 4 positive numbers a, b, c, and d, the matrix has the following form:
|              || P2 plays ||
|              || 0 | 1 |
| P1 plays | 0 | (A,A) | (B,C) |
|          | 1 | (C,B) | (D,D) |
where in each pair (r1, r2) denotes the rewards for player 1 and player 2, respectively.

Depending on relations among A, B, C, and D, the payoff matrix may be set up in such a way that
  * there is a proper dilemma,
  * no dilemma is present,
  * there is no dominant strategy,
  * the best strategy require the decisions of the players to alternate,
  * etc.
You should choose several interesting PM setups and try to find players for them.

===== Representation =====
There are many possible representations of the players/strategies:
  * finite state machine (that can be encoded in a binary string),
  * set of rules,
  * decision tree,
  * neural network,
  * ...

The chosen representation shall be consulted with the teacher.

===== Evaluation =====
IPD is a two-player game. To evaluate the quality of a player is thus possible only by playing games against other players, i.e., the quality of a player depends on the set of chosen opponents. The choice of this reference set is up to you, it may be
  * a static set of predefined players,
  * the other players in population,
  * a combination of the above options, ...
The goal is to *maximize the sum of rewards across all played IPD games*.

===== Interesting questions =====
In no particular order:
  * What is the strategy used by the best player for individual PM setups?
  * How does the initialization affect the resulting best player? What if we seed the population with a specified number of copies of known strategies?
  * Is it possible to evolve a player, that plays well for any setup of PM?
  * Is it possible to evolve a player, that plays well against any opponent?
Take these questions as an inspiration of what you can study in your project.