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17.2.2.1 Models Using a Game Theoretic Problem Description

First, a closer examination of a sample of models applying a game theoretic problem
description will be undertaken. The models investigated here build on the framework
described in Chap. 16 on games and utility in this handbook (Fioretti 2017).
Axelrod (1986) studies the evolution of a standard not to cheat via a ‘norms game’
and a ‘meta-norms game’. In the ‘norms game’, defectors may be punished
by observers. In the ‘meta-norms game’, it is also the case that observers of a
defection that do not punish the defector may be punished. Only the latter game
leads to a widespread standard of not defecting.
Coleman (1987) investigates the effect of interaction structures on the evolution of
cooperation in a prisoner’s dilemma situation. Only small groups can prevent the
exploitation of strangers.
Macy and Sato (2002) examine the effect of mobility on the emergence of trust
among strangers in a trust game. While agents with low mobility trust only their
neighbours, high mobility supports the evolution of trust among strangers.
Vieth (2003) investigates the evolution of fair division of a commodity in an
ultimatum game. Including the ability to signal emotions leads to a perfectly
fair share. If detection of emotions is costly the proposals even exceed fair share.
Bicchieri et al. (2003) present a model of a trust game. It demonstrates how a trust
and reciprocate norm emerges in interactions among strangers. This is realised
by several different conditional strategies.
Savarimuthu et al. (2007) study the convergence of different norms in the interac-
tions of two different societies. Both societies play an ultimatum game against
each other. Two mechanisms are examined: a normative advisor and a role model
agent.
In the model by Sen and Airiau (2007), a co-ordination and a social dilemma
game are examined. Agents learn norms in repeated interactions with different
agents. This is denoted as social learning to distinguish this interaction type
from repeated games with the same player. The whole population converges to a
consistent norm.
Obviously, all models have been developed for differing concrete purposes. To
examine the extent to which these models capture the explanatory problems of
the contribution problem, transformation problem and transmission problem, the
various accounts of the different models will be outlined in a table. Moreover, a
short hint to the concrete implementation is provided. This will enable an evaluation
inasmuch normative agent-based models have so far reached the goal to discover
‘the language in which social reality is written’. These models are summarised in
Table 17.1.

Lessons

The classical model employing a game theoretical approach for the problem
description is Axelrod’s model. The main contribution of this approach is a