Introduction
Cultural evolutionary systems have a characteristic called open-ended fitness landscape. When an innovation in technology or a new vocabulary in language evolves, that opens up a new pathway for selection to operate. As a result, these cultural evolutionary systems tend to increase in complexity as time progress \cite{arthur,Sol_e_2013,Clark_1985}. In the literature of technology or innovation, this is often called architectural innovation \cite{Henderson_1990,Frenken_2006}.
Many theories were created to capture the commonalities within the open-ended fitness landscape. For example, it is said that evolution in technology and language systems alike, some units (e.g. a technical element, or a word in language) is expressed more frequently than others, which creates a fat-tailed distribution \cite{zipf1949,Corominas_Murtra_2018}. Accordingly, \cite{Arthur_2006} which specifically focused on technological evolution, has found that whenever a key invention is made, this is followed by a rapid increase in other innovations, which they called the technological Cambrian explosion. Also, newly improved innovations often rapidly replace old and less efficient innovations, which demonstrated the phenomena that was pioneered by \cite{schumpeter2017}.
Technological innovation has also been studied in an area called cultural evolution \cite{mesoudi2011,henrich2017}. For example, \cite{Mesoudi_2008} showed that participants under closed fitness landscape are able to create better arrow-heads by social learning. In their experiment, participants created virtual arrow-heads that contained several dimensions (length, height, width, etc.). Using a computer program, participants could change the values of each dimension. Results of arrow-heads were given from a mathematical function that weighted each dimension with a normally distributed noise. In each phase, participants could see the results of other participants and were able to copy the arrow-heads if desired. Experimental results showed that participants with social learning outperformed participants that could only rely on individual learning.  
The open-endedness of fitness landscape and the combinatorial nature of evolution are under studied especially in technological evolution studies. This is understandable considering that open-ended fitness landscape being challenging to model, and that many models that investigate technological evolution adapt models from biology, which also models evolution as closed fitness landscape. However, as many have indicated, there are some differences between technological and biological evolution \cite{arthur,Sol_e_2013,Jacob_1977,Sol__2002,T_mkin_2007}. A bridge is needed to fill the gap between models in open-ended and closed fitness landscape.
The simplicity of the models created by the cultural evolutionists also had many implications which could be interesting to consider within open-ended fitness landscape. One such instance is the landmark paper by \cite{Henrich_2004}. He proposed that increase in group size affects the uprise and the speed of cumulative technological innovations. When each agent of a group loses the cultural trait of the previous generation by some error distribution, an increase in group size can downfall the effect of this error, and in return, cumulative innovation occurs.
Whether group size will increase the speed of cumulative innovation within open-ended fitness landscape is opened for debate. Additionally, since most of the models were simplified to increase internal validity, it is difficult to measure how much that model fits with the real world (external validity). However, considering that there might be a correlation between an increase in group size and the speed of technological development in recent century within the real world, group size might act as a driver in open-ended fitness landscape. This paper aims to address this issue using computer simulation.
In the simulation below, we modified the simulation by Arthur and Polak (2006) so that the simulation becomes similar to agent-based simulation. Agents created logical circuits that could be used in the later trial. We added conditions where agents were able to use circuits built by other agents. This simulation is useful because the environment is open-ended and also the task is close to a task in real-life. Additionally, they differentiated innovation between invention (new innovation that serves a purpose that never was used before) and improvement (already made innovation but is more efficient) which could be useful if the two innovations evolve differently. Also in the following simulation, agents in the same trial did not interact with one another that could create a synergetic interaction just as in Henrich (2004) for simplicity.