Perfect Equilibria in Replies in Multiplayer Bargaining

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td align="left"> </td><td align="center"> State </td><td align="center"><span style="width: 12.8125px;"><svg height="16.2875" id="M237" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 12.8125 16.2875" width="12.8125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg></span></td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td align="left" rowspan="2"> Player <svg height="11.4625" id="M238" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 4.7624998 11.4625" width="4.7624998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg></td><td align="center"> Proposal </td><td align="center"><span style="width: 12.8125px;"><svg height="16.2875" id="M239" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 12.8125 16.2875" width="12.8125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,7.1,7.85)"><path d="M394 607q0 -25 -15.5 -43t-39.5 -18q-19 0 -32 13t-13 35t16 41.5t40 19.5q20 0 32 -13.5t12 -34.5zM360 349l-57 -283q-38 -188 -122 -263q-72 -64 -114 -64q-16 0 -30 10.5t-14 22.5q0 24 21 45q15 13 26 6q30 -20 54 -20q41 0 65 95q37 147 86 415q6 34 6.5 42.5
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</svg></span></td></tr><tr><td align="center"> Reply </td><td align="center"><span style="width: 54.974998px;"><svg height="22.362499" id="M240" style="vertical-align:-4.19998pt" version="1.1" viewbox="0 0 54.974998 22.362499" width="54.974998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg></span></td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Journal of Applied Mathematics

tab2

Table 2

Table 2: Perfect Equilibria in Replies in Multiplayer Bargaining 