^{1}

^{2}

^{2}

^{2}

In Japan, there exist many sustainable companies. Their distinctive feature is mutualism; they often take altruistic behaviors. To explain such behaviors, we carry out iterated prisoner’s dilemma games by lattice gas model. Each lattice point is regarded as a company which contains m + 1 players with an identical strategy. Simulations reveal that All Cooperation wins, when m takes a value larger than a threshold. We obtain a power law depending on error level. This law implies altruism may prevail in a company which has many employees or high error level.

Sustainability is an important issue for company management. In Japan, there are approximately 4,000 long- lived companies which have survived for more than two centuries (Goto, 2011) [

Altruistic behaviors have been studied by many researchers, such as biologists and social psychologists (Fehr & Fischbacher, 2003 [

Recently, Yokoi et al. (2014) [

We use a typical IPD game (Axelrod 1997) [

The game (move) is infinitely repeated between the same pair of players. We use average payoff per one move. For instance, when AC and AD play with no error, then the average payoffs of AC and AD are 0 and 5, respectively.

Simulations of lattice model are carried out by either local or global interaction (Tainaka 1988) [

Next we explain the simulation procedure of global interaction (lattice gas model) [see

The population dynamics for global interaction become much simpler than those for local interaction. We carry out simulations up to

balance which is similar to paper-scissors-rock game. For example,

where the threshold

This equation has been derived for local interaction on 1-d lattice. By global simulations, we explore whether Equation (3) holds or not. In

m ｘ | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|---|

0 | TFT | TFT | TFT | TFT | TFT | TFT | TFT |

0.01 | AD | AD, PAV,TFT | PAV | PAV | PAV | PAV | PAV |

0.1 | AD | AD, PAV,TFT | PAV | PAV | PAV | PAV | PAV |

0.2 | AD | AD | AD, PAV,TFT | PAV | PAV | PAV | AC |

0.3 | AD | AD | AD | PAV | AC | AC | AC |

0.4 | AD | AD | AD | AC,AD,TFT | AC | AC | AC |

Winners are represented by the colors: AC (green), PAV (red), TFT (blue), and AD (yellow). The white regions are the cyclic cases that the winner is determined by chance.

and plots denote theoretical prediction and simulation result, respectively. It is found from

Hence, the altruistic strategy AC becomes optimal with the increase of m or x.

We have developed an iterated prisoner’s dilemma game to explain altruistic behaviors in long-lived companies. Our model is a lattice gas version of Yokoi’s model (see

If the company size m is sufficiently large, then AC becomes a winner. In both local and global simulations, the altruistic strategy AC is found to be optimal for

We assume that strategies of employees are identical in each company. This assumption may be oversimple (Luft, 2016) [

World economy faces some serious problems, such as excess bankruptcy, monopoly and inequality (Porter and Kramer 2011 [

Hiroki Yokoi,Ayako Morishita,Yasuo Tateoka,Keiichi Tainaka, (2016) Lattice Gas Model for Iterated Prisoner’s Dilemma Games: Emergency of Altruism in a Company. Theoretical Economics Letters,06,324-329. doi: 10.4236/tel.2016.62036