Maximise Global Gain in the Minority Game

<table>Time sequence of the population in room A
in the standard minority game for <svg height="10.9125" id="M16" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 71.887497 10.9125" width="71.887497" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑁</tspan>
<tspan style="font-size: 12.50px; " x="14.103384" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="26.143772" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="32.395271" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="38.646774" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="44.898273" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="51.149773" y="0">1</tspan>
</text>
</g>
</g>
</svg>, <svg height="10.9125" id="M17" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 43.037498 10.9125" width="43.037498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑀</tspan>
<tspan style="font-size: 12.50px; " x="16.028847" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="28.069235" y="0">8</tspan>
</text>
</g>
</g>
</svg>, and <svg height="10.85" id="M18" style="vertical-align:-0.1254pt" version="1.1" viewbox="0 0 37.487499 10.85" width="37.487499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.85)">
<g transform="translate(72,-63.32)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑆</tspan>
<tspan style="font-size: 12.50px; " x="11.590281" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="23.630671" y="0">2</tspan>
</text>
</g>
</g>
</svg>. The central line shows the position of 0.5 <svg height="10.325" id="M19" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 14.8375 10.325" width="14.8375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑁</tspan>
</text>
</g>
</g>
</svg>. A quasiperiodic
structure can be readily seen. At the ends of each quasiperiodic
interval, the population has a large deviation from the central line.</table>

Physics Research International

Maximise Global Gain in the Minority Game

Figure 1