# SFB 504 discussion paper
07-58

**
Sylvain Béal**

Sonderforschungsbereich 504

L 13, 15, D-68131 Mannheim

sylvain.beal@awi.uni-heidelberg.de

##
PERCEPTRON VERSUS AUTOMATON∗

**Abstract:**
- We study the finitely repeated prisoner’s dilemma in which the
players are restricted to choosing strategies which are implementable
by a machine with a bound on its complexity. One player must use a
finite automaton while the other player must use a finite perceptron.
Some examples illustrate that the sets of strategies which are induced
by these two types of machines are different and not ordered by set
inclusion. The main result establishes that a cooperation in almost all
stages of the game is an equilibrium outcome if the complexity of the
machines players may use is limited enough. This result persists when
there are more than T states in the player’s automaton, where T is
the duration of the repeated game. We further consider the finitely
repeated prisoner’s dilemma in which the two players are restricted to
choosing strategies which are implementable by perceptrons and prove
that players can cooperate in most of the stages provided that the
complexity of their perceptrons is sufficiently reduced.

**Keywords:**

**JEL-Classification:**

**Project:**
- C8 Eichberger

**Creation date:**
- 2007-08-06

**Publication Status**

**Downloadable version**
- http://www.sfb504.uni-mannheim.de/publications/dp07-58.pdf

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- pdf-file

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