Technology Choice: Relative Numbers of Choices and Related Payoffs (2)
Further consider an indefinite series of agents with random technology choices. Determine their changing payoffs, depending on the choices made by each following agent, given the following numerical payoff functions:
$$
\begin{array}{|c|c|c|}
\hline \begin{array}{l}
\text { Number } n \text { of } \\
\text { Agents } I \\
\text { Choosing } \\
\text { Respective } \\
\text { Technology }
\end{array} & \begin{array}{l}
\text { Payoff for Each } \\
\text { Agent if } n^{-} \\
\text {Agents Have } \\
\text { Chosen } T_1 \\
{\left[P_{T 1}(n)\right]}
\end{array} & \begin{array}{l}
\text { Payoff of Each } \\
\text { Agent if } n- \\
\text { Agents Have } \\
\text { Chosen } T_2 \\
{\left[P_{T 2}(n)\right]}
\end{array} \\
\hline 1 & 2 & 1 \\
\hline 2 & 3 & 2 \\
\hline 3 & 4 & 3 \\
\hline 4 & 5 & 4 \\
\hline 5 & 6 & 5 \\
\hline 6 & 7 & 6 \\
\hline 7 & 8 & 7 \\
\hline \ldots & \ldots & \ldots \\
\hline
\end{array}
$$
See the following example of some sequence:
$$
\begin{array}{llll}
\hline \text { Agent No. } & T_1 & T_2 & \Pi\left(T_{1,2} n\right) \\
\hline 1 & X & & 2 \\
2 & & X & 2,1 \\
3 & & X & 2,2,2 \\
4 & X & & 3,2,2,3 \\
5 & X & & 4,2,2,4,4 \\
6 & X & & 5,2,2,5,5,5 \\
7 & & X & 5,3,3,5,5,5,3 \\
\ldots & \ldots & \ldots & \ldots \\
\hline
\end{array}
$$
Build different choice sequences among up to 10 choosing agents in a row, and determine the different results for each. In particular, give an example for a choice sequence that yields a higher payoff for those who have chosen the inferior technology $T_2$.