On a Competitive Selection Problem

We consider the problem in which n items arrive to a market sequentially over time, where two agents compete choose best possible item. When an agent selects item, he leaves and obtains payoff given by value of is represented random variable following known distribution with support contained [0,1]. different settings for this problem. In first one, namely competitive selection no recall, observe each item upon its arrival decide whether accept or reject it, case they will not select it future. second setting, called are allowed any available arrived so far. For these problems, we describe game induced as sequential imperfect information study set subgame-perfect Nash equilibrium payoffs. We also efficiency equilibria. More specifically, address question how much better have power getting against take-it-or-leave-it fashion. To end, define price anarchy stability instance ratio between maximal sum payoffs obtained players under feasible strategy worst equilibrium, respectively. For recall case, prove that if there arriving both upper bounded constant 4/3 distribution. Even more, show bound tight.