Twoplayers $1$ and $2$ compete for a single object worth $v_1$ to payer $i=1,2.$ The winner of therin the player ullo remains aggussine longer, where the cost of bring agressine is I per ruit or time. An action $x_j$ of player i is non$-$negative real number and signifus that i uill remain aggussive the $x_i,$ the object sown by the player rullo bew remain aggussive longer but botu playons must to pay the cost of Memaining aggussixe, be$,$

$x_i=x_j{v}_i{v}_{j}0,1v_i{v}_j{U}_i(x_i,x_j,v_i)=(v_i-x_i)y,x_i>x_j,v_i(x_i,x_j,v_i)$

$=-x_{i}y{x}_i$

$x_i=x_j.$ Assume that a player's valuation $is$ private infosmation. Assume aloo that $v_i$ and $v_j$ are tro independeur reurdour variables destuibuted uniformbly $on0,1.$ Compute $an$ asymmatric Bayesian Nash Equilibuium $is$ then equiliblium efficleut for encery possible realsation $of{v}_i$ aud $v_j.$